All You Need to Know About Risk-Adjusted Ratios

With every investment made, there is an element of risk associated with it. Risk is related to market benchmarks. Risk can be explained by way of a simple example – any investor who aims to stay invested for the long-term and earn large returns on his/her investment must be aware of the probable short-term losses. The volatility of any investment also depends on the investor’s risk appetite. This is where risk-adjusted ratios help an investor understand the level of risk associated with the returns of an investment. The concept of risk-adjusted returns helps in gauging the returns of various investments with various risk levels against the benchmark. Let us look into some of the ratios.

Types of Risk-Adjusted Return Ratios

Investors can use many risk-adjusted return ratios, as these ratios will give them a better understanding of their existing as well as potential investments. These ratios are quite helpful as they consider the investment risk in any investment, which is not looked into by the simple investment return methods.

1. The Sharpe Ratio

In 1966, William F. Sharpe, an American economist, developed the Sharpe ratio. It is a ratio that determines if an investor is compensated well for the risk they have undertaken in a specific investment. In short, is used to calculate an investment’s risk-adjusted return. When two distinct investments are compared against one benchmark, having a higher Sharpe ratio will give either a greater return for the same risk level or the same amount of returns for a low-risk level compared to the other investment. The Sharpe Ratio can be defined as the Returns of the investment minus the risk-free return, which is then divided by the volatility of an investment, i,e, standard deviation.

The formula of Sharpe Ratio:

Sharpe Ratio= R– R/ Standard Deviation p


Rp is the Expected Portfolio Return,

Rf is the Risk-free Rate, and

Sigmap is the Standard Deviation of the Excess Return of the Portfolio


The Sharpe ratio could be used by investors to assess the past performance (ex-post) of their investment portfolio, wherein the formula makes use of actual returns. Alternatively, even the expected performance of the portfolio along with its expected risk-free rate could be used to calculate the estimated Sharpe ratio. Furthermore, it helps an investor understand if the excess returns of a portfolio are because of the wise investment decision or because of the high risk. 

An investor should look for an investment where the Sharpe ratio is greater than 1. A higher Sharpe ratio offers a better risk-return scenario for an investor. If the Sharpe ratio is negative, it means that either the risk-free rate is higher than the returns of the portfolio, or the portfolio’s return could be negative. In both scenarios, a Sharpe Ratio that is negative is not significant.

2. The Treynor Ratio

Jack L Treynor, an American economist and one of the Capital Asset Pricing Model inventors, developed the Treynor Ratio. This ratio estimates the return earned on an investment over the expected earnings in case there was no diversifiable risk in the investment. The ratio makes use of a beta coefficient rather than the standard deviation. The Treynor Ratio shows an investor how much return their investment can offer while bearing in mind its risk level. The beta coefficient indicates how sensitive a particular investment is in the market – in case the ratio has a high value, then it indicates that the investment would give you quite a high return inclusive of market risks.

The formula of Treynor R

Treynor Ratio =R– Rf / ßp


Rp is the expected return of the portfolio

Rf is the risk-free rate, and

Betap is the Portfolio Beta or the sensitivity of a portfolio to various changes taking place in the market. 


The Treynor Ratio calculates the performance of the portfolio in addition to being associated with the Capital Asset Pricing Model.

Investors should bear in mind, that Beta with negative values has no meaning. When two portfolios are compared, this ratio doesn’t depict the importance of the difference of both values. A higher Treynor ratio indicates that the risk-return scenario is favorable. One must remember that these Treynor Ratio values depend on past performance which might not happen in the future performance.

3. Jensen’s Alpha

Jensen’s Performance Index is also known as Jensen’s Alpha. In 1968, Michael Jenson used Jensen’s alpha as a measure to evaluate the mutual fund managers. The very concept that risky assets must have a high expected return in contrast to the less risky assets, forms the basis for Jenson’s Alpha. In case the return of an asset is higher than that of the risk-adjusted returns, then that asset has a “positive alpha” or what is termed as “abnormal returns”. Investors are on the lookout for investments having a higher alpha. Jenson’s Alpha describes an investment active return and measures its performance against an index benchmark representative of the whole market. This ratio will indicate an investment’s performance post consideration of its risk.

