1. Introduction
The detection, monitoring and control of style is perceived as a key preoccupation by hedge fund investors.
- transparency issue: disclosure of strategy drift monitoring
- style drifts should be avoided even though they do not necessarily have a negative impact on performance
- identified relatively easily and measured precisely, either from portfolio holding information or by making use of standard quantitative techniques based on portfolio returns
**Style Drift
- a change in the hedge fund's investment strategy from what was defined in the hedge fund's offering documents
- distort asset allocation and manager selection
- it will be difficult for most investors to detect style drift unless the manager reports its positions as well as its monthly or quarterly profit and losses
2. On Style & Strategies
For the detection of style drifts, investment styles may be identified according to certain parameters and these parameters may be monitored by the investor
**factors driving the performance of hedge funds
- stylistic difference explain a part of the observed performance differences among hedge funds
- return may be interpreted as a premium for an exposure to risk and risk factors that funds are exposed to enables the description of an investment style
- performance-generating process of hedge funds is complex and a linear exposure to factors based on the returns of standard asset classes is not sufficient to describe the risk taken by hedge funds
2-1. Investment Style (0f Hedge Funds)
- long/short position with substantial leverage
- style cannot be determined simply by examining holdings or correlations with indices. traditional investment style analysis must be modified to identify the risk factors to which the hedge fund is exposed
- due to the vast array of hedge fund investing strategies, there are a greater number of specialized or niche hedge fund style versus traditional fund style
3. Style Drift
Hedge fund investing deals primarily with skill-based investing. The potential investor has to understand the particular skill set of a manager and decide whether this skill set is compatible with the investment strategy. In addition, the investor has to assess whether the strategy of the manager fits in with their investment objectives.
Style and/or strategy drift can be defined:
- drift in the exposure to a predefined set of risk factors
- change in the overall quantity
The kinds of style drifts that have to be avoided are the unexpected style drifts that have not been communicated to, and agreed with, the investors for the following reasons:
- from the bottom-up perspective of manager selection and monitoring, the style drifts make part of the analyses conducted and the conclusions drawn during due diligence useless
- from the top-down view of asset allocation and portfolio construction, style drifts invalidate the assumptions made about risk-return profiles and may destroy the expected diversification benefits resulting from style and manager mix.
3-1. Due diligence
Investor should review all factors relevant to making a prudent investment decision.
3-2. Main reasons for style drifts
- poor market environment: poor style market performance
- asset flows & limited capacity of the strategy: excessive cash inflows
- underperformance with respect to their peers: poor manager performance
- large drawdowns: recent losses
- change in key investment professionals: personnel change (leadeship changes)
- change in market structure or regulatory environment
4. Detection, Monitoring & Controlling Style Drifts
- Detection & monitoring: embedded in the ongoing due diligence & risk management processes
- No single analysis gives the investor sufficient comfort to make a definitive judgement
4-1. Approaches for Monitoring & Detecting Style Drift
4-1-1. Monitoring risk factors
- The careful monitoring of the evolution and levels of the identified style- and strategy-specific risk factors = integral part of asset allocation process
- Change in the value of risk factors may precede a change in fund style
4-1-2. Returns-based analysis
- A time series analysis that confirms that the hedge fund has perfromed consistently with its stated investment objective in terms of risk, return, correlation with predefinced asset classes and benchmarks. (assessment of overall hedge fund performance over time & comparability with the strategy of the manager)
- performed during initial due diligence & updated within the context of ongoing due diligence & risk management
- the analysis of time-varying risk & return statistics: a good picture of the dynamic nature of hedge fund strategies
- the extent of style drift can be measured by the extent of changes in the sensitivities of the fund's returns to asset class index returns; significant changes = indication of changes in style and/or risk level of the fund
4-1-3. Analysis of performance attribution & risk exposures
- analysis of profit/loss attribution gives insight into where the performance is coming from
- components of fund return: asset classes, region and currency
- performance attribution analysis provides an insight into potential style drifts
- analysing exposure trends & comparing exposures between managers of the same style provides a cross-sectional and dynamic view of the risks taken by a manager
4-1-4. Peer group comparison
- managers are continuously assessed against their peers and ranked with respect to the various risk, return and performance measure => change in ranking has to be observed regularly
- ideal complement to the returns-based approach
- a cross-sectional analysis of different managers sharing a common investment style in exactly the same market environment
- linear regressions of the single hedge fund returns on the peer group average; alpha = manager's skill, beta = proxy for the level of leverage used relative to the peer group
- underperformance with respect to peers is a leading indicator of a potential style drift
- relative overperformance may be an ex-post indicator of abnormal risk level
- return break-outs (returns lie outside a predefined confidence interval): complementary use of the returns-based and peer group analysis; return break-outs detected during a returns-based analysis may be caused by change in market conditions or by a change in the type and/or level of risk taken by the hedge fund manager
4-1-5. Analysis of Positions
The analysis of single position cannot help to avoid style drifts. However, it may accelerate the detection of drifts and help to validate the accuracy of a manager's reported numbers.
- the style consistency of the fund manager can be examined via a detailed analysis of the separate holdings of the fund (Holdings-based analysis)
- position transparency is necessary
4-1-6. Communication with the fund manager
Ongoing communication with a manager allows warning signals of style drifts to be detected
Thursday, October 15, 2009
Ch8 Funds of Hedge Funds
1. Introduction
1-1. FOFs
- diversification benefits
- attractive risk-return characteristics
- low correlations to traditional asset
- allows easier access to small & institutional investors
- rapidly grown, now compose greater than a quater of all hedge funds
1-2. Crucial Aspect of an increase in the flow of institutional assets into funds
- comprehensive risk monitoring, control, significant improvement in existing risk management practices, effective disclosure, and timely reporting
- risk monitoring tools are used: VaR, stress testing, scenario analysis, and other quantitative tools
1-3. Benefits
- retailing: pooling overcomes denomination limitation
- access: overcomes limitation of small number of investors. easier cash out
- diversification: pooling allows greater diversification
- expertise: in identifying good hedge funds and soliciting information
- due diligence process: follow up and monitoring
**less survivorship bias: a better indicator of aggregate performance of hedge funds
1-4. Drawbacks
- fee: management fee is above each hedge fund's fees
- performance: may not be better than particular hedge funds
- diversification is a double-edged sword: lower risk may mean lower expected return
1-1. FOFs
- diversification benefits
- attractive risk-return characteristics
- low correlations to traditional asset
- allows easier access to small & institutional investors
- rapidly grown, now compose greater than a quater of all hedge funds
1-2. Crucial Aspect of an increase in the flow of institutional assets into funds
- comprehensive risk monitoring, control, significant improvement in existing risk management practices, effective disclosure, and timely reporting
- risk monitoring tools are used: VaR, stress testing, scenario analysis, and other quantitative tools
1-3. Benefits
- retailing: pooling overcomes denomination limitation
- access: overcomes limitation of small number of investors. easier cash out
- diversification: pooling allows greater diversification
- expertise: in identifying good hedge funds and soliciting information
- due diligence process: follow up and monitoring
**less survivorship bias: a better indicator of aggregate performance of hedge funds
1-4. Drawbacks
- fee: management fee is above each hedge fund's fees
- performance: may not be better than particular hedge funds
- diversification is a double-edged sword: lower risk may mean lower expected return
1-5. Risks
- structural risks: derived from operations; potential for deterioration in a firm's reputation, poor information reporting systems, inadequate management oversight
- strategy risks: derived from investment strategy; market risk, credit risk, trading liquidity risk, funding liquidity risk, etc
2. Set-up & Value added of FOF
- designed to blend different hedge fund styles & spread the risks over a wide variety of funds
- target: 10~15% returns & 5~10% volatility
- more challenge to be consistent with returns
2-1. Factors affecting performance
- less direct impact of survivorship bias
- issues with classification and style drift
- new FOFs and old FOFs behave differently
- may be less useful in asset allocation
3. Portfolio Management Strategies
3-1. Three core building blocks underpinning the integrated investment process of FOFs
- strategy sector selection and allocation
- manager selection, evaluation and ongoing due diligence
- continuous manager monitoring and proactive risk management
3-2. Classification of hedge funds by diversification characteristics
- Return-enhancer: high return, high correlation with stock/bond portfolio; equity market-neutral, convertible bond arbitrage
- Risk-reducer: lower return, low correlation with stock/bond portfolio; merger arbitrage, distressed securities, long/short equity
- Total diversifier: high return, low correlation with stock/bond portfolio, global asset allocation
- Pure diversifier: low or negative return with high negative correlation with stock/bond portfolio; short seller
4. Style Risk & Diversification: Selection of Strategy Sectors
An important source of alpha in a FOFs portfolio depends on sector allocation and the right selection of strategies.
- sector allocation: achieve & maintain effective diversification and match the targeted risk/reward profile
- diversification: sector & strategy correlations across the different sources of return
- balance between a predetermined sector allocation and an opportunistic switching between strategies
- qualitative understanding of the key performance drivers, main strengths/weakness of the relevant strategy is needed to select the appropriate mix of strategies in a portfolio
- dynamic risk/return profile of the different strategy sectors & correlations between strategies needs to be actively monitored and reassessed.
** Historical Performance
- superior return performance relative to other traditional asset classes
- structural risks: derived from operations; potential for deterioration in a firm's reputation, poor information reporting systems, inadequate management oversight
- strategy risks: derived from investment strategy; market risk, credit risk, trading liquidity risk, funding liquidity risk, etc
2. Set-up & Value added of FOF
- designed to blend different hedge fund styles & spread the risks over a wide variety of funds
- target: 10~15% returns & 5~10% volatility
- more challenge to be consistent with returns
2-1. Factors affecting performance
- less direct impact of survivorship bias
- issues with classification and style drift
- new FOFs and old FOFs behave differently
- may be less useful in asset allocation
3. Portfolio Management Strategies
3-1. Three core building blocks underpinning the integrated investment process of FOFs
- strategy sector selection and allocation
- manager selection, evaluation and ongoing due diligence
- continuous manager monitoring and proactive risk management
3-2. Classification of hedge funds by diversification characteristics
- Return-enhancer: high return, high correlation with stock/bond portfolio; equity market-neutral, convertible bond arbitrage
- Risk-reducer: lower return, low correlation with stock/bond portfolio; merger arbitrage, distressed securities, long/short equity
- Total diversifier: high return, low correlation with stock/bond portfolio, global asset allocation
- Pure diversifier: low or negative return with high negative correlation with stock/bond portfolio; short seller
4. Style Risk & Diversification: Selection of Strategy Sectors
An important source of alpha in a FOFs portfolio depends on sector allocation and the right selection of strategies.
- sector allocation: achieve & maintain effective diversification and match the targeted risk/reward profile
- diversification: sector & strategy correlations across the different sources of return
- balance between a predetermined sector allocation and an opportunistic switching between strategies
- qualitative understanding of the key performance drivers, main strengths/weakness of the relevant strategy is needed to select the appropriate mix of strategies in a portfolio
- dynamic risk/return profile of the different strategy sectors & correlations between strategies needs to be actively monitored and reassessed.
