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Single Index Model – Practice Problems
1. Suppose you held a welldiversified portfolio with a very large number of securities, and that
the single index model holds. If the
σ
of your portfolio was 0.14 and
σ
M
was 0.19, the
β
of the
portfolio would be approximately ________.
2. Suppose the following equation best describes the evolution of
β
over time:
β
t
= 0.30 + 0.70
β
t1
If a stock had a
β
of 0.82 last year, you would forecast the
β
to be _______ in the coming year.
3. The index model has been estimated for stocks A and B with the following results:
R
A
= 0.03 + 0.7R
M
+ e
A
R
B
= 0.01 + 0.9R
M
+ e
B
σ
M
= 0.35
σ
(e
A
) = 0.20
σ
(e
B
) = 0.10
The covariance between the returns on stocks A and B is ___________.
4. The beta of a stock has been estimated as 0.85 by Merrill Lynch using regression analysis on a
sample of historical returns. The Merrill Lynch adjusted beta of the stock would be
___________.
6. The index model has been estimated for stocks A and B with the following results:
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 Fall '07
 Callahan

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