Suppose that you currently have $300,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The efficient (tangent) portfolio has an expected return of 16.9% and a volatility of 15.3%. The risk-free rate of interest is 3.9%.The Sharpe ratio for the efficient portfolio is closest to?
Question
Suppose that you currently have $300,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The efficient (tangent) portfolio has an expected return of 16.9% and a volatility of 15.3%. The risk-free rate of interest is 3.9%.The Sharpe ratio for the efficient portfolio is closest to?
Solution
The Sharpe ratio is a measure of risk-adjusted return. It is calculated as the difference between the expected return of the investment and the risk-free rate, divided by the standard deviation (volatility) of the investment's returns.
The formula for the Sharpe ratio is:
Sharpe Ratio = (Expected return of the portfolio - Risk-free rate) / Standard deviation of the portfolio's return
Given the information in the question, we can substitute the values into the formula:
Sharpe Ratio = (16.9% - 3.9%) / 15.3%
This simplifies to:
Sharpe Ratio = 0.13 / 0.153
Calculating this gives a Sharpe ratio of approximately 0.85 for the efficient portfolio.
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