** Historical Performance
- superior return performance relative to other traditional asset classes
- considerable variation in the risk and return among styles
- hedge fund strategies performance depends on the market conditions affecting that strategy
***Historical Data Biases
- self-selection bias
- instant history bias or backfill bias
- survivorship bias
- smothed pricing: infrequently traded assets
- option-like investment strategies: not normal distributed
- fee structure and gaming
5. Risks of FOFs Manager Selection: Due Diligence Process
5-1. Investment Process
- manager selection
- evaluation & ongoing due dilegence
- continuous risk monitoring
5-2. Business Model
- careful assessment & analysis of the business model used by a FOFs manager
5-3. Quality & Depth of Resources
- pay attention to the credentials, experience and the incentive used to attract and retain top industry talent by the FOFs manager
- due diligence questionnaire by AIMA(alternative investment management association)
5-1. Investment Process
- manager selection
- evaluation & ongoing due dilegence
- continuous risk monitoring
5-2. Business Model
- careful assessment & analysis of the business model used by a FOFs manager
5-3. Quality & Depth of Resources
- pay attention to the credentials, experience and the incentive used to attract and retain top industry talent by the FOFs manager
- due diligence questionnaire by AIMA(alternative investment management association)
6. Post-Investment Risk Management Process for Multi-Manager Portfolios
** Pillars underlying successful & profitable hedge fund inveting:
- astute strategy sector selection and allocation
- pragmatic manager due deligence
- proactive & systematic manager risk monitoring
7. Defining & Managing Hedge Fund Portfolio Risk
* 2003 KPMG Financial Advisory Service Report
- FOFs dominated hedge funds
- Most common investment styles were multi-strategy and short selling
- 55% of participants distributed FOFs across several jurisdiction
- FOFs' NAV were mostly reported on a monthly basis
- Most FOFs managers used both an in-house system and one of the most common risk management packages to monitor risks
- Concentration measures(71%), sensitivities(62%) & VaR(54%) were the most common risk management measures
- 56% of FOFs managers used software programs to price some of the FOFs investment
** Pillars underlying successful & profitable hedge fund inveting:
- astute strategy sector selection and allocation
- pragmatic manager due deligence
- proactive & systematic manager risk monitoring
7. Defining & Managing Hedge Fund Portfolio Risk
* 2003 KPMG Financial Advisory Service Report
- FOFs dominated hedge funds
- Most common investment styles were multi-strategy and short selling
- 55% of participants distributed FOFs across several jurisdiction
- FOFs' NAV were mostly reported on a monthly basis
- Most FOFs managers used both an in-house system and one of the most common risk management packages to monitor risks
- Concentration measures(71%), sensitivities(62%) & VaR(54%) were the most common risk management measures
- 56% of FOFs managers used software programs to price some of the FOFs investment
8. Issue of Transparency
- most significant challenges for the industry
- most significant challenges for the industry
9. Active Risk Management & Issue of Liquidity
-integral part of the dynamic portfolio management process
- portfolio risk management team needs to identify, evaluate and monitor exposure limits to individual sectors and managers
- FOFs managers need to monitor the underlying market, liquidity and credit risks using qualitative and quantitative risk management
-integral part of the dynamic portfolio management process
- portfolio risk management team needs to identify, evaluate and monitor exposure limits to individual sectors and managers
- FOFs managers need to monitor the underlying market, liquidity and credit risks using qualitative and quantitative risk management
**FOFs manager needs to monitor individual managers as regards whether leverage limits are exceeded, stop losses are triggered, any significant style drifts occurred, or credit/liquidity/event risks emerged
Wednesday, October 14, 2009
Ch8 Hedge Funds: Past, Present, and Future
1. Hedge Funds & Mutual Funds
1-1. Mutual Funds
- active(managed) funds: most funds are actively managed
- passive (index or unmanaged) funds: tracking a benchmark
- short & borrow: prohibited, derivatives: limited
- operate on a larger scale than hedge funds
1-2. Hedge Funds
- deliver complex strategies
- short position allowed
- avoid registering with SEC by having fewer than 15 clients
**open-end vs. close-end
- open-end: share price = NAV
- close-end: share price by secondary market
***Net Asset Value(NAV) = (Asset - Liability) / (# of shares)
2. Hedge Fund Incentive Structures
2-1. Mutual Fund Managers
- Strict regulations
- Symmetric Compensation Method: % of assets under management
2-2. Hedge Fund
- Asymmetric Compensation
- 1~2% fixed base management fee (operating expenses) of asset base
- 15~25% incentive fees (portfolio management incentive) of total profits
* profits measured above a risk free rate
- high water mark: need to recover previous losses first
3. Withdrawing Capital
Hedge Fund investors can only withdraw funds at certain times during the year and only after having given some notice
e.g.) Withdraw at the end of the quater given 30 days notice
4. Disclosure Requirements
4-1. Mutual Funds
Required to audit all financial statement & to disclose holdings to the SEC
4-2. Hedge Funds
- not required to disclose holdings to investors
- transparency might compromise investor returns for a hedge fund with an information-sensitive strategy
- high frequency transparency not efficient for a strategy characterized by illiquid investments
5. Hedge Fund Diversification
- concentrated, unique risk exposures, large investment -> diversification is important
- past: low correlation, present: increasingly becoming correlated with overall market moves
- diversification with the lack of transparency require costly due diligence
- fund of funds hedge fund: a diversified portfolio with risk management service
6. Market Efficiency
- arbitrage opportunities
- activity of hedge fund managers may be increasing market efficiency using short sales and derivatives (but, no real direct evidence)
7. Hedge Fund Strategies
- Equity long/short
- Event-driven hedge
- Global macro hedge
- Fixed income arbitrage
8. Hedge Fund Considerations
- from 1994 to 2006: slightly higher average return with a much smaller standard deviation
- hedge funds growth: $1 trillion in 2005 whereas mutual funds $8.5 trillion, dramatical growth after 2000
8-1. Gauging Hedge Fund Performance
**difficult to gauge performance because of the following reasons:
- biased data can result from the low level of regulations: survivorship bias
- adjusting returns for risk exposures is difficult given the complicated strategies: complicated strategies over a given time period & risks/returns are non linear
- past performance may give a very selective view of risk
- nature of the investments make computing the value and return of a hedge fund difficult
- serially correlated rates: evidence of managers massaging their reported returns in that they are probably trying to reduce the period-to-period variability of the returns -> downward bias in the measures of risk associated with the fund
- December Effect: average return of hedge funds in December is much higher than that of the average monthly return for the rest of the year
9. Hedge Fund Performance
- non-negative alpha on average and after fees
- alphas for individual funds are persistent: a hedge fund with a high alpha in the first period has a greater probability of a high alpha in the second period
10. Risk Concerns
- relatively high mortality rate (about 10% annum)
- regulators need not be concerned about investors and financial institutions
- no evidence that liquidity risks have produced disastrous outcomes
- no clear proof that hedge funds have created volatility risk
11. Futures of Hedge Funds
11-1. Institutionalization
- increasing proportion of investments are from pensions and endowments -> requires more transparent & institutionalized
11-2. Regulation
- more hedge fund regulations
11-3. Trends in Hedge Funds & Mutual Funds
12. Hedge Fund Legal Structure
12-1. Types
- limited partnership
- limited liability corp.
- offshore corp.
12-2. Allowed
- taking short & long positions in any asset
- use all kinds of derivatives
- leverage without restrictions
12-3. Section 3(c)(1) Investment Company Act
- exemption from SEC regulations
- limited to equal or less than 100 partners (accredited investors)
- individual: greater than $1M or income greater than $200K
- entity: greater than $5M
- prohibited from advertising
12-4. Section 3(c)(7) Investment Company Act
- exemption from SEC regulations
- limited to equal or less than 500 partners (qualified purchasers)
- individual: greater than $5M
- entity: greater than $25M
- prohibited from adversing
1-1. Mutual Funds
- active(managed) funds: most funds are actively managed
- passive (index or unmanaged) funds: tracking a benchmark
- short & borrow: prohibited, derivatives: limited
- operate on a larger scale than hedge funds
1-2. Hedge Funds
- deliver complex strategies
- short position allowed
- avoid registering with SEC by having fewer than 15 clients
**open-end vs. close-end
- open-end: share price = NAV
- close-end: share price by secondary market
***Net Asset Value(NAV) = (Asset - Liability) / (# of shares)
2. Hedge Fund Incentive Structures
2-1. Mutual Fund Managers
- Strict regulations
- Symmetric Compensation Method: % of assets under management
2-2. Hedge Fund
- Asymmetric Compensation
- 1~2% fixed base management fee (operating expenses) of asset base
- 15~25% incentive fees (portfolio management incentive) of total profits
* profits measured above a risk free rate
- high water mark: need to recover previous losses first
3. Withdrawing Capital
Hedge Fund investors can only withdraw funds at certain times during the year and only after having given some notice
e.g.) Withdraw at the end of the quater given 30 days notice
4. Disclosure Requirements
4-1. Mutual Funds
Required to audit all financial statement & to disclose holdings to the SEC
4-2. Hedge Funds
- not required to disclose holdings to investors
- transparency might compromise investor returns for a hedge fund with an information-sensitive strategy
- high frequency transparency not efficient for a strategy characterized by illiquid investments
5. Hedge Fund Diversification
- concentrated, unique risk exposures, large investment -> diversification is important
- past: low correlation, present: increasingly becoming correlated with overall market moves
- diversification with the lack of transparency require costly due diligence
- fund of funds hedge fund: a diversified portfolio with risk management service
6. Market Efficiency
- arbitrage opportunities
- activity of hedge fund managers may be increasing market efficiency using short sales and derivatives (but, no real direct evidence)
7. Hedge Fund Strategies
- Equity long/short
- Event-driven hedge
- Global macro hedge
- Fixed income arbitrage
8. Hedge Fund Considerations
- from 1994 to 2006: slightly higher average return with a much smaller standard deviation
- hedge funds growth: $1 trillion in 2005 whereas mutual funds $8.5 trillion, dramatical growth after 2000
8-1. Gauging Hedge Fund Performance
**difficult to gauge performance because of the following reasons:
- biased data can result from the low level of regulations: survivorship bias
- adjusting returns for risk exposures is difficult given the complicated strategies: complicated strategies over a given time period & risks/returns are non linear
- past performance may give a very selective view of risk
- nature of the investments make computing the value and return of a hedge fund difficult
- serially correlated rates: evidence of managers massaging their reported returns in that they are probably trying to reduce the period-to-period variability of the returns -> downward bias in the measures of risk associated with the fund
- December Effect: average return of hedge funds in December is much higher than that of the average monthly return for the rest of the year
9. Hedge Fund Performance
- non-negative alpha on average and after fees
- alphas for individual funds are persistent: a hedge fund with a high alpha in the first period has a greater probability of a high alpha in the second period
10. Risk Concerns
- relatively high mortality rate (about 10% annum)
- regulators need not be concerned about investors and financial institutions
- no evidence that liquidity risks have produced disastrous outcomes
- no clear proof that hedge funds have created volatility risk
11. Futures of Hedge Funds
11-1. Institutionalization
- increasing proportion of investments are from pensions and endowments -> requires more transparent & institutionalized
11-2. Regulation
- more hedge fund regulations
11-3. Trends in Hedge Funds & Mutual Funds
12. Hedge Fund Legal Structure
12-1. Types
- limited partnership
- limited liability corp.
- offshore corp.
