What is the formula for calculating the Sharpe Ratio?

The Sharpe Ratio is a key measure used in finance to evaluate the risk-adjusted return of an investment or a portfolio. It quantifies how much excess return is received for the extra volatility that is endured by holding a riskier asset compared to a risk-free asset.

The formula for the Sharpe Ratio is represented as:

[

\text{Sharpe Ratio} = \frac{E(R_p) - R_f}{\sigma_p}

]

Where:

• (E(R_p)) is the expected return of the portfolio.

• (R_f) is the risk-free rate.

• (\sigma_p) is the standard deviation of the portfolio's excess return (which acts as a measure of risk).

This formula highlights the relationship between the portfolio's return above the risk-free rate and the standard deviation of that return, providing insight into how well the portfolio compensates investors for the risk taken. The Sharpe Ratio increases with greater excess returns or less volatility, thus signaling a more attractive investment.

The other choices presented do not accurately represent the Sharpe Ratio. For instance, using portfolio beta in a formula relates to the Capital Asset Pricing Model (CAPM) rather than risk-adjusted return via the Sharpe Ratio.