Calculating Sharpe Ratio for an Efficient Portfolio: A Step-by-Step Guide

The Sharpe ratio is a measure of risk-adjusted return that helps investors compare different investment portfolios. It is calculated by subtracting the risk-free rate of return from the portfolio's expected return and dividing the result by the portfolio's volatility.

Let's consider an example: 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 15.7% and a volatility of 12.8%. The risk-free rate of interest is 3.6%.

To calculate the Sharpe ratio for the efficient portfolio, we will use the following formula:

Sharpe ratio = (Expected return - Risk-free rate) / Volatility

For the efficient portfolio:

Expected return = 15.7% Volatility = 12.8% Risk-free rate = 3.6%

Sharpe ratio = (15.7% - 3.6%) / 12.8% Sharpe ratio = 12.1% / 12.8% Sharpe ratio ≈ 0.945

Therefore, the Sharpe ratio for the efficient portfolio is closest to 0.945. This means that for every unit of risk taken, the efficient portfolio generates a return of approximately 0.945 units. A higher Sharpe ratio indicates a better risk-adjusted return, making the efficient portfolio a potentially more attractive investment option compared to the initial portfolio.