12-2. Allowed
- taking short & long positions in any asset
- use all kinds of derivatives
- leverage without restrictions
12-3. Section 3(c)(1) Investment Company Act
- exemption from SEC regulations
- limited to equal or less than 100 partners (accredited investors)
- individual: greater than $1M or income greater than $200K
- entity: greater than $5M
- prohibited from advertising
12-4. Section 3(c)(7) Investment Company Act
- exemption from SEC regulations
- limited to equal or less than 500 partners (qualified purchasers)
- individual: greater than $5M
- entity: greater than $25M
- prohibited from adversing
Tuesday, October 13, 2009
Ch8 Individual Hedge Fund Strategies
1. Equity Hedge Strategies
1-1. Long/Short Equity
- Long a core set of stocks
- Short sales of other borrowed stocks (partially or fully hedging): generating returns when price declines, hedging brad market risk, and earning interest on proceeds
- leverage
- exposure to broad equity risk premium, small firm & value stock risk premia
- significant alpha -> experience- & skill-driven
- dead weight in traditional index-benchmark equity investment
- most managers have a long bias
- the focus of strategy: stock selection with regional, sector-specific or particular style emphasis
- NOT market timing, prediction of the broad stock market direction
e.g.) long undervalued and short overvalued, core long positions with a partial hedge overlay with short index futures, long OTM puts and short covered call
Bottom-Up Approach
- fundamental analysis -> determination of undervalued or overvalued
- analysis of industry sector
- qualitative analysis: a detailed due diligence process & analysis of maangement
Top-Down Approach
- economic trends & upcoming investment themes in certain industry sectors: vlaue vs. growth
- inefficiencies on micro & small capitalization stocks
Index
- HFR Long/Short Equity Hedge Index
- CSFB Tremont Long/Short Equity Index
1-2. Equity Market Neutral
- simultaneously long & short matched stock positions -> taking advantage of a relative outperormance of the long positions vs. the short positions
- generating returns that are completely uncorrelated to the overall equity market
- insulating portfolios from broad market rist factors = total portfolio net exposure = zero; dollar neutral, country neutal, currency neutral, sector neutral, size neutral, style neutral (value vs. growth)
Statistical Arbitrage
- model-based short-term trading
- quantitative & technical analysis
- profit opportunity in undervalued & overvalued; mean-reversion
- pair trading: long & short position in two stocks that are closely related
- black box investing; characteristics of the model are usually not disclosed to investors
three Steps
- screening & ranking: rule-based decision
- stock selection: value factors (rule-based decition; selection criteria: price-to-book, price-to-earning, price-to-sales, discounted CF, ROE, operating margins, earnings growth) or momentum factors (price or earnings momentum, moving average, relative strength & trading volumes)
- portfolio construction
e.g.) long outperformed (winner stocks) & short underperformed (loser stocks),
Fama-French HML (high minus low; long high book-to-market stock & short low book-to-market), SMB (small minus big; long small firms & sell large cap), and UMD (up minus down; long recent winner & short recent loser)
Market Neutral Long/Short Equity
1-3. Equity Market Timing
- mutual fund timing
- using a variety of technical trading models to screen the global equity markets for short-term opportunities in particular industry or geographic sectors
- switch between long equity exposure (taken at favorable moment) and risk-free
- inefficiencies of equity markets
- technical trend-following models based on short & medium-term momentum -> buy and sell signals
two strategies:
- sector timing: micro upward trends in single industry sectors **stale prices
- time zone arbitrage
studies:
- small cap lag the price action of large cap by 1~2 days
1-4. Short Selling
- selling of stocks not currently owned by the seller in order to take a directional bet on their anticipated price decline
- short rebate interest: interest earnings on proceeds
- substantial collateral: 30~50% of the market value
- short with derivatives or short with long/OTM call options (= long/short equty strategy with a short bias)
- key driver = security selection
payoff:
- profit from buying back stock at a lower price
- short debate interest
approaches:
- bottom-up approach: aggressive accounting techniques
consideration:
- share availability
- stability of the borrowing (call back)
- level of short rebate interest
- short squeezes
- invers relationship between performance and exposure
2. Relative Value Strategies
2-1. Convertible arbitrage
- long convertible security and short underlying stock
- equivalent to holding a bond position plus an option on some underlying stock
- arbitrage opportunities by identifying pricing disparities between the equity and the convertible bond
- buying volatility (cheap convertible securities) & hedging
- leverage: 1:1 to 5:1
- credit risk & interest risk
e.g.) long convertible bonds & short underlying stock/option or index futures/options,
low credit quality or distressed convertibles & stock
income sources:
- static returns: coupon & short stock rebates
- gamma trading on stock volatility
- price inefficiencies
Static Returns
- coupon/dividend plus short rebate (minus dividends)
- consideration: credit risk, omicron (dependency between bond price and credit spread)
- related to systematic risk factor; not related to pricing inefficiency
Gamma Trading
- long valatility; achieved from long gamma & long vega
- Long Gamma: delta neutral = when a stock price increases, delta increases, and sells more stock
- being long gamma: changing delta always works out in favor of the overall position of long convertible bond with a hedged short position in the underlying stock
- being long vega: as the stock price volatility changes, the convertible's value will change due to the commensurated change in the inherent option value (conversion premium)
- long gamma & vega has little to do with exploiting pricing inefficiencies -> driver of convertible arbitrage strategy
- short theta
2-2. Fixed Income Arbitrage
- profits by trading the spread relationship (spread position) between related fixed income securities and their derivatives to profit from relative movements or to accrue positive carry retusns over time
- neutralizing exposure to most systematic risk factors (e.g. yiedl curve changes, interest rate, credit, FX, etc)
- short volatility strategies
- flight to quality: when interest rates move rapidly, creadit spreads widen & liquidity dries up
- complexity premium
e.g.) spread trades
- yield curve trades (bonds with different maturities), corporate vs. Treasury yield spreads, municipal vs. Treasury yield spreads, cash vs. future, on-the-run vs. Treasury bonds
- arbitrage between similar bonds: different duration
- Butterflies (yield curve arbitrage): e.g. long cheap 5-year, 7-year & short expensive 6-year
- Basis trades: spread between physical securities and their futures
- Asset swap: long fixed-rate bonds vs. pay fixed positions in interest swaps or vice versa (reverse asset swaps)
- TED spread: spread between T-bill futures and Eurodallar futures
- yield spread between on-the-run & off-the-run bonds
other strateges (non-market neutral)
- yield curve spread trading based on a forecast of the directional changes of the yield curve
- credit spread trading
- cross-currency government vs. government spread trades
- ABS
- MBS against CMO
pricing inefficiencies:
- agency biases
- structural reasons: tax, accounting or regulatory issues
- market segmentation
2-3. Volatility Arbitrage
- benefit from the level and change of volatilities in particular instruments
- long position in cheap volitalities and short position in expensive volatilities
2-4. Capital Structure Arbitrage
- long and short positions in difference financial instruments within the capital structure of an idividual company.
- discrepancies movements of the equity & bond prices
e.g.) buying bond & selling stock vice versa, short CDS & long a stock put vice versa, long one bond issue & short another bond tranche
3. Event-Driven Strategis
- event: firm-specific (idosyncratic nature)
strategies:
- cash takeovers & stock-for-stock mergers (merger arbitrage)
- divestments, spin-offs, special dividends and refinancings
- ligigation plays: legal case such as bankruptcy
- post-bankruptcy: companies emerging out of Chapter 11 proceedings
- index events: changes in index composition
- holding company and share calss arbitrage: buying shares of holding company & selling shares of its assets or vice versa
3-1. Merger Arbitrage
Before the effective date of a merger, the stock of the acquired company will typically sell at a discount to its acquisition value as officially announced.
- buying stock in a company being acquired and selling stock in its acuqirers.
3-2. Distressd Securities
- investing in the debt and/or equity of companies having financial difficulty
- deeply discounted prices
- successful reorganization and profitable returns
3-3. Regulation D
- investing in publicly listed companies, mostly of micro and small cap, that are in need of capital through privately negotiated structure.
- private equity placements pursuant to Regulation D
- the investment is structured in the form of privately placed, unregistered, high coupon, convertible securities or debentures with maturities ranging anywhere from 18 to 60 months.
- invetment are made pursuant to an exemption from registration as provided by Regulation D of the U.S. Securities Act of 1933
- selling the fully tradable and registered shares in the public markets & realizing the spread between the market price and the discounted price of the stock (15 ~ 40%)
- bottom-up analysis
4. Opportunistic/Global Macro Strategies
- bets on the direction of a market, a currency, an interest rate, a commodity, or any macroeconomic variable
- high leverage & extensive use of derivatives
4-1. Futures Funds (Managed Future Funds)
- commodity pools that include commodity trading advisor funds
- bets on directional moves in the positions they hold in a single asset class, such as currency, fixed income, or commodities and tend to use may actively traded futures contracts
Systematic Strategies
- generating buy & sell decisions from computer models combining various technical factors and indictors
- executed in highly liquid markets with low transaction costs
- trend-following: dominant trading style
- long straddle
- short-term models using counter-trend signals
- trading based on technical pattern recognitions (Elliot waves)
- Taking positions according to the degree to which a commodity is trading in contango or backwardation
- overfitting (curve fitting)
Discretionary Strategies
- proprietary approaches based on fundamentals
- directional long-term positions based on fundamentals & short-term bets based on information flow
4-2. Emerging-Market Funds
best on all types of securities in emerging markets
5. Funds of Funds
- created to allow easier acces to small investors as well as instituional investors
benefits:
- retailing
- access
- diversification
- expertise
- due diligence process
drawbacks:
- fee
- performance
- diversification is a two-edged sword
1-1. Long/Short Equity
- Long a core set of stocks
- Short sales of other borrowed stocks (partially or fully hedging): generating returns when price declines, hedging brad market risk, and earning interest on proceeds
- leverage
- exposure to broad equity risk premium, small firm & value stock risk premia
- significant alpha -> experience- & skill-driven
- dead weight in traditional index-benchmark equity investment
- most managers have a long bias
- the focus of strategy: stock selection with regional, sector-specific or particular style emphasis
- NOT market timing, prediction of the broad stock market direction
e.g.) long undervalued and short overvalued, core long positions with a partial hedge overlay with short index futures, long OTM puts and short covered call
Bottom-Up Approach
- fundamental analysis -> determination of undervalued or overvalued
- analysis of industry sector
- qualitative analysis: a detailed due diligence process & analysis of maangement
Top-Down Approach
- economic trends & upcoming investment themes in certain industry sectors: vlaue vs. growth
- inefficiencies on micro & small capitalization stocks
Index
- HFR Long/Short Equity Hedge Index
- CSFB Tremont Long/Short Equity Index
1-2. Equity Market Neutral
- simultaneously long & short matched stock positions -> taking advantage of a relative outperormance of the long positions vs. the short positions
- generating returns that are completely uncorrelated to the overall equity market
- insulating portfolios from broad market rist factors = total portfolio net exposure = zero; dollar neutral, country neutal, currency neutral, sector neutral, size neutral, style neutral (value vs. growth)
Statistical Arbitrage
- model-based short-term trading
- quantitative & technical analysis
- profit opportunity in undervalued & overvalued; mean-reversion
- pair trading: long & short position in two stocks that are closely related
- black box investing; characteristics of the model are usually not disclosed to investors
three Steps
- screening & ranking: rule-based decision
- stock selection: value factors (rule-based decition; selection criteria: price-to-book, price-to-earning, price-to-sales, discounted CF, ROE, operating margins, earnings growth) or momentum factors (price or earnings momentum, moving average, relative strength & trading volumes)
- portfolio construction
e.g.) long outperformed (winner stocks) & short underperformed (loser stocks),
Fama-French HML (high minus low; long high book-to-market stock & short low book-to-market), SMB (small minus big; long small firms & sell large cap), and UMD (up minus down; long recent winner & short recent loser)
Market Neutral Long/Short Equity
1-3. Equity Market Timing
- mutual fund timing
- using a variety of technical trading models to screen the global equity markets for short-term opportunities in particular industry or geographic sectors
- switch between long equity exposure (taken at favorable moment) and risk-free
- inefficiencies of equity markets
- technical trend-following models based on short & medium-term momentum -> buy and sell signals
two strategies:
- sector timing: micro upward trends in single industry sectors **stale prices
- time zone arbitrage
studies:
- small cap lag the price action of large cap by 1~2 days
1-4. Short Selling
- selling of stocks not currently owned by the seller in order to take a directional bet on their anticipated price decline
- short rebate interest: interest earnings on proceeds
- substantial collateral: 30~50% of the market value
- short with derivatives or short with long/OTM call options (= long/short equty strategy with a short bias)
- key driver = security selection
payoff:
- profit from buying back stock at a lower price
- short debate interest
approaches:
- bottom-up approach: aggressive accounting techniques
consideration:
- share availability
- stability of the borrowing (call back)
- level of short rebate interest
- short squeezes
- invers relationship between performance and exposure
2. Relative Value Strategies
2-1. Convertible arbitrage
- long convertible security and short underlying stock
- equivalent to holding a bond position plus an option on some underlying stock
- arbitrage opportunities by identifying pricing disparities between the equity and the convertible bond
- buying volatility (cheap convertible securities) & hedging
- leverage: 1:1 to 5:1
- credit risk & interest risk
e.g.) long convertible bonds & short underlying stock/option or index futures/options,
low credit quality or distressed convertibles & stock
income sources:
- static returns: coupon & short stock rebates
- gamma trading on stock volatility
- price inefficiencies
Static Returns
- coupon/dividend plus short rebate (minus dividends)
- consideration: credit risk, omicron (dependency between bond price and credit spread)
- related to systematic risk factor; not related to pricing inefficiency
Gamma Trading
- long valatility; achieved from long gamma & long vega
- Long Gamma: delta neutral = when a stock price increases, delta increases, and sells more stock
- being long gamma: changing delta always works out in favor of the overall position of long convertible bond with a hedged short position in the underlying stock
- being long vega: as the stock price volatility changes, the convertible's value will change due to the commensurated change in the inherent option value (conversion premium)
- long gamma & vega has little to do with exploiting pricing inefficiencies -> driver of convertible arbitrage strategy
- short theta
2-2. Fixed Income Arbitrage
- profits by trading the spread relationship (spread position) between related fixed income securities and their derivatives to profit from relative movements or to accrue positive carry retusns over time
- neutralizing exposure to most systematic risk factors (e.g. yiedl curve changes, interest rate, credit, FX, etc)
- short volatility strategies
- flight to quality: when interest rates move rapidly, creadit spreads widen & liquidity dries up
- complexity premium
e.g.) spread trades
- yield curve trades (bonds with different maturities), corporate vs. Treasury yield spreads, municipal vs. Treasury yield spreads, cash vs. future, on-the-run vs. Treasury bonds
- arbitrage between similar bonds: different duration
- Butterflies (yield curve arbitrage): e.g. long cheap 5-year, 7-year & short expensive 6-year
- Basis trades: spread between physical securities and their futures
- Asset swap: long fixed-rate bonds vs. pay fixed positions in interest swaps or vice versa (reverse asset swaps)
- TED spread: spread between T-bill futures and Eurodallar futures
- yield spread between on-the-run & off-the-run bonds
other strateges (non-market neutral)
- yield curve spread trading based on a forecast of the directional changes of the yield curve
- credit spread trading
- cross-currency government vs. government spread trades
- ABS
- MBS against CMO
pricing inefficiencies:
- agency biases
- structural reasons: tax, accounting or regulatory issues
- market segmentation
2-3. Volatility Arbitrage
- benefit from the level and change of volatilities in particular instruments
- long position in cheap volitalities and short position in expensive volatilities
2-4. Capital Structure Arbitrage
- long and short positions in difference financial instruments within the capital structure of an idividual company.
