Question

Consider the two (excess return) index-model regression results for stocks A and B. The riskfree rate over the period was 7%, and the market’s average return was 12%. Performance is measured using an index model regression on excess returns.
Stock A Stock B
Index model regression estimates 1% + 1.2(rM – rf) 2% + .8(rM – rf)
R-square 0.623 0.46
Residual standard deviation, σ(e) 11.1% 19.9%
Standard deviation of excess returns 22.4% 26.5%
a.
Calculate the following statistics for each stock: (Round your answer to 4 decimal places. Omit the "%" sign in your response.)

Stock A Stock B
i. Alpha % %
ii. Information ratio
iii. Sharpe measure
iv. Treynor measure
b. Which stock is the best choice under the following circumstances?
i. This is the only risky asset to be held by the investor. (Click to select)Stock AStock B
ii.
This stock will be mixed with the rest of the investor’s portfolio, currently composed solely of holdings in the market-index fund.

(Click to select)Stock BStock A
iii.
This is one of many stocks that the investor is analyzing to form an actively managed stock portfolio.

(Click to select)Stock BStock A

Answer 1

Answer:

a. i. Alpha of stock A is 1 and of stock B is 2

ii. Information ratio of stock A is  0.090 and of stock B is 0.1005

iii. Sharpe measure  of stock A is 0.3215 and of stock B is 0.2264

iv. Treynor measure of stock A is 5.83 and of stock B is 7.5

b. i. Stock A

ii.  Stock B

iii.  Stock B

Explanation:

a. i. To calculate Alpha of both Stock A and Stock B we would have to use the following formula:

βα∝p=rp-(rf+βp(rm-rf)

Therefore Alpha stock A= 1

Alpha stock B= 2

ii. To calculate the Information ratio of both Stock A and Stock B we would have to use the following formula:

information ratio=∝p/σep

information ratio stock A=1/11.1=0.090

information ratio stock B=2/19.9=0.1005

iii. To calculate the Sharpe measure of both Stock A and Stock B we would have to use the following formula:

Sharpe measure= Sp=(rp-rf)/σp

Sharpe measure stock A= (1%+1.2(12%-7%))/22.4%

Sharpe measure stock A=0.3125

Sharpe measure stock B= (2%+0.8(12%-7%))/26.5%

Sharpe measure stock B=0.2264

iv. To calculate the Treynor measure of both Stock A and Stock B we would have to use the following formula:

Treynor measure=(rp-rf)βp

Treynor measure of stock A= (1%+1.2(12%-7%))/1.2

Treynor measure of stock A=5.83

Treynor measure of stock B=(2%+0.8(12%-7%))/0.8

Treynor measure of stock B=7.5

B. i. In this circumstance sharpe ratio is helpful in ranking the portfolio of stocks. Stock A performed better than Stock B. Therefore, Stock A is the best choice.

ii. When the stock will be mixed with the rest of the investor’s portfolio you need to see the alpha. Stock B has higher alpha, therefore stock B is the best choice

iii. When theinvestor is analyzing to form an actively managed stock portfolio you need to see the Treynor Measure. Stock B has higher Treynor measure. Therefore Stock B is the best choice.