19-EquityPort Page 589 Friday, March 12, 2004 12:40 PM
Equity Portfolio Management 589Instead, an optimization method combined with a multifactor risk
model can be used to construct the desired portfolio. The necessary
inputs to this process are the tilt exposure sought and the benchmark
stock market index. Additional constraints can be placed, for example,
on the number of stocks to be included in the portfolio. The Barra opti-
mization model can also handle additional specifications such as fore-
casts of expected returns or alphas on the individual stocks.
In our illustration, the tilt exposure sought is towards low P/E
stocks, that is, towards high earnings yield stocks (since earnings yield is
the inverse of P/E). The benchmark is the S&P 500. We seek a portfolio
that has an average earnings yield that is at least 0.5 standard deviations
more than that of the earnings yield of the benchmark. We do not place
any limit on the number of stocks to be included in the portfolio. We
also do not want the active exposure to any other risk index factor
(other than earnings yield) to be more than 0.1 standard deviations in
magnitude. This way we avoid placing unintended bets. While we do
not report the holdings of the optimal portfolio here, Exhibit 19.14 pro-
vides an analysis of that portfolio by comparing the risk exposure of the
50-stock optimal portfolio to that of the S&P 500.SUMMARY
■ The investing process involves forming reasonable return expecta-
tions, controlling portfolio risk to demonstrate investment prudence,
controlling trading costs, and monitoring total investment perfor-
mance.
■ The different degrees of active management and different degrees of
passive management can be measured in terms of tracking error.
■ The active return is the difference between the actual portfolio return
for a given period and the benchmark index return for the same
period.
■ Alpha is defined as the average active return over some time period.
■ The information ratio is the ratio of alpha to the tracking error.
■ Tracking error is the standard deviation of the active return and
occurs because the risk profile of a portfolio differs from that of the
risk profile of the benchmark index.
■ Backward-looking tracking error measures the tracking error based
on active returns; forward-looking tracking error measures the poten-
tial tracking error of a portfolio.
■ Portfolio size, benchmark volatility, and portfolio beta have an
impact on tracking error.