- discrepancies movements of the equity & bond prices
e.g.) buying bond & selling stock vice versa, short CDS & long a stock put vice versa, long one bond issue & short another bond tranche
3. Event-Driven Strategis
- event: firm-specific (idosyncratic nature)
strategies:
- cash takeovers & stock-for-stock mergers (merger arbitrage)
- divestments, spin-offs, special dividends and refinancings
- ligigation plays: legal case such as bankruptcy
- post-bankruptcy: companies emerging out of Chapter 11 proceedings
- index events: changes in index composition
- holding company and share calss arbitrage: buying shares of holding company & selling shares of its assets or vice versa
3-1. Merger Arbitrage
Before the effective date of a merger, the stock of the acquired company will typically sell at a discount to its acquisition value as officially announced.
- buying stock in a company being acquired and selling stock in its acuqirers.
3-2. Distressd Securities
- investing in the debt and/or equity of companies having financial difficulty
- deeply discounted prices
- successful reorganization and profitable returns
3-3. Regulation D
- investing in publicly listed companies, mostly of micro and small cap, that are in need of capital through privately negotiated structure.
- private equity placements pursuant to Regulation D
- the investment is structured in the form of privately placed, unregistered, high coupon, convertible securities or debentures with maturities ranging anywhere from 18 to 60 months.
- invetment are made pursuant to an exemption from registration as provided by Regulation D of the U.S. Securities Act of 1933
- selling the fully tradable and registered shares in the public markets & realizing the spread between the market price and the discounted price of the stock (15 ~ 40%)
- bottom-up analysis
4. Opportunistic/Global Macro Strategies
- bets on the direction of a market, a currency, an interest rate, a commodity, or any macroeconomic variable
- high leverage & extensive use of derivatives
4-1. Futures Funds (Managed Future Funds)
- commodity pools that include commodity trading advisor funds
- bets on directional moves in the positions they hold in a single asset class, such as currency, fixed income, or commodities and tend to use may actively traded futures contracts
Systematic Strategies
- generating buy & sell decisions from computer models combining various technical factors and indictors
- executed in highly liquid markets with low transaction costs
- trend-following: dominant trading style
- long straddle
- short-term models using counter-trend signals
- trading based on technical pattern recognitions (Elliot waves)
- Taking positions according to the degree to which a commodity is trading in contango or backwardation
- overfitting (curve fitting)
Discretionary Strategies
- proprietary approaches based on fundamentals
- directional long-term positions based on fundamentals & short-term bets based on information flow
4-2. Emerging-Market Funds
best on all types of securities in emerging markets
5. Funds of Funds
- created to allow easier acces to small investors as well as instituional investors
benefits:
- retailing
- access
- diversification
- expertise
- due diligence process
drawbacks:
- fee
- performance
- diversification is a two-edged sword
Saturday, October 10, 2009
Ch6 Credit Derivatives (1)
1. Credit Default Swaps
The most poplular credit derivatives
1-1. Terminology
- reference entity
- credit event
- notional principal: par value
- CDS spread
- settlement
1-2. Credit Default Swaps & Bond Yields
The n-year CDS spread should be approximately equal to the excess of the par yield on an n-year corporate bond over the par yield on an n-year risk-free bond.
- if CDS spread less than the difference: buying assets & buying protection
- if CDS spread greater than the difference: borrowing @risk-free, shorting & selling CDS protection
**CDS Spread = Risk-free rate; approximately equal to (LIBOR/Swap - 10 basis points)
1-3. Cheapest-to-Diliver (CTD) Bond
In the event of default, the protection buyer choose for delivery the bond that can be purchased most cheaply.
e.g.) the most recent settlement price = 93_08
Bond 1: quoted price = $99.50, conversion factor = 1.0382
Bond 2: quoted price = $143.50, conversion factor = 1.5188
Bond 3: quoted price = $119.75, conversion factor = 1.2615
2. Valuation of Credit Default Swaps
Step 1: Calculate P.V. of expected payment
Step 2: Calculate P.V. of expected payoff in the event of default
Step 3: Calculate P.V. of accrual payment in the event of default
Step 4: Calculate CDS spread
2-1. Marking to Market a CDS
e.g.) CDS spread = 150 basis points, P.V. of expected payments = 4.1130 x CDS spread, P.V. of expected payoff = 0.0511 per $
=> P.V. of expected payments = 4.1130 x .0150 = 0.0617 per $
0.0617 - 0.0511 = 0.0106 per $
Mark-to market value of swap to buyer of protection = -0.0106 per $
2-2. Estimating Default Probabilities
The default probabilities used to value a CDS should be risk-neutal default probabilities.
2-3. Binary Credit Default Swaps
A binary credit default swap is structured similarly to a regular CDS except that the payoff is a fixed dollar amount.
3. Credit Indices
- CDX NA 1G: a portfolio of 125 investment grade companies in North America
- iTraxx Europe: a portfolio of 125 investment grade names in Europ
4. CDS Forwards & Options
4-1. Forward CDS: obligation to buy or sell a particular CDS on a particular reference entity at a particular future time T.
4-2. CDS option: option to buy or sell a particular CDS on a particular reference entity at a particular future time T
5. Baset CDS
- add-up basket CDS
- first-to-default CDS & nth-to-default CDS
6. Total Return Swaps (TRS)
- TRS buyer (protection seller): Total return + Depreciation Amount
- TRS issuer (protection buyer): LIBOR + spread
7. Asset-Backed Security (ABS)
8. Collateralized Debt Obligations (CDOs)
8-1. Cash CDOs
8-2. Synthetic CDOs
8-3. Single Tranche Trading
The market uses CDS indices portfolios to define standard CDO tranches. The trading of these standard tranches is know as single tranche trading.
A single tranche trade is an agreement where one side agrees to sell protection against losses on a tranche and the other side agrees to buy the protection. The tranche is not part of a synthetic CDO that someone has created but cash flows are calculated in the same way as if it were part of such a synthetic CDO.
9. Valuation of Synthetic CDO
10. Alternatives to the Standard Market Model
10-1. Heterogeneous Model
The standard market model is a homogeneous model in the sense that the time-to-default probability distributions are assumed to be the same for all companies and the copula correlations for any pair of companies are the same. The homogeneity assumption can be relaxed sh that the more general model is used.
10-2. Other Copulas
- one-factor Gaussian copulas: Student t copula, Clayton copula, Archimedean copula, Marshall-Olkin copula
10-3. Multiple Factors
10-4. Random Factor Loadings
10-5. Implied Copula Model
10-6. Dynamic Models
The most poplular credit derivatives
1-1. Terminology
- reference entity
- credit event
- notional principal: par value
- CDS spread
- settlement
1-2. Credit Default Swaps & Bond Yields
The n-year CDS spread should be approximately equal to the excess of the par yield on an n-year corporate bond over the par yield on an n-year risk-free bond.
- if CDS spread less than the difference: buying assets & buying protection
- if CDS spread greater than the difference: borrowing @risk-free, shorting & selling CDS protection
**CDS Spread = Risk-free rate; approximately equal to (LIBOR/Swap - 10 basis points)
1-3. Cheapest-to-Diliver (CTD) Bond
In the event of default, the protection buyer choose for delivery the bond that can be purchased most cheaply.
e.g.) the most recent settlement price = 93_08
Bond 1: quoted price = $99.50, conversion factor = 1.0382
Bond 2: quoted price = $143.50, conversion factor = 1.5188
Bond 3: quoted price = $119.75, conversion factor = 1.2615
2. Valuation of Credit Default Swaps
Step 1: Calculate P.V. of expected payment
Step 2: Calculate P.V. of expected payoff in the event of default
Step 3: Calculate P.V. of accrual payment in the event of default
Step 4: Calculate CDS spread
2-1. Marking to Market a CDS
e.g.) CDS spread = 150 basis points, P.V. of expected payments = 4.1130 x CDS spread, P.V. of expected payoff = 0.0511 per $
=> P.V. of expected payments = 4.1130 x .0150 = 0.0617 per $
0.0617 - 0.0511 = 0.0106 per $
Mark-to market value of swap to buyer of protection = -0.0106 per $
2-2. Estimating Default Probabilities
The default probabilities used to value a CDS should be risk-neutal default probabilities.
2-3. Binary Credit Default Swaps
A binary credit default swap is structured similarly to a regular CDS except that the payoff is a fixed dollar amount.
3. Credit Indices
- CDX NA 1G: a portfolio of 125 investment grade companies in North America
- iTraxx Europe: a portfolio of 125 investment grade names in Europ
4. CDS Forwards & Options
4-1. Forward CDS: obligation to buy or sell a particular CDS on a particular reference entity at a particular future time T.
4-2. CDS option: option to buy or sell a particular CDS on a particular reference entity at a particular future time T
5. Baset CDS
- add-up basket CDS
- first-to-default CDS & nth-to-default CDS
6. Total Return Swaps (TRS)
- TRS buyer (protection seller): Total return + Depreciation Amount
- TRS issuer (protection buyer): LIBOR + spread
7. Asset-Backed Security (ABS)
8. Collateralized Debt Obligations (CDOs)
8-1. Cash CDOs
8-2. Synthetic CDOs
8-3. Single Tranche Trading
The market uses CDS indices portfolios to define standard CDO tranches. The trading of these standard tranches is know as single tranche trading.
A single tranche trade is an agreement where one side agrees to sell protection against losses on a tranche and the other side agrees to buy the protection. The tranche is not part of a synthetic CDO that someone has created but cash flows are calculated in the same way as if it were part of such a synthetic CDO.
9. Valuation of Synthetic CDO
10. Alternatives to the Standard Market Model
10-1. Heterogeneous Model
The standard market model is a homogeneous model in the sense that the time-to-default probability distributions are assumed to be the same for all companies and the copula correlations for any pair of companies are the same. The homogeneity assumption can be relaxed sh that the more general model is used.
