One of the concepts used in risk and return calculations is standard deviation, which measures the dispersion of actual returns around the expected return of an investment. Since standard deviation is the square root of the variance, variance is another crucial concept to know. The variance is calculated by weighting each possible dispersion by its relative probability (take the difference between the actual return and the expected return, then square the number).

The standard deviation of an investment's expected return is considered a basic measure of risk. If two potential investments had the same expected return, the one with the lower standard deviation would be considered to have less potential risk.

Risk measures
There are three other risk measures used to predict volatility and return:

  • Beta - This measures stock price volatility based solely on general market movements. Typically, the market as a whole is assigned a beta of 1.0. So, a stock or a portfolio with a beta higher than 1.0 is predicted to have a higher risk and, potentially, a higher return than the market. Conversely, if a stock (or fund) had a beta of .85, this would indicate that if the market increased by 10%, this stock (or fund) would likely return only 8.5%. However, if the market dropped 10%, this stock would likely drop only 8.5%.

    Learn how to properly use this measure to help you meet your criteria for risk within the article Beta: Gauging Price Fluctuations.


     
  • Alpha - This measures stock price volatility based on the specific characteristics of the particular security. As with beta, the higher the number, the higher the risk.

Alpha = [(sum of y) - ((b)(sum of x))]÷n

Where:
n = number of observations (36 months)
b = beta of the fund
x = rate of return for the market
y = rate of return for the fund

An alpha of 1.0 means the fund outperformed the market 1%.

  • Sharpe ratio - This is a more complex measure that uses the standard deviation of a stock or portfolio to measure volatility. This calculation measures the incremental reward of assuming incremental risk. The larger the Sharpe ratio, the greater the potential return.

Sharpe Ratio = (total return - risk free rate of return)
σ

Look Out!
The reverse of "the larger the Sharpe ratio, the greater the return" also holds true. The "lower the Sharpe ratio, the lower the potential return". If a security\'s Sharpe ratio were equal to "0", there would be no reward for taking on the higher risk, and the investor would be better off simply holding Treasuries (whose return is equal to the risk-free return component of the equation).



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