8-6
12.
The regression results provide quantitative measures of return and risk based on
monthly returns over the five-year period.
β
for ABC was 0.60, considerably less than the average stock’s
β
of 1.0.
This
indicates that, when the S&P 500 rose or fell by 1 percentage point, ABC’s return
on average rose or fell by only 0.60 percentage point.
Therefore, ABC’s systematic
risk (or market risk) was low relative to the typical value for stocks.
ABC’s alpha
(the intercept of the regression) was
–
3.2%, indicating that when the market return
was 0%, the average return on ABC was –3.2%.
ABC’s unsystematic risk (or
residual risk), as measured by
σ
(e), was 13.02%.
For ABC, R
2
was 0.35, indicating
closeness of fit to the linear regression greater than the value for a typical stock.
β
for XYZ was somewhat higher, at 0.97, indicating XYZ’s return pattern was very
similar to the
β
for the market index.
Therefore, XYZ stock had average systematic
risk for the period examined.
Alpha for XYZ was positive and quite large,
indicating a return of almost 7.3%, on average, for XYZ independent of market
return.
Residual risk was 21.45%, half again as much as ABC’s, indicating a wider
scatter of observations around the regression line for XYZ.
Correspondingly, the fit
of the regression model was considerably less than that of ABC, consistent with an
R
2
of only 0.17.
The effects of including one or the other of these stocks in a diversified portfolio
may be quite different.
If it can be assumed that both stocks’ betas will remain
stable over time, then there is a large difference in systematic risk level.
The betas
obtained from the two brokerage houses may help the analyst draw inferences for
the future.
The three estimates of ABC’s
β
are similar, regardless of the sample
period of the underlying data.
The range of these estimates is 0.60 to 0.71, well
below the market average
β
of 1.0.
The three estimates of XYZ’s
β
vary
significantly among the three sources, ranging as high as 1.45 for the weekly data
over the most recent two years.
One could infer that XYZ’s
β
for the future might
be well above 1.0, meaning it might have somewhat greater systematic risk than
was implied by the monthly regression for the five-year period.
These stocks appear to have significantly different systematic risk characteristics.
If
these stocks are added to a diversified portfolio, XYZ will add more to total volatility.
13.
For Stock A:
α
A
= r
A
−
[
r
f
+
β
A
(r
M
−
r
f
)] = 11
−
[6
+
0.8(12
−
6)] = 0.2%
For stock B:
α
B
= 14
−
[6
+
1.5(12
−
6)] =
−
1%
Stock A would be a good addition to a well-diversified portfolio.
A short position
in Stock B may be desirable.