10-2. Other Copulas
- one-factor Gaussian copulas: Student t copula, Clayton copula, Archimedean copula, Marshall-Olkin copula
10-3. Multiple Factors
10-4. Random Factor Loadings
10-5. Implied Copula Model
10-6. Dynamic Models
Friday, October 9, 2009
Ch2 Estimating Volatilities & Correlations
1. Video clips
EWMA: http://www.youtube.com/watch?v=P_tr9_Ue220&feature=PlayList&p=DC2DBF1418970E52&playnext=1&playnext_from=PL&index=51
Moving Average Approaches: http://www.youtube.com/watch?v=8D9jEFSI1w8&feature=PlayList&p=DC2DBF1418970E52&index=52&playnext=2&playnext_from=PL
GARCH(1,1): http://www.youtube.com/watch?v=KJbR0nRinD4
Ch6 Understanding the Securitization of Subprime Mortgage Credit
1. Subprime Securitization Process
*internal credit enhancement:
- subordination: first internal credit enhancement
- hold back: SPV buy assets at discount by originator
- cash colleral account
- excess spread
*external credit enhancement:
- insurance, wraps & guarantees
- LOC
- basket CDS
- put option on assets
*Subprime
- Debt Servie-to-Income > 50%
- FICO less than 660
- 60 day delinquency in last 24 months
- 2+ 30 day delinquencies in last 12 months
- Judgment, foreclosure in prior 24 months
- Bankruptcy in last 5 years
1-1. Mortgage Process
- Friction 1: Mortgagor & Originator; possibility of predatory (unfair) lending -> stretch the bounds of the application resulting in larger than optimal lending
- Friction 2: Originator & Arranger (issuer) - the originator creates bankruptcy the remote trust and the arranger perform due diligence, but operate at an information disadvantage to the originator -> adverse selection problem
- Friction 3: Arranger & Third-Parties; adverse selection and information problem; retain higher quality mortgage & securitize lower quality mortgage; Warehouse lender fund less than 100% of estimated collateral value; Asset portfolio manager use a adequate due diligence; Rating agencise determine the amount of credit enhancement but dependent on the information provided by the arranger
- Friction 4: Servicer & Mortgagor; the servicer manage the CF of the MBS pool and follow up on delinquencies and foreclosure; moral hazard problem
- Friction 5: Servicer & Third-Parties; lack of effort can impact the asset manager and credit rating agencies without directly affecting CF distribution -> moral hazard problem
- Friction 6: Asset manager & Investor; moral hazard by managers & principle agency problem
- Friction 7: Investor & Credit Rating Agencies; conflict of interest (compensated by the arranger) -> model error
**video clips: Frictions in subprime securitization http://www.youtube.com/watch?v=F_GwmUUJX3E
2. Characteristics of the Subprime Mortgage Market
2-1. Characteristics
- subprime borrower
- ARM (adjustable rate mortgage) & a teaser rate for a short period
- borrowers bear interest rate risk
- performance of subprime pools indicates defaults and foreclosures way above historical levels
2-2. Structure of securitization process
**protection
- subordination: creating tranches of differing priority levels
- excess spread: excess spread = (weighted average coupon) - (servicing, hedging & other expenses) - (weighted average payout)
- shifting interest: senior receive all principal in the pool while mezzanine interest only
- performance trigger: overcollateralization
- interest rate swaps: fixed rate & LIBOR
3. Credit Rating Process
3-1. Rating process
An unconditional view: through-the-cycle
Two Steps:
- estimation of loss distribution
- simulation of CF
After obtaining the estimates, rating agencies indicate the level of credit enhancement necessary to achieve the desired rating
**video clips: credit enhancements in a securitization: http://www.youtube.com/watch?v=Ip0lZ-TjdHI&feature=related
3-2. Difference between credit ratings for subprime securities & corporate ratings
- corporate bond ratings based on the firm-specific characteristics <-> MBS: systematic risk & degree of correlation between assets are important, claims on a static pool
- MBS: future economic conditions
- if PDs are same, the MBS will exhibit much wider variation in losses
3-3. Credit ratings cycle & housing cycle
- through-the-cycle: no excessive upgrades (downgrades) even though housing market heats up (slow down)
- AAA rating during a boom period -> as the housing market slow down, MBS would migrate to AA
- As economic conditions change, the effect may amplify up and down markets
3-4. CF Analysis of Excess Spread
3-4-1. Interrelated factors for forcasting the degree of excess spread
- credit enhancement: amount of collateral that can be impaired before the tranche suffers an economic loss
- timing of losses: front-loading the losses (conservative approach)
- prepayment rates: CPR (conditional prepayment rate); hybrids will have higher than predicted defaults on or about the reset date due to the sudden change
- interest rates
- trigger events
- weighted average loan rate decrease
- prepayment penalties
- pre-funding accounts
- hedging instruments
3-5. Annual review of mortgage pools
- Important performance measures: Loss Coverage Ratio (LCR)
LCR = (current credit enhance ment for tranche) / (estimated unrealized losses)
- if the LCR is breached, a full review is warranted
4. Predatory Lending & Borrowing
4-1. Predatory lending: borrower becomes worse off
4-2. Predatory borrowing: misrepresentation in the mortgage application from the borrower side or overstating (falsifying) creditworthiness for rapid home application in high price real estate markets
*internal credit enhancement:
- subordination: first internal credit enhancement
- hold back: SPV buy assets at discount by originator
- cash colleral account
- excess spread
*external credit enhancement:
- insurance, wraps & guarantees
- LOC
- basket CDS
- put option on assets
*Subprime
- Debt Servie-to-Income > 50%
- FICO less than 660
- 60 day delinquency in last 24 months
- 2+ 30 day delinquencies in last 12 months
- Judgment, foreclosure in prior 24 months
- Bankruptcy in last 5 years
1-1. Mortgage Process
- Friction 1: Mortgagor & Originator; possibility of predatory (unfair) lending -> stretch the bounds of the application resulting in larger than optimal lending- Friction 2: Originator & Arranger (issuer) - the originator creates bankruptcy the remote trust and the arranger perform due diligence, but operate at an information disadvantage to the originator -> adverse selection problem
- Friction 3: Arranger & Third-Parties; adverse selection and information problem; retain higher quality mortgage & securitize lower quality mortgage; Warehouse lender fund less than 100% of estimated collateral value; Asset portfolio manager use a adequate due diligence; Rating agencise determine the amount of credit enhancement but dependent on the information provided by the arranger
- Friction 4: Servicer & Mortgagor; the servicer manage the CF of the MBS pool and follow up on delinquencies and foreclosure; moral hazard problem
- Friction 5: Servicer & Third-Parties; lack of effort can impact the asset manager and credit rating agencies without directly affecting CF distribution -> moral hazard problem
- Friction 6: Asset manager & Investor; moral hazard by managers & principle agency problem
- Friction 7: Investor & Credit Rating Agencies; conflict of interest (compensated by the arranger) -> model error
**video clips: Frictions in subprime securitization http://www.youtube.com/watch?v=F_GwmUUJX3E
2. Characteristics of the Subprime Mortgage Market
2-1. Characteristics
- subprime borrower
- ARM (adjustable rate mortgage) & a teaser rate for a short period
- borrowers bear interest rate risk
- performance of subprime pools indicates defaults and foreclosures way above historical levels
2-2. Structure of securitization process
**protection
- subordination: creating tranches of differing priority levels
- excess spread: excess spread = (weighted average coupon) - (servicing, hedging & other expenses) - (weighted average payout)
- shifting interest: senior receive all principal in the pool while mezzanine interest only
- performance trigger: overcollateralization
- interest rate swaps: fixed rate & LIBOR
3. Credit Rating Process
3-1. Rating process
An unconditional view: through-the-cycle
Two Steps:
- estimation of loss distribution
- simulation of CF
After obtaining the estimates, rating agencies indicate the level of credit enhancement necessary to achieve the desired rating
**video clips: credit enhancements in a securitization: http://www.youtube.com/watch?v=Ip0lZ-TjdHI&feature=related
3-2. Difference between credit ratings for subprime securities & corporate ratings
- corporate bond ratings based on the firm-specific characteristics <-> MBS: systematic risk & degree of correlation between assets are important, claims on a static pool
- MBS: future economic conditions
- if PDs are same, the MBS will exhibit much wider variation in losses
3-3. Credit ratings cycle & housing cycle
- through-the-cycle: no excessive upgrades (downgrades) even though housing market heats up (slow down)
- AAA rating during a boom period -> as the housing market slow down, MBS would migrate to AA
- As economic conditions change, the effect may amplify up and down markets
3-4. CF Analysis of Excess Spread
3-4-1. Interrelated factors for forcasting the degree of excess spread
- credit enhancement: amount of collateral that can be impaired before the tranche suffers an economic loss
- timing of losses: front-loading the losses (conservative approach)
- prepayment rates: CPR (conditional prepayment rate); hybrids will have higher than predicted defaults on or about the reset date due to the sudden change
- interest rates
- trigger events
- weighted average loan rate decrease
- prepayment penalties
- pre-funding accounts
- hedging instruments
3-5. Annual review of mortgage pools
- Important performance measures: Loss Coverage Ratio (LCR)
LCR = (current credit enhance ment for tranche) / (estimated unrealized losses)
- if the LCR is breached, a full review is warranted
4. Predatory Lending & Borrowing
4-1. Predatory lending: borrower becomes worse off
4-2. Predatory borrowing: misrepresentation in the mortgage application from the borrower side or overstating (falsifying) creditworthiness for rapid home application in high price real estate markets
Sunday, October 4, 2009
Ch6 Studies on Credit Risk Concentration
1. IRB Risk Weight Function Assumptions
Basel II's IRB approach to credit risk assumes the bank's credit portfolio is diversified (granular or perfectly fine-grained). This assumption is convenient but unrealistic.
1-1. Credit Risk
- Systematic risk: unexpected changes in financial market conditions
- Nonsystematic (idiosyncratic) risk: borrower-specific risks
1-2. Two Approaches for Calculating Capital Requirements
- Standardized Approach
- IRB Approach
1-3. Function for Calulating Credit Risk Capital Requirements
Asymptotic Single-Risk Factor (ASRF) model: IRB risk weight function
- Portfolio invariance
- Capital requirements are based soley on systematic risk -> underestimation of total risk
3. Contagion
Exposures to independent obligors that exhibit default dependencies which exceed what one should expect on the basis of their sector affiliations.
- the probability of an obligor's default conditional on another obligor defaulting is higher than the unconditional probability of default for the same obligor.
- difficult to estimate & currently not properly accounted for in credit risk portfolio model
- lack of info regarding biz interactions between banks & relationships between a bank's custmers and other firms
4. Stress Testing Sector Concetration
4-1. Desirable properties for stress tests
- plausibility
- consistency
- adaptability to the portfolio
- adaptability to internal reporting requirements
4-2. Plausibility
credibility of the stress scenario which is believable and have a certain probability of actual occurring.
e.g.) evaluating data from historical stress events
4-2. Consistency
consistency across the relevant risks within the portfolio
- use a consistent quantitative framework which captures and aggregares the relevant risks and serves as the basis for risk management actions.
e.g.) historical dependencies (correlations) of risk factors & stressing the systematic risk factors
4-3. Adaptability to the portfolio
- The test focuses on exposures which are significant in the portfolio
4-4. Adaptability to the internal reporting
- The results can be easily deciphered so that the firm can take an appropriate action RE: future composition of portfolio
5. Open Technical Issues
5-1. Adequacy of sector schemes
- same sector: similar characteristics? or colse correlation of asset returns?
5-2 Definition of a benchmark for concentration risk correlation
5-3. Data-related issues
Basel II's IRB approach to credit risk assumes the bank's credit portfolio is diversified (granular or perfectly fine-grained). This assumption is convenient but unrealistic.
