The Hidden Power of Sharpe Ratio and How to Use It
The Sharpe ratio expresses the risk-adjusted return on a security taking into account the variance and the standard deviation in the security’s returns. As the numerator and the denominator are both calculated in percentages, the ratio is expressed as a net number.
Correlating Risk and Return
Sometime ago, investors and fund managers rated the performance of their portfolio, relying solely on the rate of return. Although they were aware of the risk involved, they did not know how to quantify it and, therefore, to estimate its impact on their portfolio return. In the recent years, researchers classified the investment portfolios into different categories based on their risk and rate of return. The modern portfolio theory in the 1960s clearly correlated the portfolio returns with the portfolio’s standard deviation.
The Sharpe Ratio
The Sharpe Ratio is a widely used measurement for estimating the risk-adjusted returns of a portfolio. The ratio considers the average return in excess of the risk-free rate to estimate the risk of a security. In other words, it determines how much excessive return you earn by assuming a higher level of volatility in your portfolio. Therefore, the Sharpe ratio calculates the risk-reward relationship of a portfolio per unit of the total portfolio risk.
The formula is:
Rp = expected portfolio returns
Rf = risk-free interest rate
σ = standard deviation of the portfolio
How to Calculate the Sharpe Ratio of a Portfolio
Assume a portfolio, consisting of 4 stocks with different allocation and expected annual returns. The first step is to calculate the portfolio return by multiplying the allocation of each stock to its expected return and summing up:
Rp = (27.0% x 17.38%) + (34.0% x 15.65%) + (17.0% x 11.24%) + (22.0% x 12.51%) = 14.68%
The portfolio standard deviation is the average of the standard deviation of all stocks involved in the portfolio and the risk-free rate is 1.87%.
By applying the Sharpe ratio formula, you get: (14.68% – 1.87%) /2.39% = 5.36
Breaking Down the Sharpe Ratio Formula
The (Rp – Rf) part of the Sharpe ratio formula shows you if you can actually make money with your investment strategy. This is why the Rp should be greater than the Rf, i.e. the rate that you would get on a T-bill, incurring no risk at all.
Assume that your strategy is profitable and that you earn more than the interest rate you would earn on a T-bill. The formula divides the nominator with the standard deviation in order to determine your risk profile. If you follow a risky investment strategy, the Sharpe ratio will be low because the nominator (Rp-Rf) will be divided by a higher number.
In the above example, the ratio shows that for every point of return, you are assuming 5.36 points of risk. Instead, if your portfolio’s standard deviation was higher than 2.39%, let’s say 3.40%, the Sharpe ratio would be 3.77 because you would assume a higher level of risk compared to the expected returns.
In general, the higher the ratio, the higher the portfolio return per unit of risk. The lower the ratio, the higher the risk you are assuming for each unit of additional return. Thus, at the end of the day, the Sharpe ratio levels out your investments by providing an indication on the securities that you should shoulder excessive risk.
What is the standard deviation?
The standard deviation of an investment represents its volatility. Securities with a high standard deviation are considered as riskier than securities with a low standard deviation. Although often assessing the volatility of an investment may be complex, the standard deviation can accurately tell you what percentage of your portfolio is expected to rise or decline compared to its average returns over a certain period of time. Therefore, if your portfolio returns are highly volatile, incurring sharp fluctuations, it is an indication that your investment portfolio is exposed to a higher risk as its performance does not follow a pattern but it rather fluctuates. In other words, a high standard deviation indicates that your portfolio is more sensitive to market changes.
What About a Negative Sharpe Ratio?
A negative Sharpe ratio indicates that the return on your portfolio is lower than the risk-free rate that you would get by investing in T-Bills. In the above example, if the return on your portfolio were 1.48%, the Sharpe ratio would be -0.33 because (Rp – Rf) = 1.48% – 1.87% = -0.39%.
At the same time, volatility is always a positive number. This is because the volatility of an investment shows how much the investment fluctuates. Given that the movement of the security will be either upward or downward, volatility can take a price between 0 and the infinity. Therefore, a security that does not fluctuate has a volatility of 0. In other words, a stock cannot have a volatility lower than 0 because it moves; thus, the lowest possible volatility is the zero volatility. That said, if you get a negative Sharpe ratio, it means that the return on your portfolio is lower than the risk-free rate.