Final answer:
Standard deviation measures the total risk of securities by quantifying the volatility of an investment's return, indicating the dispersion of returns around the mean. Higher standard deviation corresponds to higher risk and potentially higher average expected returns to justify the investment.
Step-by-step explanation:
When examining the returns of securities, standard deviation measures the total risk. It is a statistical metric that provides a numerical measure of the overall amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The concept is crucial in finance, as it quantifies the volatility of an investment's return over time. Investments that exhibit higher variability in their returns are considered riskier, as their returns are less predictable; hence, standard deviation becomes a core component in risk management and portfolio optimization.
For instance, over a sustained period, stocks generally have had higher average returns than bonds or savings accounts, attributed to their higher risk. Stocks can significantly vary in value within short periods, as evidenced by the substantial swings in the S&P 500 index in consecutive years. The potential payoff range for a high-risk investment is substantially broader, which is why high-risk investments should, on average, offer high expected returns to compensate for the increased uncertainty.