- April 30, 2022
- Team Kalkine

**What is Risk-Adjusted Return? **

Risk-adjusted return is a technique to measure the return on an investment for which credit, market, operational and financial risk is taken into account that must be accepted in order to achieve it. It helps investor to take decision on whether the investment is worth to invest with the risk or not.

In simple word, Risk-adjusted return measures the return in an investment after taking into account the degree of risk that must be taken to receive profit. It can be applied to individual stocks, entire portfolio, and investment funds.** **

- Risk may be defined as the difference between the actual result and expected results.
- Risk-adjusted return measures the return in an investment after taking into account the degree of risk that must be taken to receive profit.
- Risk-adjusted return measures the return an investor received depending on their risk tolerance throughout a given period of time.

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**What is Risk? **

Risk may be defined as the difference between the actual result and expected results and it include the possibility of losing part of or all of an original investment. In the Capital Asset Pricing Model (CAPM) it is defined as the volatility of return. It is believed that riskier the asset the expected return would be higher to compensate investors from the higher volatility and increased risk and lower the risk in asset the expected return would be lower. Risk is expressed in number or a rating or in relation to something such as a market benchmark.

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**Understanding Risk-Adjusted Return**

Risk-adjusted return measures the return an investor received depending on their risk tolerance throughout a given period of time. Risk tolerance is the tendency of an investor to take on volatility for specific financial condition. If two or more investment offers same return but have different risk, the investment with lower risk will have a better risk-adjusted return and investor will choose it over the other investment.

Some common risk measure includes atandard deviation, beta, alpha, the Sharpe ratio and R-squared. When selecting or comparing any potential investments, an investor should use same risk measure to get a relative performance perspective as different measure give different analytical result.

Risk-Adjusted return helps in solving three main problems:

- It takes into consideration the changes in the risk-free rate which the other risk-return ratios do not find out.
- It enables direct comparison between two or more investment opportunity.
- It enables direct comparison with the returns of the benchmark index.

**Risk-Adjusted Return methods **

**Sharpe Ratio**

The Sharpe ratio evaluates return on an asset that exceeds the risk-free rate per unit of volatility or total risk, also known as standard deviation. It is developed in 1966 by Nobel Prize winner William F. Sharpe. While comparing two potential investments opportunity with same risk against a similar benchmark, the investment with higher Sharpe ratio offers a better return than with lower Sharpe ratio. It has become one of the most popular methods to calculate risk-adjusted returns. However it can only give accurate result if the data has a normal distribution.

**Sharpe Ratio= (Rp – Rf)/ ****σp**

Where:

Rp = Expected Portfolio Return

Rf = Risk Free Rate

Sigma(p) = Portfolio Standard Deviation

The Sharpe ration help investor in determining that if the investment high return are a result of too much risk or prudent investment decisions. Even if any investment in portfolio reap the return as compared to similar investment options, still investment may be consider worth investing if those return are free from an additional risk.

**Treynor Ratio**

Treynor Ratio measures profit earned in excess of the profit which can be earned on an investment that has no unsystematic risk. It is similar to Sharpe Ratio as they both are reward-volatility ration, but Treynor ratio uses a beta coefficient in place of standard deviations. The Treynor ratio was developed by Jack L. Treynor and is dependent upon Beta (β), which evaluate the sensitivity of an investment as compared to the movement in the market to evaluate the risk.

**Treynor Ratio = (Rp –Rf)/ ****βp**

Where;

Rp = Expected Portfolio Return

Rf = Risk Free Rate

Beta(p) = Portfolio Beta

Treynor ratio is a measure of portfolio performance that is affected by factors that are external and can’t be controlled also known as Beta or Systematic risk. If the Treynor ration on any investment is high, it means that the investor has generated higher return that the assumed market risk and it also help in understanding how each investment in a portfolio is performing and how efficiently capital is being utilized.

**Jensen’s Alpha**

Alpha is also referred as excess return or abnormal rate of return and it is often consider as an ability to beat the market. It measures the performance of an investment against a market benchmark and the excess of return as compared to the return generated by the benchmark is the Alpha of the investment.

**Jensen’s Alpha = Rp – Rf – ****βp (Rm – Rf)**

Where;

Rp = Expected Portfolio Return

Rf = Risk Free Rate

Beta(p) = Portfolio Beta

Rm = Market Return

If,

Alpha = 0: the investment has generated return adequate for the risk taken

Alpha < 0: the investment has not generated enough for its risk or was too risky for the return

Alpha>0: the investment has generated return in excess of the risk assumed

**R-Squared**

R-Squared also known as R2 or the coefficient of determination is a statistical measure that represents the percentage of variance in the dependent variable that may be explained by the independent variables. It determines how well the data fit the regression model.

- Its values range from 0 to 1 and are commonly expressed as percentage from 0 to 100%.
- An R-squared of 100% indicates that the fluctuation in investment can be completely justified by the fluctuation in the benchmark.
- A high R-Squared between 85% and 100% means that the investment’s performance patterns reflect that of the benchmark.

**Sortino Ratio**

Sortino Ratio is a variation of the Sharpe ratio used to measure the additional return for each unit of downside risk. It is calculated by computing the difference between an investment’s average return rate and the risk-free rate. Then the result is divided by the standard deviation of negative returns. Standard deviation consists of both downward and upward volatility, however most investors are concerned about the downward volatility.

**Sortino Ratio = (Rp – Rf)/**** σd**

Where:

Rp = Expected Portfolio Return

Rf = Risk Free Rate

Sigma(d) = Standard Deviation of Negative Asset Returns

**Modigliani Risk-Adjusted Performance**

Modigliani Risk-Adjusted Performance also known as Modigliani- Modigliani measure or M2 or RAP is a measure of the risk adjusted return of a portfolio adjusted for the risk of the portfolio compared to an index. It is computed as a percentage return which makes it easier to interpret.

**M2 = Rp -Rm**

Where:

Rp = return on the adjusted portfolio

Rm = return on the market portfolio