What are Risk-Adjusted Returns ? : Sharpe Ratio, Sortino Ratio, Alpha, and Beta explained

Risk-adjusted returns are an essential concept for investors who want to assess how much return they are earning relative to the amount of risk they are taking on. Simply focusing on returns can be misleading, as higher returns may come with higher risk. Understanding and using risk-adjusted return metrics such as the Sharpe ratio, Sortino ratio, alpha, and beta allows investors to better assess the true performance of an investment or portfolio.

In this guide, we’ll dive into the key risk-adjusted return metrics, explaining their significance, how they are calculated, and how to use them to make more informed investment decisions.

1. What Are Risk-Adjusted Returns?

Risk-adjusted returns are measures of the return on an investment relative to the amount of risk involved. These metrics help investors understand whether they are being adequately compensated for the risk they are taking. By accounting for volatility and other risk factors, investors can compare the performance of different investments on a more equal footing.

Investors use risk-adjusted return metrics to:

Evaluate performance: Understand if the returns are worth the risk.

Compare investments: Compare different assets or portfolios with varying risk profiles.

Optimize portfolios: Build diversified portfolios that maximize returns for a given level of risk.

2. Sharpe Ratio: Measuring Total Risk

What is the Sharpe Ratio?
The Sharpe ratio is one of the most commonly used metrics for risk-adjusted returns. It measures the excess return (or risk premium) per unit of total risk (volatility), where total risk is represented by the standard deviation of returns. The Sharpe ratio is useful for evaluating the overall risk-return tradeoff of an investment or portfolio.

Formula for the Sharpe Ratio:

Sharpe Ratio=(Rp−Rf)/σp

Where:

Rp = Portfolio return (or investment return)

Rf = Risk-free rate (e.g., return on a government bond or treasury bill)

σp = Standard deviation of the portfolio return (representing risk or volatility)

Interpretation of the Sharpe Ratio:

Higher Sharpe Ratio: Indicates that the investment is providing a better return for each unit of risk. A higher value generally suggests that the investment is more efficient in terms of risk-adjusted return.

Sharpe Ratio > 1: Generally considered a good risk-adjusted return, where the returns are higher than the risk.

Sharpe Ratio < 1: Indicates that the investment may not be generating sufficient returns for the level of risk it carries.

Example:

If a portfolio has a return of 12%, a risk-free rate of 3%, and a standard deviation of 10%, the Sharpe ratio would be:

Sharpe Ratio=(12%−3%)/10%=9%/10%=0.9

This suggests that the portfolio’s return is 0.9 times the amount of risk it is taking on.

3. Sortino Ratio: Focusing on Downside Risk

What is the Sortino Ratio?
The Sortino ratio is similar to the Sharpe ratio but differs in that it only considers downside risk (the risk of negative returns) rather than total volatility. It’s a more focused metric for evaluating risk-adjusted returns, especially for investors who are more concerned with downside risk than overall price fluctuations.

Formula for the Sortino Ratio:

Sortino Ratio=(Rp−Rf)/σd

Where:

Rp = Portfolio return (or investment return)

Rf = Risk-free rate

σd = Standard deviation of negative returns (downside risk)

Interpretation of the Sortino Ratio:

Higher Sortino Ratio: A higher ratio indicates that the investment or portfolio has produced a good return relative to the downside risk (volatility in negative returns).

Sortino Ratio > 1: Suggests that the return is considered good when taking into account the downside risk.

Sortino Ratio < 1: Indicates that the downside risk may not be justified by the returns.

Example:

If a portfolio has a return of 15%, a risk-free rate of 3%, and downside deviation (negative volatility) of 8%, the Sortino ratio would be:

Sortino Ratio=(15%−3%)/8%=12%/8%=1.5

This suggests that for every unit of downside risk, the portfolio is generating 1.5 times the excess return over the risk-free rate.

4. Alpha: Measuring Outperformance Against a Benchmark

What is Alpha?
Alpha is a measure of an investment’s excess return relative to a benchmark index (such as the S&P 500) after adjusting for risk. It represents the value that a portfolio manager or strategy adds (or subtracts) compared to what would be expected based on the risk taken. A positive alpha indicates that the investment outperformed the benchmark, while a negative alpha suggests underperformance.

Formula for Alpha:

α=Rp−[Rf+β(Rm−Rf)]

Where:

Rp = Portfolio return

Rf = Risk-free rate

Rm = Market return (benchmark index return)

β = Beta (measuring the portfolio's sensitivity to the market)

Interpretation of Alpha:

Positive Alpha: The investment outperformed the benchmark after adjusting for risk.

Negative Alpha: The investment underperformed relative to the benchmark, given the amount of risk taken.

Example:

If a portfolio’s return is 10%, the risk-free rate is 2%, the market return is 8%, and the portfolio’s beta is 1.2, the alpha would be:

α=10%−[2%+1.2(8%−2%)]=10%−[2%+7.2%]=10%−9.2%=0.8%

This suggests the portfolio has outperformed its benchmark by 0.8% after accounting for market risk.

5. Beta: Measuring Volatility Relative to the Market

What is Beta?
Beta is a measure of a stock’s or portfolio’s volatility in relation to the broader market (usually represented by a benchmark index like the S&P 500). It indicates how much the investment’s returns move relative to the market’s movements.

Formula for Beta:

β=Covariance(Ri,Rm)/Variance(Rm)

Where:

Ri = Return of the individual stock or portfolio

Rm = Return of the market

Covariance measures how the individual stock’s return moves in relation to the market, and variance measures the market’s volatility.

Interpretation of Beta:

Beta = 1: The stock or portfolio moves in line with the market. If the market goes up by 10%, the stock is expected to go up by 10% as well.

Beta > 1: The stock or portfolio is more volatile than the market. A beta of 1.5 means the stock is expected to move 1.5 times the market movement.

Beta < 1: The stock or portfolio is less volatile than the market. A beta of 0.5 means the stock is expected to move only half as much as the market.

Example:

If a stock has a beta of 1.2, this means it tends to move 20% more than the broader market. If the market rises by 10%, the stock is expected to rise by 12%. Conversely, if the market falls by 10%, the stock would likely fall by 12%.

6. How to Use Risk-Adjusted Returns

Risk-adjusted return metrics help investors:

Compare Investments: Investors can use these ratios to compare investments or portfolios with different risk profiles, allowing for more informed decisions.

Optimize Portfolios: By using metrics like alpha, beta, Sharpe ratio, and Sortino ratio, investors can optimize their portfolios to achieve the best return for a given level of risk.

Assess Manager Performance: Active portfolio managers can be evaluated using alpha and Sharpe ratio, helping investors determine whether the manager is adding value beyond what can be explained by risk.

7. Conclusion

Risk-adjusted returns are essential for understanding the true performance of an investment, considering both its returns and the risks involved. Key metrics like the Sharpe ratio, Sortino ratio, alpha, and beta provide different lenses through which investors can assess and compare investments.

Sharpe Ratio helps assess overall return relative to total risk.

Sortino Ratio focuses on downside risk, important for those who are concerned with negative returns.

Alpha measures outperformance relative to a benchmark.

Beta provides insight into the volatility of an investment compared to the market.

By incorporating these metrics into their investment analysis, investors can make more informed, data-driven decisions that help optimize their portfolios for the best risk-return tradeoff.

Happy investing!