Two investment advisers are comparing performance. One averaged a 19% rate of re

Question

Two investment advisers are comparing performance. One averaged a 19% rate of return and the other a 16% rate ofretum. However, the beta of the first investor was 1.5, whereas that of the second was 1. 20 Can you tell which investor was a better selector of individual stocks (aside from the issue of general movements in the market)? If the T-bill rate were 6% and the market return during the period were 14%, which investor would be the superior stock selector? What if the T-bill rate were 3% and the market return were 15%? a. b C.

Explanation / Answer

a.] "First" Investor , was a better selector becasue, his actual average rate of return of investments (19%) is greater than the "Second" investor's(16%) actual average rate of return of investments

b.] Required rate of return of "First" Investor = Risk free rate + beta * (market return- risk free rate)

= 6% + 1.5 * (14% - 6%)

= 6% + 12%

= 18%

Alpha generated by "First" Investor = Actual rate of return -   Required rate of return

= 19% - 18%

= 1%

  Required rate of return of "Second" Investor = Risk free rate + beta * (market return- risk free rate)

= 6% + 1 * (14% - 6%)

= 6% + 8%

= 14%

Alpha generated by "Second" Investor = Actual rate of return -   Required rate of return

= 16% - 14%

= 2%

Therefore, "Second" Investor would be the superior stock selector due to larger alpha of 2% than "First" Investor (1%)

c.] Required rate of return of "First" Investor = Risk free rate + beta * (market return- risk free rate)

= 3% + 1.5 * (15% - 3%)

= 3% + 18%

= 21%

   Alpha generated by "First" Investor = Actual rate of return - Required rate of return

   = 19% - 21%

= (2%)

  Required rate of return of "Second" Investor = Risk free rate + beta * (market return- risk free rate)

= 3% + 1* (15% - 3%)

= 3% + 12%

= 15%

Alpha generated by "Second" Investor = Actual rate of return -   Required rate of return

= 16% - 15%

= 1%

Therefore, "Second" Investor would be the superior stock selector due to larger alpha of 1% than "First" Investor (-2%)

  

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