Question

A portfolio manager in Absurdistan is using the Sharpe ratio to compare two Absurdistani assets and based on the result preferred one of them. Assuming the expected risk and expected return for both assets do not change, does the Sharpe Ratio envision any future circumstance when the portfolio manager might change her mind, or will one asset always be preferred?

Asset x: Return 6%, Risk 3%
A. Asset Y: Return 10%, Risk 11%
B. Asset Y will always be preferred. Asset X will always be preferred.
C. Sometimes Asset X will be preferred and sometimes Asset Y will be preferred

Answer 1

Asset X will always be preferred.

Step-by-step explanation:

Sharpe Ratio of Asset = [Expected return of asset - Risk free rate] / Standard deviation of asset

For Asset X, the expected return of Asset X = 6% and Risk or Standard deviation of Asset X = 3%. Let assume that the Risk free rate = 2% (To derive our purpose).

Sharpe Ratio of Asset X = (6% - 2%)/3%

Sharpe Ratio of Asset X = 4%/3%

Sharpe Ratio of Asset X = 1.33

For Asset Y, the expected return of Asset X = 10% and Risk or Standard deviation of Asset X = 11%. Let assume that the Risk free rate = 2% (To derive our purpose).

Sharpe Ratio of Asset Y = (10% - 2%)/11%

Sharpe Ratio of Asset Y = 8%/11%

Sharpe Ratio of Asset Y = 0.727

Observation: Despite that the risk free rate is constant for both assets, Sharpe ratio is higher for Asset A, therefore, Asset A will always be preferred.