26 The Basics of financial economeTrics
that is, αβSS+ ,,MMr t, and some error εS,t from the exact model at time t. The
term αS is commonly interpreted as a measure of performance of the security
above or below its performance that is attributed to the market performance. It
is often referred to as the average abnormal performance of the stock.
While we have described the characteristic line for a stock, it also applies
to any portfolio or funds. To illustrate, we use the monthly returns between
January 1995 and December 2004, shown in Table 2.2, for two actual mutual
funds which we refer to as fund A and fund B. Both are large capitalization
stock funds. As a proxy for the market, we use the S&P 500 stock index.^8
For the estimation of the characteristic line in excess return form given by
equation (2.12), we use the excess return data in Table 2.2. We employ the
estimators in equations (2.6) and (2.7). For fund A, the estimated regression
coefficients are aA = –0.21 and bA,S&P500 = 0.84, and therefore rA = –0.21 +
0.84 ⋅ rS&P500. For fund B we have aB = 0.01 and bB,S&P500 = 0.82, and there-
fore rB = 0.01 + 0.82 ⋅ rS&P500.
Interpreting the results of the performance measure estimates of a, we
see that for fund A there is a negative performance relative to the market
while it appears that fund B outperformed the market. For the estimated
betas (i.e., b) for fund A, we determine that with each expected unit return of
the S&P 500 index, fund A yields, on average, a return of 84% of that unit.
This is roughly equal for fund B where for each unit return to be expected
for the index, fund B earns a return of 82% that of the index. So, both funds
are, as expected, positively related to the performance of the market.
The goodness-of-fit measure (R^2 ) is 0.92 for the characteristic line for
fund A and 0.86 for fund B. So, we see that the characteristic lines for both
mutual funds provide good fits.
Controlling the risk of a Stock portfolio
An asset manager who wishes to alter exposure to the market can do so by
revising the portfolio’s beta. This can be done by rebalancing the portfolio
with stocks that will produce the target beta, but there are transaction costs
associated with rebalancing a portfolio. Because of the leverage inherent
in futures contracts, asset managers can use stock index futures to achieve
a target beta at a considerably lower cost. Buying stock index futures will
increase a portfolio’s beta, and selling will reduce it.
The major economic function of futures markets is to transfer price risk
from hedgers to speculators. Hedging is the employment of futures contracts
as a substitute for a transaction to be made in the cash market. If the cash
(^8) The data were provided by Raman Vardharaj. The true fund names cannot be
revealed.