Ch5 VaR Mapping(1)

1. Mapping for Risk Measurement
1-1. Mapping: A process by which the current values of the portfolio positions are replaced by exposures on the risk factors.
- many positions can be aggregated into, or simplified to, a small set of exposures, primitive risk factors, without loss of risk information: aggregation at the highest level
*such aggregation is not appropriate for the pricing of the portfolio
- mapping is the only solution when the characteristics of the instrument change over time.

1-2. video clips
mapping for a bond portfolio: http://www.youtube.com/watch?v=CYQ2_Xzr8uk
undiversified VaR: http://www.youtube.com/watch?v=SqZaAl5g_8U
diversified VaR: http://www.youtube.com/watch?v=cjguDOUswDA&feature=related
mapping for forward contracts: http://www.youtube.com/watch?v=Um8e_teI_dw

mapping for European stock option: http://www.youtube.com/watch?v=3wEBJbUuKfQ

1-3. Mapping as a solution to data problem
- no history such as a mutual fund with a strategy of investing in IPOs -> exposures on similar risk factors already in the system
- stale data -> longer time intervals or a regression of A returns on B returns if A price = stale price

1-4. Mapping process
- exact allocation of exposures on the risk factors
- estimated exposures

1-5. General & specific risk
The choice of the set of primitive factors
- tradeof between better quality of the approximation & faster processing
- influences the size of specific risks; risks that is due to issuer-specific price movements after accounting for general market factors

1-5-1. a portfolio of N stocks

- Variance of Rp = general market risk + aggregate of specific risk for the entire portfolio

1-5-2. a corporate bond portfolio where:
Zj = a set of J government bond yields
Sk = a set of K credit spreads
**In practice, there may not be sufficient history to measure the specific risk of individual bonds, which is why it is often assumed that all issuers within the same risk class have the same risk