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Market index portfolio standard deviation
Stock A beta
Stock A standard deviation
Change in beta
Change in standard deviation
The standard deviation of the market-index portfolio is 20%. Stock A has a beta of
1.5 and a residual standard deviation of 30%.
a. What would make for a larger increase in the stock’s variance: an increase of
.15 in its beta or an increase of 3% (from 30% to 33%) in its residual standard
deviation?
b. An investor who currently holds the market-index portfolio decides to reduce
the portfolio allocation to the market index to 90% and to invest 10% in stock A.
Which of the changes in (a) will have a greater impact on the portfolio’s standard
deviation?
Security Expected return Beta
Market index
Stock A
Actual market return
Solution
Investors expect the market rate of return this year to be 10%.
The expected rate of return on a stock with a beta of 1.2 is
currently 12%. If the market return this year turns out to be 8%,
how would you revise your expectation of the rate of return on
the stock?