1-1. Credit Risk
- Systematic risk: unexpected changes in financial market conditions
- Nonsystematic (idiosyncratic) risk: borrower-specific risks
1-2. Two Approaches for Calculating Capital Requirements
- Standardized Approach
- IRB Approach
1-3. Function for Calulating Credit Risk Capital Requirements
Asymptotic Single-Risk Factor (ASRF) model: IRB risk weight function
- Portfolio invariance
- Capital requirements are based soley on systematic risk -> underestimation of total risk
1-3-1. Assumptions
- Risk weights should be portfolio invariant (independent): only the systematic component of credit risk is a factor for calculation of capital requirements -> difficulites of calibrating the risk weight function for a well-diversified bank
- Expected losses are covered by revenue or provisions
- Unexpected losses will be covered by bank capital
- Unexpected losses will exceed capital at a small pre-determined acceptable probability
1-3.2 Problem
- infinitely granular portfolios do not exist in practice
- low granularity leads to higher capital requirements
**portfolio invariance:
- if we add a loan to a portfolio, the additional capital charge is based on the loan's features, not on the portfolio
- the risk of the loan is a function only of the single systematic risk factor
2. Credit Risk Concentration
2-1. Concentration risk: disproportionately large exposure to a single borrower (name concentration) or a common sector (sector concentration) or economic variable
2-2. Name Concentration
2-2-1. imperfect granularity: portfolio not properly diversified
- ASRF model assumption violation: 'portfolio is composed of numerous relatively small exposures'
- underestating the true level of risk
**granularity: the number of the exposures in the portfolio
2-2-2. Granularity adjustment model: Gordy & Lutkebohmert Model
Development of an upperbound for the granularity adjustment
Problems with adjustment:
- not work well on small portfolios
- based on a different model of credit risk (inconsistent with IRB model) -> basis risk or model mismatch
Alternative models:
- Vasicek model: systematic risk be leveraged to account for the extra idiosyncratic risk
- Emmer & Tasche model: based on Merton model
2-2-3. tradeoff between lowering the cutoff point of exposures and the implied reduction in capital (Gordy & Lutkebohmert): lowering the cutoff results in a relatively small change in the upper bound calculation
2-3. Sector Concentration
Heavy exposure to a specific geographic area or industry
Underestimation of economic capital
**The size of the underestimation is a function of the portfolio weight in a specific sector and the correlation of the sector to systematic risk. As the correlation between sector risk and systematic risk increases, the model moves closer to the single risk factor model
2-3-1. Gap between real EC and ASRF performance
The gap is substantial and dependent on model structure and correlation estimates
The sector model estimates lower EC than the IRB model.
** Duellmann & Masschelein (Multi-Factor Model)
- measured the impact of various degrees of sector concentration on EC.
Estimates of EC: diversified portfolio 7.8%, portfolio similar to regional bank 9.5%, mid-sized bank 10.7%, portfolio concentration in one asset 11.7%
- market model & sectoral model: the market model generates estimates of capital 10~90% higher than a sector model. The difference in capital estimates varies over time depending on the stability of asset correlations and an increase in PD over the period.
**Binomial Expansion Technique (BET) by Moody's
- mapping of an actual portfolio with potential complicated credit risk dependencies across individual exposures onto a hypothetical portfolio of homogeneous uncorrelated exposures
- mapping performed by calibration of two parameters: (common) PD for the exposures & diversity score
- infection model by Duellmann: extension of BET; infection probability between exposures
3. Contagion
Exposures to independent obligors that exhibit default dependencies which exceed what one should expect on the basis of their sector affiliations.
- the probability of an obligor's default conditional on another obligor defaulting is higher than the unconditional probability of default for the same obligor.
- difficult to estimate & currently not properly accounted for in credit risk portfolio model
- lack of info regarding biz interactions between banks & relationships between a bank's custmers and other firms
4. Stress Testing Sector Concetration
4-1. Desirable properties for stress tests
- plausibility
- consistency
- adaptability to the portfolio
- adaptability to internal reporting requirements
4-2. Plausibility
credibility of the stress scenario which is believable and have a certain probability of actual occurring.
e.g.) evaluating data from historical stress events
4-2. Consistency
consistency across the relevant risks within the portfolio
- use a consistent quantitative framework which captures and aggregares the relevant risks and serves as the basis for risk management actions.
e.g.) historical dependencies (correlations) of risk factors & stressing the systematic risk factors
4-3. Adaptability to the portfolio
- The test focuses on exposures which are significant in the portfolio
4-4. Adaptability to the internal reporting
- The results can be easily deciphered so that the firm can take an appropriate action RE: future composition of portfolio
5. Open Technical Issues
5-1. Adequacy of sector schemes
- same sector: similar characteristics? or colse correlation of asset returns?
5-2 Definition of a benchmark for concentration risk correlation
5-3. Data-related issues
Wednesday, September 30, 2009
Ch8 Performance Analysis (1)
1. Introduction
The goal of perfromance analysis is to distinguish skilled from unskilled investment managers
- time series analysis: separate skill form luck by measuring return and risk
- cross-sectional comparison: distinguish winners from losers
Performance analysis can help the manager avoid two major pitfalls in implementing an active strategy.
- incidental risk: growth stocks -> concentrations on certain industy and group of stocks with high volatility
- incremental decision making: sequence of individual asset decisions
The goal of perfromance analysis is to distinguish skilled from unskilled investment managers
- time series analysis: separate skill form luck by measuring return and risk
- cross-sectional comparison: distinguish winners from losers
Performance analysis can help the manager avoid two major pitfalls in implementing an active strategy.
- incidental risk: growth stocks -> concentrations on certain industy and group of stocks with high volatility
- incremental decision making: sequence of individual asset decisions
2. Skill & Luck
2-1. Dimensions of skill & luck
- Blessed
- Insufferable
- Fortorn
- Doomed
*the challenge is to separate the blessed & the insufferable
2-2. Standard Error of Information Ration (IR)
where:
Y = number of years of observation
**IR: a ratio of portfolio returns above the returns of a benchmark to the volatility of those returns. IR measures a portfolio manager's ability to generate excess returns relative to a benchmark and attempts to identify the consistency of the investor. Generally, portfolios with higher betas will tend to have lower information ratios and vice versa, However, the higher beta enhances the portfolio's alpha and contributes to a higher information ratio if the benchmark underperforms the risk-free return during a period.
IR = (Rp - Ri) / Sp-i
where:
Rp = Return of the portfolio
Ri = Return of the benchmark
Sp-i = Tracking error (standard deviation of the difference between returns of the portfolio & the returns of the benchmark), residual risk
3. Defining-Based Performance Analysis
3-1. Returns
3-2. Returns Regression
- regressing the time series of portfolio excess returns against benchmark excess returns
4. Cross-Sectional Comparisons
4-1. Drawbacks of cross-sectional comparisons
- do not represent the complete population of institutional investment manages
- survivorship bias
- ingnore the size
- do not adjust for risk (cannot untangle luck & skill)
Saturday, September 26, 2009
Ch8 Portfolio Construction (2)
5. Portfolio Revisions
- trading decisions based on expected active return, active risk, & transaction costs
- underestimating transX costs -> frequent trading -> suffering higher than expected transX costs & lower than expected alpha
- as the horizon of the forecast alphas decreases -> returns become noiser with shorter horizons. rebalancing for very short horizons would involve frequent reactions to noise, not signal. But the transaction costs stay the same, whether we are reacting to signal or noise.
- trading decisions based on expected active return, active risk, & transaction costs
- underestimating transX costs -> frequent trading -> suffering higher than expected transX costs & lower than expected alpha
- as the horizon of the forecast alphas decreases -> returns become noiser with shorter horizons. rebalancing for very short horizons would involve frequent reactions to noise, not signal. But the transaction costs stay the same, whether we are reacting to signal or noise.
**individual stock's alpha
e.g.) Boeing's alpha = 0.54%, beta = 0.56, monthly risk-free rate = 0.4%
=> Rj = Rf + beta x (Rm - Rf) = Rf (1 - beta) + beta x Rm
Rf(1 - beta) = 0.4% (1 - 0.56) = 0.18%
0.54% - 0.18% = 0.36% > 0 -> Boeing performed 0.36% better than expected
Annualized Excess Return = (1 - .0036) ^ 12 - 1 = 4.41%
- we can capture the impact of new information, and decide whether to trade, by compaing the marginal contribution to value added for stock n, MCVAn, to the transactions costs. The marginal contribution to value added shows how value added, as measure by risk-adjusted alpha, changes as the holding of the stock is increased with an offsetting decrease in the cash position.
- as our holding in stock n increases, alpha n measures the effect on portfolio alpha
- the change in value added also depends upon the marginal impact on active risk of adding more of stock n, MCARn, which measures the rate at which active risk changes as we add more of stock n
- let PCn be the purchase cost and SCn the sales cost for stock n. The situation before new information arrive is
e.g.) Boeing's alpha = 0.54%, beta = 0.56, monthly risk-free rate = 0.4%
=> Rj = Rf + beta x (Rm - Rf) = Rf (1 - beta) + beta x Rm
Rf(1 - beta) = 0.4% (1 - 0.56) = 0.18%
0.54% - 0.18% = 0.36% > 0 -> Boeing performed 0.36% better than expected
Annualized Excess Return = (1 - .0036) ^ 12 - 1 = 4.41%
- we can capture the impact of new information, and decide whether to trade, by compaing the marginal contribution to value added for stock n, MCVAn, to the transactions costs. The marginal contribution to value added shows how value added, as measure by risk-adjusted alpha, changes as the holding of the stock is increased with an offsetting decrease in the cash position.
- as our holding in stock n increases, alpha n measures the effect on portfolio alpha
- the change in value added also depends upon the marginal impact on active risk of adding more of stock n, MCARn, which measures the rate at which active risk changes as we add more of stock n
- let PCn be the purchase cost and SCn the sales cost for stock n. The situation before new information arrive isFriday, September 25, 2009
Ch8 Portfolio Construction (1)
1. Introduction
Inprementation includes both portfolio construction and trading.
*standard object: maximizing (active returns - active risk penalty)
1-1. Inputs for portfolio construction
- portfolio (measurement with near certainty)
- alphas (unreasonable and subject to hidden biases)
- covariance estimates (noisy estimates)
- transaction cost estimates (noisy estimates)
- active risk aversion
1-2. Active Portfolio Management
Maximizing the expected utility of the excess return over a chosen benchmark
- active managers attempt to beat the market by forming portfolios capable of producing actural returns that exceed risk-adjusted expected returns.
**passive portfolio management: it just estables a portfolio that possibly tracks the chosen benchmark. Passive portfolio managers try to capture the expected return consistent with the risk level of their portfolios.
1-3. Benchmark Portfolio
It might be an equity fund (S&P 500 Index), a bond fund (Lehman Brothers Bond Fund), or a balanced fund (mix of stocks and bonds). In other applications, it could be a stream of liabilities, such as a pension fund. We assume that the selected benchmark carries only the market risk.
2. Alphas & Portfolio Construction
2-1. Constraints
Most active managers construct portfolio subject to certain constraints: no short, restriction on the amount of cash held within portfolio, asset coverage, etc. These limits can make the portfolio less efficient.
Managers often add their own restrictions to the process to make portfolio construction more robust: neutral economic sectors, restrictions on allocations to certain stock, avoidance of a position based on a forecast of the benchmark portfolio's performance
2-2. Modified Alphas
Modified alphas address the various constraints that each manager might have.
Inprementation includes both portfolio construction and trading.
*standard object: maximizing (active returns - active risk penalty)
1-1. Inputs for portfolio construction
- portfolio (measurement with near certainty)
- alphas (unreasonable and subject to hidden biases)
- covariance estimates (noisy estimates)
- transaction cost estimates (noisy estimates)
- active risk aversion
1-2. Active Portfolio Management
Maximizing the expected utility of the excess return over a chosen benchmark
- active managers attempt to beat the market by forming portfolios capable of producing actural returns that exceed risk-adjusted expected returns.
**passive portfolio management: it just estables a portfolio that possibly tracks the chosen benchmark. Passive portfolio managers try to capture the expected return consistent with the risk level of their portfolios.
1-3. Benchmark Portfolio
It might be an equity fund (S&P 500 Index), a bond fund (Lehman Brothers Bond Fund), or a balanced fund (mix of stocks and bonds). In other applications, it could be a stream of liabilities, such as a pension fund. We assume that the selected benchmark carries only the market risk.
2. Alphas & Portfolio Construction
2-1. Constraints
Most active managers construct portfolio subject to certain constraints: no short, restriction on the amount of cash held within portfolio, asset coverage, etc. These limits can make the portfolio less efficient.
Managers often add their own restrictions to the process to make portfolio construction more robust: neutral economic sectors, restrictions on allocations to certain stock, avoidance of a position based on a forecast of the benchmark portfolio's performance
2-2. Modified Alphas
Modified alphas address the various constraints that each manager might have.
