It would be nice if every investor achieved his required rate of return on his investments. In reality, this is not the case. This is the risk associated with investing. Investors use the required rate of return to decide whether making an investment is worth the risk. The expected rate of return is found by identifying each possible rate of return and assigning a respective probability to each.

## Required Rate of Return

The required rate of return is subjective and varies from investor to investor. Required rate of return is the return you desire on an investment before sinking your money into it. For example, on a technology stock, you set a required rate of return of 15 percent. Another investor in the same stock may set a required rate of return of 10 percent. Your required rate of return determines whether you should invest in the stock or seek an alternative investment. If you believe the investment is too risky, you may invest in another stock with a better chance of achieving your investment return such as a utility company.

## Expected Rate of Return

The expected rate of return uses probabilities to weigh the various return outcomes that an investment may produce. The probability distribution varies according to the investor. For example, if you own a stock and you expect a 20 percent chance of the stock returning 30 percent, a 50 percent chance of it returning 12 percent and a 30 percent chance of it returning 10 percent, the expected rate of return is (20 percent x 30 percent) + (50 percent x 12 percent) + (30 percent x 10 percent) for a result of 16 percent.

## Systematic and Unsystematic Risk

Essentially, expected rate of return and required rate of return are both about risk. Each stock or investment has its own set of unique risks not including widespread market risk such as an economic downturn and other macroeconomic variables. Portfolio theory likes to classify risk into two categories: systematic risk and unsystematic risk. Systematic risk affects all investments because it is market risk. Unsystematic risk is specific to the investment. An example of unsystematic risk is the possibility of management making a bad decision that has a negative affect on the company's stock price.

## Beta

Beta is measure of volatility or systematic risk of a stock compared with the overall market. Calculation of beta involves regression analysis. You won't need to perform regression analysis but you need to know what it means. A beta of 1 means that a stock is exactly as risky as the market. For example, if the S&P 500 provides a return of 12 percent, a stock with a beta of 1 returns 12 percent to investors. A stock with a beta of 2 means that it is twice as risky as the market. Beta forms the basic building block for building an investment portfolio with the goal of diversifying risk. The idea is to combine stocks with counterbalancing betas to diversify away risk as much as possible.

## Using Beta to Calculate Expected Return

Investors use beta to calculate expected return of a stock using the Capital Asset Pricing Model. Essentially, CAPM states a stock's return is a function of a risk-free rate of return plus its beta multiplied by the expected market return minus the risk-free rate. The risk-free rate of return is the return you receive on a safe investment such as a U.S. Treasury bill. Given a risk-free rate of 3.5 percent, stock beta of 1.6 and expected market return of 15 percent, the expected return on the stock is 3.5 percent + 1.6 x (15 percent - 3.5 percent) or 21.9 percent.

#### References

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