According to modern portfolio theory, or MPT, degrees of risk aversion are defined by the additional marginal return an investor needs to accept more risk. The required additional marginal return is calculated as the standard deviation of the return on investment, or ROI, otherwise known as the square root of the variance.
The general level of risk aversion in the markets can be seen in two ways: by the risk premium assessed on assets above the riskfree level and by the actual pricing of riskfree assets, such as United States Treasury bonds. The stronger the demand for safe instruments, the larger the gap between the rate of return of risky versus nonrisky instruments. Prices for Treasurys should also increase, pushing yields lower.
Modern Portfolio Theory and Risk
When MPT was introduced, its definition of risk, or the standard deviation from the mean, seemed unorthodox. Over time, standard deviation probably became the mostused gauge for investment risk.
Standard deviation shows how dramatically an asset's returns oscillate over a period of time. A trading range around the mean price can be created using the upswings and downswings as measured by standard deviation. Investors use this information to estimate possible returns for future portfolios.
Those who are more riskaverse tend to want assets with lower standard deviations. A lower deviation from the mean suggests the asset's price experiences less volatility and there is a lower probability for major loss. Aggressive investors are comfortable with a higher standard deviation because it suggests higher returns are also possible.
The reason standard deviation is so widely accepted is it is always expressed in the same units and same proportions as the underlying data. For example, the standard deviation of height is expressed in feet or inches, while the standard deviation for stock prices is quoted in terms of dollar price per share. Other risk metrics develop in accordance with MPT, including beta, Rsquared and turnover rate.
Possible Flaws With MPT and Risk
Though historically rare, it is possible to have a mutual fund or investment portfolio with a low standard deviation and lose money. Losing periods in the market tend to be steep and shortlived; low standard deviation assets tend to lose less in shorttime periods than others. However, since risk information is backwardlooking, there is no guarantee future returns follow the same pattern.
A larger, trickier issue is that standard deviation is relative in nature. Suppose an investor looks at two balanced mutual funds. One has a standard deviation of five units and the other a standard deviation of 10 units. Without other information, MPT cannot tell the investor if five is low, average or high. If five is low, 10 might be average. If five is high, 10 might be extremely high. Investors using standard deviation should take the time to find the appropriate context.

What is the difference between standard deviation and z score?
Understand the basics of standard deviation and Zscore; learn how each is calculated and used in the assessment of market ... Read Answer >> 
What metrics should I use to evaluate the riskreturn tradeoff for a mutual fund?
Understand the key metrics used to analyze mutual funds and how investors can use each measurement to determine the riskreward ... Read Answer >> 
What is a relative standard error?
Find out how to distinguish between mean, standard deviation, standard error and relative standard error in statistical survey ... Read Answer >> 
How can you calculate volatility in Excel?
Historical volatility is a longterm assessment of risk. Here's how to calculate it in Excel. Read Answer >> 
How is correlation used in modern portfolio theory?
Discover how modern portfolio theory and the efficient frontier use correlation between investment assets to predict an optimal ... Read Answer >> 
Is there a positive correlation between risk and return?
Learn about the positive correlation between risk and the potential for return, and understand how risk is used to construct ... Read Answer >>

Investing
The Uses And Limits Of Volatility
Check out how the assumptions of theoretical risk models compare to actual market performance. 
Investing
5 ways to measure mutual fund risk
Statistical measures such as alpha and beta can help investors understand investment risk on mutual funds and how it relates to returns. 
Investing
PRHSX: Risk Statistics of Health Sciences Mutual Fund
Examine the risk metric of the T. Rowe Price Health Sciences Fund. Analyze beta, capture ratios and standard deviation to assess volatility and systematic risk. 
Managing Wealth
Manage Investments And Modern Portfolio Theory
Modern Portfolio Theory suggests a static allocation which could be detrimental in declining markets, making it necessary for continuous risk assessment. Downside risk protection may not be the ... 
Trading
How To Convert Value At Risk To Different Time Periods
Volatility is not the only way to measure risk. Learn about the "new science of risk management". 
Investing
Calculating Tracking Error
Tracking error is the difference between the return on a portfolio or fund, and the benchmark it is expected to mirror (or track). 
Investing
Understanding Quantitative Analysis Of Hedge Funds
Learn how hedge fund performance quantitatively requires metrics such as absolute and relative returns, risk measurement, and benchmark performance ratios. 
Investing
How Risk Free Is the RiskFree Rate of Return?
This rate is rarely questionedâ€”unless the economy falls into disarray. 
Investing
5 Ways to Rate Your Portfolio Manager
These five performance ratios will help you measure how good your money manager is at increasing the value of your portfolio.

Standard Deviation
The standard deviation is a statistic that measures the dispersion ... 
Risk Measures
Risk measures give investors an idea of the volatility of a fund ... 
Standard Error
Standard error is the standard deviation of a sample population. 
Risk Management
Risk management occurs anytime an investor or fund manager analyzes ... 
Sharpe Ratio
The Sharpe ratio is the average return earned in excess of the ... 
Tail Risk
Tail risk is portfolio risk that arises when the possibility ...