The formula of Jensen’s Alpha:

Jensen’s Alpha (aJ) = Rp – [Rf +ßp. (RM – Rf)


Rp is the Expected Return of the Portfolio,

Rf is the Risk-free Rate,

Beta(p) is the Portfolio Beta or sensitivity of the portfolio, and

Rm is the Market Return. 


If the Alpha is lesser than 0, it indicates that the risk involved in the investment was higher than the expected return. If the Alpha is equal to 0, it indicates that the return earned on the investment is sufficient for the amount of risk taken. If the Alpha is greater than 0, it indicates that the return earned is higher than the risk.

4. Sortino Ratio

The Sortino ratio, simply a modification of the Sharpe ratio, was named after Frank A. Sortinois. Here, the portfolio return is divided by something known as the “Downside Risk” – the negative returns of a portfolio. This ratio distinguishes the harmful volatility from the total overall volatility. This is done by using the investment’s downside deviation rather than the portfolio returns total standard deviation. The ratio deducts the risk-free rate from the portfolio’s return, which is then divided by the downside deviation.

The formula for Sortino Ratio:

Sortino Ratio = Rp –Rf /Sigmad


Rp is the Expected Return of the Portfolio,

Rf is the Risk-free Rate, and 

Sigma(d) is the Standard Deviation of a Negative Asset Return


The ratio evaluates a stock’s downside risk. It is quite similar to the Sharpe ratio, where higher values depict low risk about its returns. The only aspect that differentiates the Sortino Ratio from the Sharpe Ratio is that the downside risk is considered instead of the overall risk i.e. upside and downside. Since this ratio focuses on solely the negative deviation of the returns from its mean, investors believe it gives a better picture of the risk-adjusted performance of a portfolio.

5. R-Squared

R-Squared is a tool that evaluates the risk of an investment. The fund’s movements are measured based on the benchmarked index movements. The values of this ratio can be in the range of 0%-100%. A value of 100% indicates that the fund movements are justified by that of the benchmark index. 

The formula for R-Squared:

R-Squared = Square of correlation


Correlation is the Covariance between the Benchmark Index and the Portfolio ( SD of Portfolio * Benchmark SD),

SD refers to standard deviation.


A high R-squared value indicates a high correlation of the fund with its benchmark and a low r-squared value indicates the reverse. A low R-squared value doesn’t indicate anything bad for the investment. R-squared values are divided into three rows: 

1-40%: the investment has a low correlation to its benchmark

40%-70%: the investment has an average correlation to its benchmark 

70%-100%: the investment has a high correlation to its benchmark

6. The Modigliani-Modigliani Measure

In 1997, the Modigliani-Modigliani Measure was developed by Franco Modigliani and Leah Modigliani, his granddaughter. The Modigliani-Modigliani measure or the M2 measure evaluates the investment’s risk-adjusted return. It indicates the risk-adjusted return of an investment in comparison with a benchmark. The value is indicated as percentage units.

Formula of Modigliani-Modigliani Measure:

Modigliani-Modigliani Measure M2 : SR *sigma(benchmark) + rf


SR is the Sharpe Ratio,

Rf is the risk-free rate.

The M2 measure is quite diversified and helps in portfolio management. It enables the investor to understand incentives that a portfolio offers at a given risk level compared to that of the benchmark portfolio and risk-free rate. M2 Measure helps an investor compare two or even more portfolios. 


Risks and returns go hand-in-hand with any investment. The best way of analyzing the risk associated with an investment is by using various risk-adjusted ratios, that give investors an idea about the risk levels a specific investment has in contrast to its benchmark. Risk-adjusted ratios enable the comparison of investments taking into consideration the risk levels of each. It helps in evaluating the risk-free rate changes that take place. These ratios will help an investor enhance their risk-adjusted returns as they can modify their stock position by the market volatility. It is important for everyone to understand the different types of risk-adjusted return ratios and how they tell us more about the performance of our investments. Hope this article has been able to provide all the information you need on risk-adjusted ratios.