Question

3. The risk-free rate is 0% and the expected return on the market is 10%. You are given the same stocks as in Q 2. Assuming, as in Q 2(b), that you hold the stock as part of a well-diversified portfolio, which stocks would you buy if the expected return on the stocks were as below: Stock Expected return in %

Answer 1

We will calculate the sharpe ratio and treynor ratio from the given information.

Sharpe ratio is risk adjusted rate of return which measures the excess return from risk free rate earned per unit risk or volatility of stock.

formula S.R = (R - Rf) / std. dev

Treynor ratio is similar except it measuresexcess return from risk free rate earned per unit systematic risk or beta.

formula T.R = (R - Rf) / beta

If a stock has a higher sharpe ratio and/or a higher treynor ratio then we are rewarded more for the amount of risk taken as compared to other stocks. Hence we will invest in a stock with the highest sharpe and/or treynor ratio

Calculating the Sharpe ratio and Treynor ratio for all the stocks is given in the following table

Stock	Expected Return	Std. Dev	beta	Sharpe ratio	Treynor ratio
A	5	20	0.5	0.25	10
B	12	10	1	1.2	12
C	0	9	-0.5	0	0
D	15	5	2	3	7.5

Since stock B has the highest Sharpe and Treynor ratio, we will buy stock B.