Understanding Excess Returns (Alpha): A Comprehensive Guide

The term “excess returns” is used to denote how a fund has performed compared to a benchmark. Excess return, which is also known as alpha, can provide an indication of whether a respective fund, stock, or security has overperformed or underperformed, and it is computed with the Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)The Capital Asset Pricing Model (CAPM) is a model that describes the relationship between expected return and risk of a security. CAPM formula shows the return of a security is equal to the risk-free return plus a risk premium, based on the beta of that security.

The benchmark allows for investors to analyze and compare the performances of various funds by looking at how they have performed in relation to the benchmark. By getting or calculating the value, investors can identify the funds that made larger excess returns.

Excess returns can be either positive or negative. Positive excess returns suggest that a fund’s performance is greater than the benchmark, whereas negative returns suggest that a fund has underperformed compared to the benchmark.

The metric is also referred to as the abnormal rate of return, also known as alpha, and it depicts the part of a fund’s return that is not justified by the benchmark or the market rate of return. An example of a benchmark is the S&P 500S&P 500 IndexThe Standard and Poor’s 500 Index, abbreviated as S&P 500 index, is an index comprising the stocks of 500 publicly traded companies in the. The S&P 500 is a popular benchmark for indices because it tracks major U.S. stocks.

Summary

• The term “excess returns” is used to denote how a fund has performed compared to a benchmark.
• Excess return, which is also known as alpha, can provide an indication of whether a respective fund has overperformed or underperformed, and it is computed with the Capital Asset Pricing Model (CAPM).
• Excess returns allow analysts and investors to make risk adjustments and evaluate a manager’s skills and abilities to add value to a fund’s portfolio. Also, the metric allows investors to make direct comparisons between two funds.

Computing Excess Returns

Excess returns, essentially, is the value that is greater than the projected market rate of return. Rates of return are commonly projected through the use of financial asset models, such as the Capital Asset Pricing Model.

The CAPM formula can be seen below:

Expected Return (Ra) = RF + β(MR – RF)

Where:

• Ra = Expected return on a security
• RF = Risk-free rateRisk-Free RateThe risk-free rate of return is the interest rate an investor can expect to earn on an investment that carries zero risk. In practice, the risk-free rate is commonly considered to equal to the interest paid on a 3-month government Treasury bill, generally the safest investment an investor can make.
• β = Beta of the security
• MR = Expected return of the market

The formula can be adjusted to accommodate excess returns, as seen below:

Excess Return = RF + β(MR – RF) – TR

Where:

• Ra = Expected return on a security
• RF = Risk-free rate
• β = Beta of the security
• MR = Expected return of the market
• TR = Actual or Total Return from the security

Example – Calculating Excess Return Using the CAPM

For illustrative purposes, consider the following information about a stock that Jason (an analyst) is evaluating:

The stock is currently traded on the New York Stock Exchange (NYSE), whose headquarters are domiciled in the U.S. The U.S. 10-year Treasury rate is 3.5%, and the historical average yearly return for stocks in the US market is 8.5%. The beta of the respective stock is 1.5, which indicates that over the last two years, the return has been and is 1.5 times as volatile as the benchmark – S&P 500. The total return from the stock was 18.7%.

To find out what the excess returns are, Jason must first compute the stock’s expected return following the Capital Asset Pricing model and then find the excess returns.

The expected return can be calculated as:

Expected Return = Risk Free Rate + [Beta * Market Return Premium]

= 3.5% + [1.5 * 8.5%]

= 16.25%

The excess returns can be computed as:

Excess Returns = Total Return – Expected Return

= 18.7% – 16.25%

= 2.45%

Based on the results above, Jason is able to see that the stock overperformed compared to the benchmark and that the 2.45% excess return cannot be justified by the market.

Importance of Excess Returns

Excess returns allow analysts and investors to make risk adjustments and evaluate a manager’s skills and abilities to add value to a fund’s portfolio. Also, the metric allows investors to make direct comparisons between two funds.

Related Readings

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In order to help you become a world-class financial analyst and advance your career to your fullest potential, these additional resources will be very helpful:

• BetaBetaThe beta (β) of an investment security (i.e. a stock) is a measurement of its volatility of returns relative to the entire market. It is used as a measure of risk and is an integral part of the Capital Asset Pricing Model (CAPM). A company with a higher beta has greater risk and also greater expected returns.
• Excess Cash FlowExcess Cash FlowExcess cash flow refers to the cash held by a company that can trigger a mandatory repayment of debt according to the company’s bond
• New York Stock Exchange (NYSE)New York Stock Exchange (NYSE)The New York Stock Exchange (NYSE) is the largest securities exchange in the world, hosting 82% of the S&P 500, as well as 70 of the biggest
• Rate of ReturnRate of ReturnThe Rate of Return (ROR) is the gain or loss of an investment over a period of time copmared to the initial cost of the investment expressed as a percentage. This guide teaches the most common formulas