Consider the two (excess return) index-model regression results for stocks A and

Question

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 7%, and the market's average return was 14%. Performance is measured using an index model regression on excess returns Stock A 1.2(rH- 0.635 11.3% 22.6% Stock B + 0.8(rH- 0.466 20.1% 26·9% 1% rf) 2% rf) Index model regression estimates R-square Residual standard deviation, (e) Standard deviation of excess returns + a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.) Stock A Stock B i. Alpha ii. Information ratio ii. Sharpe ratio iv. Treynor measure

Explanation / Answer

a. Computation of statistics for each stock:

s. no.

Details

Formula

Stock A

Stock B

1

Alpha (regression intercept)

p =rp-rf+beta(rm-rf)

1%

2%

2.

Information ratio

p / residual standard deviation

1/ 11.3 = 0.0885

2/20.1 = 0.0995

3.

Sharpe ratio

(rp-rf) / standard deviation of excess return

{1% +1.2(14%-7%)}/ 22.6% = 0.4159

{2% +0.8(14%-7%)}/ 26.9% = 0.2825

4.

Treynor measure

(rp-rf) / beta

{1% +1.2(14%-7%)}/ 1.2 = 7.8333

{2% +0.8(14%-7%)}/ 0.8 = 9.5

b. (i) If this is the only risky asset held by the investor, then Sharpe’s measure is the best choice for measure. Here, we can see the Sharpe measure is higher for Stock A, then A is the best choice.
(ii) If the stock is mixed with the rest of the investor's portfolio, currently composed solely of holding in the market index fund, then the contribution to the overall Sharpe measure appropriate for determining the appraisal ratio; therefore, Stock B is preferred.
(iii) If the stock is one of many stocks, then Treynor’s measure is the appropriate measure because this ratio measures the excess return with systematic risk and thus, Stock B is preferred.

s. no.

Details

Formula

Stock A

Stock B

1

Alpha (regression intercept)

p =rp-rf+beta(rm-rf)

1%

2%

2.

Information ratio

p / residual standard deviation

1/ 11.3 = 0.0885

2/20.1 = 0.0995

3.

Sharpe ratio

(rp-rf) / standard deviation of excess return

{1% +1.2(14%-7%)}/ 22.6% = 0.4159

{2% +0.8(14%-7%)}/ 26.9% = 0.2825

4.

Treynor measure

(rp-rf) / beta

{1% +1.2(14%-7%)}/ 1.2 = 7.8333

{2% +0.8(14%-7%)}/ 0.8 = 9.5

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