Question

You are working as an assistant to the manager of a fund that is very well diversified.

The manager has asked you to suggest which of the following stocks that should be included in the portfolio, based on an appropriate measure.

If t-bills generates a return of 2.5 %, which of the following stocks is best suited to be included into the portfolio, and why?

	E(r)	σ	β
Iano	8.1 %	37.6 %	1.7
Back	8.4 %	14.6 %	1.9
Hanc	8.1 %	22.6 %	1.8

(In the computations displayed in the answers, percentages are represented in decimal version.)

Select one:

a. The Iano stock is preferred since it's Treynor measure of 0.048 is the highest one.

b. The Hanc stock is preferred since both the Sharpe and the Treynor measure is better than for the other stocks

c. The Back stock is preferred since it's Treynor measure of 0.031 is the highest one.

d. The Iano stock is preferred since it's Treynor measure of 0.033 is the highest one.

e. The Back stock is preferred since it's Sharpe measure of 0.257 is the best one

Answer 1

Sharpe ratio = (E(r) - r_f) / σ (where r_f is the risk free rate).

Treynor ratio =  (E(r) - r_f) / β

Both ratios are calculated for each stock as below :

A C D B Elr) o 2 3 lano 4 Back 5 Hanc 8.10% 37.60% 8.40% 14.60% 8.10% 22.60% E F Sharpe Treynor Ratio Ratio 1. 7 0.149 0.033 1.9 0.404 | 0.031 1.8 0.248 0.031

A C D B Elr) lo 11.7 2 3 lano 4 Back 5 Hanc 0.081 0.084 0.081 0.376 0.146 0.226 Sharpe Ratio =(B3-2.5%)/C3 =(B4-2.5%)/C4 =(B5-2.5%)/C5 Treynor Ratio =(B3-2.5%)/D3 =(B4-2.5%)/D4 =(B5-2.5%)/D5 1.9 1.8

For any stock, a higher Sharpe or Treynor measure is preferred since a stock with a higher measure indicates that the stock earns a higher reward for the given risk.

The answer is (d).

(a) is incorrect - It's Treynor measure is 0.033.

(b) is incorrect - Hanc does not have the best measure in both measures.

(c) is incorrect - Iano stock has the highest Treynor measure

(e) is incorrect - Back stock has the best Sharpe measure.