Market Risk Chapter 10 © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. McGraw-Hill/Irwin Part B.

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Market Risk Chapter 10 © 2008 The McGraw-Hill Companies, Inc., All Rights Reserved. McGraw-Hill/Irwin Part B

10-2 Equities  For equities, Total risk = Systematic risk + Unsystematic risk  If the portfolio is well diversified then DEAR = dollar value of position × stock market return volatility where the market return volatility is taken as 1.65  M.

10-3 Aggregating DEAR Estimates  Cannot simply sum up individual DEARs.  In order to aggregate the DEARs from individual exposures we require the correlation matrix.  Three-asset case: DEAR portfolio = [DEAR a 2 + DEAR b 2 + DEAR c  ab × DEAR a × DEAR b + 2  ac × DEAR a × DEAR c + 2  bc × DEAR b × DEAR c ] 1/2 This should look very familiar from FNCE 4030

10-4 In calculating DEAR, adverse change in rates defined as 99th percentile (rather than 95th under RiskMetrics) Minimum `holding period is 10 days (means that RiskMetrics’ daily DEAR multiplied by )*. Capital charge will be higher of:  Previous day’s VAR (or DEAR  )  Average Daily VAR over previous 60 days times a multiplication factor  3. *Proposal to change to minimum period of 5 days under Basel II, end of Large Banks: BIS versus RiskMetrics

10-5 Skewness

10-6 Kurtosis (Fat Tails) Normal Cauchy

10-7