Question

Assume that you put 55% of your wealth in Tesla stock and the rest of your wealth in the risk-free treasury bill. You believe Tesla has an expected return of 7.6% and the risk-free rate has an expected return of 3.2%. You also know that Tesla has a variance of 13.5%. What is the expected Sharpe Ratio of your portfolio? Enter you answer with two decimal points (i.e., 0.45 or 0.78 or 1.23). The question will allow for slight rounding errors.

Answer 1

0.12.

Step-by-step explanation:

Sharpe ratio is a financial metric that is used by investors to understand the return of investment compared to its risk. It is calculated by deducting risk-free rate from return, and dividing the result by standard deviation. Sharpe ratio tells us how much of risk premium (Return - Risk-free rate) is generated by the security per unit of risk. This ratio considers standard deviation as a proxy of risk. A higher Sharpe ratio is attractive and the formula to it is;

Exp. Sharpe ratio = (Expected Return - Risk-free rate) / Standard deviation

Variance of Tesla's return is given. It needs to be converted to standard deviation. To do so, take square root of variance. This will give you standard deviation of 37%.

Putting values in Sharpe ratio equation:

⇒ Expected Sharpe ratio = (.076 - .032) / .37 = .12.

This means that the Tesla stock generate a return of 12% per unit of risk.