(c) Equities. Many large FIs also take positions in equities. As is well known from
the Capital Asset Pricing Model (CAPM), there are two types of risk to an equity po-
sition in an individual stock i:^18
Systematic risk reflects the comovement of that stock with the market portfolio
(reflected by the stock’sbeta(i) and the volatility of the market portfolio (mt),
while unsystematic risk is specific to the firm itself (eit).
In a very well-diversified portfolio, unsystematic risk (^2 eit) can be largely diver-
sified away (i.e., will equal zero), leaving behind systematic (undiversifiable) market
risk (^2 i^2 mt). If the FI’s trading portfolio follows (replicates) the returns on the stock
market index, the of that portfolio will be 1 since the movement of returns on the
FI’s portfolio will be one to one with the market,^19 and the standard deviation of the
portfolio,it, will be equal to the standard deviation of the stock market index, mt.
Suppose the FI holds a $1 million trading position in stocks that reflect a U.S.
stock market index (e.g., the Wilshire 5000). Then = 1 and the DEARfor equities
is:
If over the last year, the mof the daily returns on the stock market index was 2%,
then 1.65 m= 3.3% (i.e., the adverse change or decline in the daily return on the
stock market exceeded 3.3% only 5% of the time). In this case:
That is, the FI stands to lose at least $33,000 in earnings if adverse stock market re-
turns materialize tomorrow.
In less well diversified portfolios or portfolios of individual stocks, the effect of
unsystematic risk eiton the value of the trading position would need to be added.
Moreover, if the CAPM does not offer a good explanation of asset pricing compared
to, say, multi-index arbitrage pricing theory (APT), a degree of error will be built into
theDEARcalculation.^20
(d) Portfolio Aggregation. The preceding sections analyzed the daily earnings at
risk of individual trading positions. The examples considered a seven-year, zero-
coupon, fixed-income security ($1 million market value), a position in spot Swf ($1
$33,000DEAR 1 $1,000,000 2 1 0.033 2 1 $1,000,000 2 1 1.65sm 2DEAR 1 Dollar market value of position 2 1 Stock market return volatility 21 s^2 it 2 1 b^2 ismt^22 1 s^2 eit 2Total riskSystematic riskUnsystematic risk8 • 10 MARKET RISK(^18) This assumes that systematic and unsystematic risks are independent of each other.
(^19) If≠1, as in the case of most individual stocks, DEAR= dollar value of position ×j×1.65m,
wherejis the systematic risk of the ith stock.
(^20) As noted in the introduction, derivatives are also used for trading purposes. To calculate its DEAR,
a derivative has to be converted into a position in the underlying asset (e.g., bond, FX, or equity).