### Using Standard Deviation to Measure Risk

Risk can be measured against return expectation or loss tolerance using standard deviation and the r-squared measure can be used to measure variance.

Alpha and beta risks are only part of a greater mathematical analysis of a portfolio's risk-return profile. The standard deviation and R-squared are also important in the measurement of risk and associated return. The standard deviation mathematically demonstrates the spread of data away from the mean. A normal curve, also called a bell curve, is typically used to demonstrate standard deviation. At the center of this curve is the mean, or average. The standard deviation would affect the flatness of the curve. For example, if 100 stock prices were plotted on a curve, and the distribution curve were assumed to be normal, then a low standard deviation would result in a tall, thin curve. This type of curve indicates that the stock prices are close to the mean, with little variance among them. Conversely, if the standard deviation is high, then the curve will be short and fat, indicating that the prices vary dramatically.
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#### Standard Deviation for Stock Prices

**R-squared measure**is a risk-return measure that shows the amount of variance of one variable because of the movement of another. For investment in securities, R-squared is generally used to compare a fund's movement with an index. If a stock goes up 10 percent and the overall market index goes down 10 percent, this may indicate a correlation between the two, which will give a variance. R-squared is given as a percentage. At 100 percent, the movement of the two variables is perfectly aligned. A 100 percent R-squared measure of the movement of funds and the movement of an index means that the fund moves exactly like the index does. A 0 percent value means that there is no relationship between the two. Taken as one system of analysis, alpha and beta are used to give a predictive line, called a regression line, that shows risk and return against an index. R-squared is said to be a measure of good fit, as it demonstrates the extent to which the data match the values expected. The standard deviation shows the distribution of the data that make up the line.#### R-Squared for Stock Movement

### Market Risk as a Predictor of Return

The greatest predictor of return is market risk.

Investing in a single stock comes with significant risk. The stock can go up or down. If it drops to zero, the investment is gone. To avoid this, modern portfolio theory suggests creating a portfolio that blends various security instruments. A portfolio may include stocks, bonds, mutual funds, and derivatives, and it should cross sectors. This will help manage diversifiable risk. **Diversifiable risk** is risk that can be mitigated by mixing investments across sectors and types. A portfolio that is only composed of technology stock would be hit hard if the technology sector declined. A diversified portfolio will have securities with negatively correlating pairs or securities with no correlations.

**nondiversifiable risk**, also called undiversifiable risk, is a risk that cannot be mitigated by mixing investments across sectors and types. For example, a nationwide recession will drop the values of all securities despite the sector or type. This type of risk is also called market risk. Returns are generally compared to risk-free securities, such as Treasury bills. Overall, returns are the risk-free return plus the market risk premium. Because the risk-free rate is the baseline, or where the lowest return can be found with the least amount of risk, the market risk predicts the greatest portion of the return.