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.

*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.

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

- 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)