You are given the following information concerning several mutual funds: Fund Re

Question

You are given the following information concerning several mutual funds:

Fund

Return in Excess of the Treasury Bill Rate

Beta

A

12.40%

1.14

B

13.2

1.22

C

11.4

0.9

D

9.8

0.76

E

12.6

0.95

During the time period, the Standard & Poor’s stock index exceeded the Treasury bill rate by 10.5 percent (i.e., rm rf = 10.5%).

a) Rank the performance of each fund without adjusting for risk and adjusting for risk using the Treynor index.

Which, if any, outperformed the market? (Remember, the beta of the market is 1.0.)

b) The analysis in part (a) assumes each fund is sufficiently diversified so that the appropriate measure of risk is the beta coefficient.

Suppose, however, this assumption does not hold and the standard deviation of each fund’s return was as follows:

Fund

Standard Deviation of Return

A

0.045 (=4.5%)

B

0.031

C

0.01

D

0.014

E

0.035

Thus, fund A earned a return of 12.4 percent, but approximately 68 percent of the time this return has ranged from 7.9 percent to 16.9 percent.

The standard deviation of the market return is 0.01 (i.e., 1 percent), so 68 percent of the time, the return on the market has ranged from 9.5 to 11.5

percent. Rank the funds using this alternative measure of risk. Which, if any, outperformed the market on a risk-adjusted basis?

You are given the following information concerning several mutual funds:

Fund

Return in Excess of the Treasury Bill Rate

Beta

A

12.40%

1.14

B

13.2

1.22

C

11.4

0.9

D

9.8

0.76

E

12.6

0.95

During the time period, the Standard & Poor’s stock index exceeded the Treasury bill rate by 10.5 percent (i.e., rm rf = 10.5%).

a) Rank the performance of each fund without adjusting for risk and adjusting for risk using the Treynor index.

Which, if any, outperformed the market? (Remember, the beta of the market is 1.0.)

b) The analysis in part (a) assumes each fund is sufficiently diversified so that the appropriate measure of risk is the beta coefficient.

Suppose, however, this assumption does not hold and the standard deviation of each fund’s return was as follows:

Fund

Standard Deviation of Return

A

0.045 (=4.5%)

B

0.031

C

0.01

D

0.014

E

0.035

Thus, fund A earned a return of 12.4 percent, but approximately 68 percent of the time this return has ranged from 7.9 percent to 16.9 percent.

The standard deviation of the market return is 0.01 (i.e., 1 percent), so 68 percent of the time, the return on the market has ranged from 9.5 to 11.5

percent. Rank the funds using this alternative measure of risk. Which, if any, outperformed the market on a risk-adjusted basis?

Explanation / Answer

funds return in excess of treasury return beta treynor index Rank A 12.4 1.14 10.87719 4 b 13.2 1.22 10.81967 5 c 11.4 0.9 12.66667 3 d 9.8 0.76 12.89474 2 e 12.6 0.95 13.26316 1 Market index 10.5 1 10.5 Fund E has the highest treyner ratio but all the funds out performed the market return fund return in excess of treasury return standard deviation share ratio Rank A 12.4 4.5 2.755556 5 b 13.2 3.1 4.258065 3 c 11.4 1 11.4 1 d 9.8 1.4 7 2 e 12.6 3.5 3.6 4 Market index 10.5 1 10.5 here according to the share index only the fund c is having higher return than market index and rest of the funds are underperformed from market index return

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