*practical issues
i. risk aversion
- Aversion to specific factor risk: help the manager address the risks associated with having a position with the potential for huge losses, and the potential dispersion across portfolio
- Quantifying risk aversion -> enabling manager to understand a client's utility in a mean-variance framework
e.g.) IR = 0.8, desired level of active risk = 10%
=> implied level of risk aversion = 0.8 / (2 x 10) = 0.04
**Utility = Excess Return - (Risk Aversion x Variance)
ii. optimal risk
iii. alpha coverage
- forcasting returns on stocks that are not in the benchmark -> expanding the benchmark to include those stocks with zero weight, but active weights can be assigned to generate active alpha.
- a lack of forecast returns for stocks in the benchmark -> inferring alphas based on the alphas for other factors -> calculating value-weighted fraction of stocks with forecasts & average alpha for group N1:
-> subtracting this measure from each alpha and set zero for the stocks without forecasts. These alphas are benchmark-neutral.
i. risk aversion
- Aversion to specific factor risk: help the manager address the risks associated with having a position with the potential for huge losses, and the potential dispersion across portfolio
- Quantifying risk aversion -> enabling manager to understand a client's utility in a mean-variance framework
e.g.) IR = 0.8, desired level of active risk = 10%
=> implied level of risk aversion = 0.8 / (2 x 10) = 0.04
**Utility = Excess Return - (Risk Aversion x Variance)
ii. optimal risk
iii. alpha coverage
- forcasting returns on stocks that are not in the benchmark -> expanding the benchmark to include those stocks with zero weight, but active weights can be assigned to generate active alpha.
- a lack of forecast returns for stocks in the benchmark -> inferring alphas based on the alphas for other factors -> calculating value-weighted fraction of stocks with forecasts & average alpha for group N1:
-> subtracting this measure from each alpha and set zero for the stocks without forecasts. These alphas are benchmark-neutral.
3. Alpha Analysis
3-1. Benchmark & Cash Neutal Alphas
- Benchmark-neutral alphas
*the benchmark portfolio has zero alpha by definition. Setting the benchmark alpha to zero insures that the alphas are benchmark neutral, and avoids benchmark timing.
**market timing: managers of actively managed mutual funds are interested in shifting the investment policy with changes of returns on both their investment portfolios and the benchmark portfolio from time to time.
**abnormal returns
3-1. Benchmark & Cash Neutal Alphas
- Benchmark-neutral alphas
*the benchmark portfolio has zero alpha by definition. Setting the benchmark alpha to zero insures that the alphas are benchmark neutral, and avoids benchmark timing.
**market timing: managers of actively managed mutual funds are interested in shifting the investment policy with changes of returns on both their investment portfolios and the benchmark portfolio from time to time.
**abnormal returns
- Cash-neutral alphas
The alphas will not lead to any active cash position
- Modified Benchmark-Neutral Alpha = Modified Alpha - Beta * Benchmark Alpha
=> the alpha of the benchmark = 0
3-2. Scale the Alphas
- Alpha has a natural structure
Alpha = volatility * IC * score
where:
IC = information coefficient
volatility = residual risk
- In the above table, Std Dev of Modified Alphas = 0.57% -> shrank IC by 62%
*we expect IC & volatility for a set of alphas to be approximately constant, with the score having mean zero & Std. Dev. one accross the set
-> Alpha should have Mean = zero, Std Dev = IC * volatility
e.g.) IC = 0.05, residual risk = 30%
=> an alpha scale of 1.5% (=0.05 x 30%) --> mean alpha = 0 & 2/3 of stocks having alphas between -1.5 ~ 1.5% & 5% of stocks having alphas larger than +3.0% or less than -3.0%
3-3. Trim Alpha Outliers
- Examine all stocks with alphas greater than in magnitude than, say, three times the scale of the alphas
- A detailed analysis: alphas that depend upon questionable data -> set to zero (while others appear genuine) -> genuine alphas: three times scale in magnitude
- Normal distribution (extreme approach) with benchmark alpha = 0 & required scale factor -> utilizing ranking information in the alphas and ignoring the size of the alphas -> rechecking benchmark neutrality and scaling
3-4. Neutralization
- Neuralization: removing biases or undesirable bets from alphas. Benchmark neutralization means that the benchmark has 0 alpha.
- The multiple-factor approach to portfolio analysis separates return along several dimensions. A manager can identify each of those dimensions as either a source of risk or as a source of value added. The manager does not have any ability to forecast the risk factors. He should neutralize the alphas aginst the risk factors
- The neutralized alphas will only include information on the factors he can forecast plus specific asset information. Once neutralized -> the alphas of the risk factors = zero
e.g.) industry alpha -> zero
=> (cap-weighted) alpha for each industry - industry average alpha
4. Transactions Costs
- one-dimensional problem: to find the correct tradeoff between alpha & active risk
- two-demensional problem: transaction costs added
- Armotizing the transactions costs to compare them to the annual rate of gain from the alpha & the annual rate of loss from the active risk. The rate of amortization will depend on the anticipated holding period.
- Annualized Transaction Cost = Round-Trip Csot / Holding Period (in years)
Ch5 Mortgage Backed Securities(3)
5. Path Dependence
- path independent: the value of the CFs at a given point in time is independent of the path that interest rates followed up to that point
- path independent: the value of the CFs at a given point in time is independent of the path that interest rates followed up to that point
Ch5 Mortgage Backed Securities(2)
4. Valuation Models
4-1. Static Cash Flow Model
Assumption
Prepayment rates can be predicted as a function of the age of the mortgages in a pool.
*prepayment rate increases gradually with mortgage age and then levels of at some constant prepayment rate
Process
Step 1: Computer the (static) cash flow yield, given the set of (static) cash flow & a market price
Step 2: Measure the nominal spread; comparing the cash flow yield on an MBS with that on comparable bonds.
Advantages
*simple to use
- Allowance for the calculation of YTM
- Prepayment is solely a function of mortgage age and future cash flows can be forecasted
Two severe problems
- the model is not pricing model: CFs of mortgage are not fixed owing to prepayments & etc -> they do not specify appropriate yield for a mortgage
- the model provide misleading price-yield and duration-yield curves since cash flows are not fixed
4-2. Implied Models
The model estimate the interest rate sensitivity of MBSs.
Assumptions
Mortgage sensitivity changes gradually over time.
Advantage
More advanced than the static cash flow model that uses YTM
Disadvantages
- They are not true pricing models.
- Mortgage sensitivity can change dramatically over time
4-3. Prepayment Models
More sophisticated models that actually employ two separate models: a turnover model & refinancing model
*historical information + prepayment function
- incentive functions: modeling refinancing activity based on the term structure of interest rates; lagged rates = past interest rates
Non-interest-rate factors
- Mortgage age
- Points paid
- Amount outstanding
- Season of the year
- Geopraphy
4-1. Static Cash Flow Model
Assumption
Prepayment rates can be predicted as a function of the age of the mortgages in a pool.
*prepayment rate increases gradually with mortgage age and then levels of at some constant prepayment rate
Process
Step 1: Computer the (static) cash flow yield, given the set of (static) cash flow & a market price
Step 2: Measure the nominal spread; comparing the cash flow yield on an MBS with that on comparable bonds.
Advantages
*simple to use
- Allowance for the calculation of YTM
- Prepayment is solely a function of mortgage age and future cash flows can be forecasted
Two severe problems
- the model is not pricing model: CFs of mortgage are not fixed owing to prepayments & etc -> they do not specify appropriate yield for a mortgage
- the model provide misleading price-yield and duration-yield curves since cash flows are not fixed
4-2. Implied Models
The model estimate the interest rate sensitivity of MBSs.
Assumptions
Mortgage sensitivity changes gradually over time.
Advantage
More advanced than the static cash flow model that uses YTM
Disadvantages
- They are not true pricing models.
- Mortgage sensitivity can change dramatically over time
4-3. Prepayment Models
More sophisticated models that actually employ two separate models: a turnover model & refinancing model
*historical information + prepayment function
- incentive functions: modeling refinancing activity based on the term structure of interest rates; lagged rates = past interest rates
Non-interest-rate factors
- Mortgage age
- Points paid
- Amount outstanding
- Season of the year
- Geopraphy
Thursday, September 24, 2009
Ch5 Mortgage Backed Securities(1)
1. Overview
Definition: a loan that is collateralized with a specific piece of real property
- primary market
- secondary market; securitization
**MBS (mortgage-backed security), pass-through structure
2. Fixed-Rate, Level-Payment Mortgages
2-1. Conventional Mortgage: the most common residential mortgage
2-2. fixed-rate, level payment, fully amortized mortgage loans
*features
- principal increase as time passes
- interest decrease as time passes
- servicing fee declines as time passes
- prepayment risk
e.g.) 30 year, $500,000 level payment, fixed rate of 12%
=> Xmonthly = 500000 x 12% x (1 + 12%) ^ 12 / ((1 + 12%) ^ 12 - 1) = 5,143.06
- scheduled principal repayment (scheduled amortization) -> incremental reduction of outstanding principal
- Mortage Rate = Net Interest (Net Coupon) + Servicing Spread
**reduction in principal is unaffected by the servicing fee
3. Prepayment Risk
3-1. Repayment option
The prepayment option is valuable when mortgage rates have fallen. In the case, the value of an existing mortgage exceeds the principal outstanding.
- borrower: similar to a call option of a collable bond (American call option on an otherwise identical, nonprepayble mortgage); Strike price = outstanding principal amount
- homeowner: very much in the position of an issuer of a callable bond
- current coupon rate: initial principal amount = P.V. of Mortgage CF - Value of Prepayment Option
**due on sale
**lock-in effect: if points, refinancing bank fee, are high, these will discourage the borrower's willingness to refinance
3-2. Main factors to affect prepayments
i. prevailing mortgage rates
- Spreade between the current mortgage rate and the original mortgage rate; Historically mortgate rages fall by more than 2% -> refinancing activity increase (media effect)
- Path of mortgage rates: burnout effect
- Level of mortgage rates: low interest rates increase the affordability of housing and increas housing turnover -> increase refinancing & prepayment rates
ii. characteristics of the underlying mortgage loans
- original mortgage rate
- amount of seasoning
- origination of loan (FHA/VA or conventional)
- type of loan (30-year fixed, 30-year balloon)
- geographical location
iii. seasonal factors
iv. general economic activity
v. others: natural disasters, default
Definition: a loan that is collateralized with a specific piece of real property
- primary market
- secondary market; securitization
**MBS (mortgage-backed security), pass-through structure
2. Fixed-Rate, Level-Payment Mortgages
2-1. Conventional Mortgage: the most common residential mortgage
2-2. fixed-rate, level payment, fully amortized mortgage loans
*features
- principal increase as time passes
- interest decrease as time passes
- servicing fee declines as time passes
- prepayment risk
e.g.) 30 year, $500,000 level payment, fixed rate of 12%
=> Xmonthly = 500000 x 12% x (1 + 12%) ^ 12 / ((1 + 12%) ^ 12 - 1) = 5,143.06
- scheduled principal repayment (scheduled amortization) -> incremental reduction of outstanding principal
- Mortage Rate = Net Interest (Net Coupon) + Servicing Spread
**reduction in principal is unaffected by the servicing fee
3. Prepayment Risk
3-1. Repayment option
The prepayment option is valuable when mortgage rates have fallen. In the case, the value of an existing mortgage exceeds the principal outstanding.
