How to Calculate the Expected Return of a Portfolio Using CAPM

Some simple math to assess the risk and reward ratio in your investments.

Nov 6, 2015 at 11:29AM

One simple but powerful method investors can use to assess the risk and reward of a stock portfolio is using the Capital Asset Pricing Model, or CAPM, model for expected returns.

The basics of CAPM
The CAPM model takes into account two major risks that impact returns and combines them to tell an investor how much compensation should be expected to justify taking those risks.

First, there's the time value of money, which is incorporated via the risk free interest rate. The risk free interest rate is the return investors are willing to accept for an investment with no risk. Generally, the U.S. three-month Treasury bill is accepted to be the risk free rate because it is considered the safest investment possible, backed by the full faith and credit of the U.S. government.

Any investment with additional risk should come with a commensurate increase in returns above the risk free rate. That's because investors have no incentive to take on additional risk if returns are the same or lower than the risk free rate.

The CAPM model also includes a component to account for the risk of the specific portfolio or security. This portion of the equation is called the "risk premium," meaning it represents the returns an investor will require to compensate for the additional risk above the risk free rate.

The model does this by multiplying the portfolio or stock's beta, or β, by the difference in the expected market return and the risk free rate. Beta is a measure of a security or portfolio's volatility in relation to the market; a beta above one means the investment is more volatile than the market, and a beta below one means it is less volatile than the market.

You can learn to calculate an individual stock's beta here, and the beta for your entire portfolio here.

Putting the CAPM model into action
To use the CAPM model with your portfolio, we can use the CAPM formula with numbers from your own portfolio.

Camp Formula

For example, if you calculate your portfolio's beta to be 1.3, the three-month Treasury bill yields 0.02% as of October of 2015, and the expected market return is 8%, then we can use the formula to determine the expected return for your portfolio against the risks of time and volatility.

Capm

Based on the risks input into the formula, an investor should expect a return of at least 10.4% to compensate for this level of risk.

With the risk free return so close to zero, the largest driver of this hypothetical expected return is the 1.3 beta. That drives the risk premium portion of the model above the expected market return to the 10.4% an investor should expect based on the market risks in this example.

It's important to keep in mind that this formula is a theoretical tool. It won't necessarily predict how your investment or portfolio will perform. Instead of using it as a predictor of returns, use it instead as a risk management tool to help you understand how much risk you are taking and how much reward you should expect to get in compensation for that risk.

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