- borrower: similar to a call option of a collable bond (American call option on an otherwise identical, nonprepayble mortgage); Strike price = outstanding principal amount
- homeowner: very much in the position of an issuer of a callable bond
- current coupon rate: initial principal amount = P.V. of Mortgage CF - Value of Prepayment Option
**due on sale
**lock-in effect: if points, refinancing bank fee, are high, these will discourage the borrower's willingness to refinance
3-2. Main factors to affect prepayments
i. prevailing mortgage rates
- Spreade between the current mortgage rate and the original mortgage rate; Historically mortgate rages fall by more than 2% -> refinancing activity increase (media effect)
- Path of mortgage rates: burnout effect
- Level of mortgage rates: low interest rates increase the affordability of housing and increas housing turnover -> increase refinancing & prepayment rates
ii. characteristics of the underlying mortgage loans
- original mortgage rate
- amount of seasoning
- origination of loan (FHA/VA or conventional)
- type of loan (30-year fixed, 30-year balloon)
- geographical location
iii. seasonal factors
iv. general economic activity
v. others: natural disasters, default
Ch5 An Overview of Mortgages & Mortgage Market
1. Overview
1-1. Mortgage: A loan secured by property
- primary market (mortgage market) until 1970
- secondary market: mortgage-backed security (MBS), pass-through security
1-2. Lien Status: seniority in the event of foreclosure
- firs-lien status: mortgage lender
- second-lien status: less than 80% ownership
1-3. Original Loan Term: 30-year, 15-year, balloon payments option
1-4. Interest-Rate Type
- Fixed-Rate Mortgages
- Adjustable-Rate Mortgages (ARMs)
- Hybrid ARMs
1-5. Credit Guarantees
- Government Sponsored Entities (GSEs)
- Federal Housing Administration (FHA)
- Department of Veterans Affairs (VA)
1-6. Loan Balance
- Underwriting standards are primarily concerned with the maximum LTV (loan-to-value) ratio, payment-to-income ratio, & loan amount
- Nonconforming mortgage loans: agency securities that fail to meet the agency's underwriting standards
- Jumbo loans: balances larger than the conforming limits
1-7. Borrower Type
- Traditional borrowers: high credit scores & stable incomes
- Subprime borrowers: impaired credit
- Alternative A (Alt-A) borrowers: those who have decent credit, but unstable income levels. they do not provide the same level of documentation as traditional borrowers
1-8. Major Players in the Mortgage Industry
- Direct lender: underwriters who fund the loans; work with loan brokers through wholesale channel or work with borrowers through retail channel
- Depository institutions: using deposits to support loan practices <--> notdepository institutions who selling the loans to investors in the secondary mortgage market
- Originators underwrite & support loan production. They usually lends for a short-period time and unlimately ends up selling the loans to large banks
1-9. Loan Underwriting Process
i. evaluating of a borrower's creditworthiness
- credit score: FICO score (over 660 = prime credit)
- LTV (loan-to-value ratio):
LTV = Current Mortgage Amount / Current Appraised Value
**the lower LTV ratio, the more comfortable the mortgage lender is in making the loan
- income ratios: level of a borrower's income level compared to the total size of the mortgage payment; Front ratios & Back ratios
- documentation: inc. income, employment, & tax return; in the event of no or little documentation -> borrowers may not be denied credit, but the mortgage rate assigned will reflect the riskiness of the loan
**Front ratios: total monthly payments / monthly income on a pre-tax basis
**Back ratios: total loan payments inc. other borrower loans
r = monthly interest rate
T = loan term (in months)
B(n) = original loan balance
***mortgage payment factor
**Monthly Payment Formula
- payments allocated more heavily to interest in the initial stages of the loan (fixed-rate loan)
- over time, the loan balance is declining -> more of payment goes toward principal
2-2. ARM Payments
1-1. Mortgage: A loan secured by property
- primary market (mortgage market) until 1970
- secondary market: mortgage-backed security (MBS), pass-through security
1-2. Lien Status: seniority in the event of foreclosure
- firs-lien status: mortgage lender
- second-lien status: less than 80% ownership
1-3. Original Loan Term: 30-year, 15-year, balloon payments option
1-4. Interest-Rate Type
- Fixed-Rate Mortgages
- Adjustable-Rate Mortgages (ARMs)
- Hybrid ARMs
1-5. Credit Guarantees
- Government Sponsored Entities (GSEs)
- Federal Housing Administration (FHA)
- Department of Veterans Affairs (VA)
1-6. Loan Balance
- Underwriting standards are primarily concerned with the maximum LTV (loan-to-value) ratio, payment-to-income ratio, & loan amount
- Nonconforming mortgage loans: agency securities that fail to meet the agency's underwriting standards
- Jumbo loans: balances larger than the conforming limits
1-7. Borrower Type
- Traditional borrowers: high credit scores & stable incomes
- Subprime borrowers: impaired credit
- Alternative A (Alt-A) borrowers: those who have decent credit, but unstable income levels. they do not provide the same level of documentation as traditional borrowers
1-8. Major Players in the Mortgage Industry
- Direct lender: underwriters who fund the loans; work with loan brokers through wholesale channel or work with borrowers through retail channel
- Depository institutions: using deposits to support loan practices <--> notdepository institutions who selling the loans to investors in the secondary mortgage market
- Originators underwrite & support loan production. They usually lends for a short-period time and unlimately ends up selling the loans to large banks
1-9. Loan Underwriting Process
i. evaluating of a borrower's creditworthiness
- credit score: FICO score (over 660 = prime credit)
- LTV (loan-to-value ratio):
LTV = Current Mortgage Amount / Current Appraised Value
**the lower LTV ratio, the more comfortable the mortgage lender is in making the loan
- income ratios: level of a borrower's income level compared to the total size of the mortgage payment; Front ratios & Back ratios
- documentation: inc. income, employment, & tax return; in the event of no or little documentation -> borrowers may not be denied credit, but the mortgage rate assigned will reflect the riskiness of the loan
**Front ratios: total monthly payments / monthly income on a pre-tax basis
**Back ratios: total loan payments inc. other borrower loans
2. Basic Mortgage Mathematics
2-1. Level payment mortgage
where:2-1. Level payment mortgage
r = monthly interest rate
T = loan term (in months)
B(n) = original loan balance
***mortgage payment factor
**Monthly Payment Formula
- payments allocated more heavily to interest in the initial stages of the loan (fixed-rate loan)- over time, the loan balance is declining -> more of payment goes toward principal
2-2. ARM Payments
3. Mortgage & MBS Risks
3-1. Risk-Based Pricing
- separation of subprime borrowers from prime borrowers
- nontraditional borrowers: low FICO scores, riskier characteristics
3-2. Prepayment Risk
- payment in excess of the required payment or payment of the entire loan
- curtailments: prepayments for less than the outstanding principal balance
- prepayements or curtailments reduce the amount of interest the lender receives over the life of the loan.
*prepayment penalties not allowed for residential mortgage
Prepayments occur for the following reasons:
- The sale of the property
- The destruction of the property by fire or other disaster
- A default on the part of the borrower
- Curtailments
- Refinancing
3-3. Mortgage Pass-Through Securities
- a claim against a pool of mortgages (securitized mortgage)
- mortgates in the pool have different maturities & rates
- WAM (weighted average maturity) = weighted average of all the mortgages in the pool
- WAC (weighted average coupon) = weighted average of the mortgage rates in the pool
- pass-through rates: less than the average coupon rate of the underlying mortgages
**invetment characteristics: a function of cash flow featrues & strength of government guarantee
- liquid securities (through securitization)
- more than one class of pass-through securities my be issued against a single mortgage pool
- timing difference between the time the mortgage service provider receives the mortgage payments and the time the cash flows are passed through ot the security holders
3-4. Measruing Prepayments Speeds
Prepayments cause the timing & amount of cash flows from the mortage pool and MBS to be uncertain. The prepayment behavior is not constant over the life of a loan; unlikely to prepay immediately after the loan, but the propensity to prepay increases over time.
3-4-1. SMM & CPR
- single monthly mortality (SMM) measures the monthly principal prepayments on a mortage portfolio as a percentage of the balance at the beginning of the month in question
- conditional prepayment rate (CPR): most common metric used to describe prepayments. CPR increases at a constant and predetermined rate (ramp)
CPR = 1 - (1 - SMM)^12
3-4-2. PSA Model
The most common model for measuring prepayments in a ramping framework
*PSA(public security association -> bond market association)
- base PSA Model (100% of the model or 100% PSA)
- assumption: prepayments begin at a rate of 0.2% CPR in the first month, increase at a rate of 0.2% CPR per month until they reach 6.0% CPR in month 30, and remain at 6% CPR for the remaining term of the loan.
* 200% PSA: speeds double that of the base PSA model
- PSA model depends on the age of the loan or on the weighted-average loan age
e.g.) 4.0% CPR in month 20
=> 4.0% = 20 (0.2%) PCA -> 100% PCA
e.g.) 25th months CPR & SMM for 150% PSA
=> CPR(month 25) = 25 x 0.2% = 5%
150% PSA = 1.5 x 5% = 7.5%
SMM = 1 - (1 - 7.5%)^(1/12) = 0.6476%
**nonlinear relationship between CPR and SMM
***PSA standard benchmark is nothing more than a market convention. It is not a model for predicting prepayment rates for MBS. Empirical studies have shown that actual CPRs differ substantially from those assumed by the PSA bench mark
3-5. Credit Risk
Senior classes of private-label securities rated AAA because of credit guarantees from GNMA or GSEs, however, the analysis of mortgage credit is important for the following reasons:
- assessment of the credit quality of portfolio holdings & the adequacy of loss reserve level (lenders)
- evaluation of potential loss-adjusted returns (buyers of subordinated securities)
- an uderstanding of trends in mortgage lending and credit quality
3-6. Posteriori Evaluation of a Mortgage Pool
i. Stratifictions of Weighted-average credit scores & LTV ratios along with documentation style & geographic concentration
ii. Delinquencies measures
- percentage of the pool that is paying on time in relation to those who are delaying payments
- OTS (Office of Thrift Supervision) method: current (- 30 days) and 30/60/90+ days delinquent
iii. Default measures
- defaults quantified
CDR (conditional default rate): annualized value of the unpaid principal balance of newly defaulted loans over the course of a month as a percentage of the total unpaid balance of the pool at the beginning of the month
CDX (cummulative default rate): proportion of the total face value of loans in the pool that have gone into default as a percentage of the totoal face value of the pool
iv. Severity
- face value of the losses on a loan after the foreclosure process is completed and the property is disposed of
Sunday, September 20, 2009
Ch5 The Science of Term Structure Models
1. Rate and Price Trees
1-1. video clips:
one step for option price: http://www.youtube.com/watch?v=kml52n2zmQs&feature=PlayList&p=1F93169FC44F4F23&playnext=1&playnext_from=PL&index=35
two step binomial: http://www.youtube.com/watch?v=YJls_RgTniw&feature=related
1-2. Binomial Model: A model that assumes that interest rates can take only one of two possible values in the next period
- interest rate tree: set of possible interest paths
1-1. video clips:
one step for option price: http://www.youtube.com/watch?v=kml52n2zmQs&feature=PlayList&p=1F93169FC44F4F23&playnext=1&playnext_from=PL&index=35
two step binomial: http://www.youtube.com/watch?v=YJls_RgTniw&feature=related
1-2. Binomial Model: A model that assumes that interest rates can take only one of two possible values in the next period
- interest rate tree: set of possible interest paths
2. Risk-Neutral Pricing
*interest rate drift: difference between the risk-neutral and true probabilities
3. Fixed-Income Securities & Black-Sholes-Merton Model
3-1. BSM Model: equity option-pricing model
**Assumptions
i. no upper limit to the price of the underlying asset
ii. constant risk-free rate <--> bond: shor-term rates
iii. constant price volatility <--> price volatility decreases as the bond approaches maturity
3-1. BSM Model: equity option-pricing model
**Assumptions
i. no upper limit to the price of the underlying asset
ii. constant risk-free rate <--> bond: shor-term rates
iii. constant price volatility <--> price volatility decreases as the bond approaches maturity
4. Callable Bonds
A call option gives the issuer the right to buy back the bond at fixed prices at one or more points in the future, prior to the date of maturity.
- negative convexity as interest rates fall
- callability effectively caps the investor's capital gains as yields fall
- increased reinvestiment risk when yields fall
- less price volatility
A call option gives the issuer the right to buy back the bond at fixed prices at one or more points in the future, prior to the date of maturity.
- negative convexity as interest rates fall
- callability effectively caps the investor's capital gains as yields fall
- increased reinvestiment risk when yields fall
- less price volatility
5. Putable Bonds
The put feature give the bondholder the right to sell the bond back to the issure at a set price.
The put price serves as a floor value for the price of the bond
The put feature give the bondholder the right to sell the bond back to the issure at a set price.
The put price serves as a floor value for the price of the bond
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