Nine Questions About Investment Risk

Answer to Question 5: "Duration" is a risk measure commonly applied to fixed-income investment.

With fixed-income investments, a major risk is that interest rates will rise after the investment is acquired. An interest rate increase at that point will lower the principal value of a fixed-income investment. A metric called "duration" measures the degree of risk associated with each percentage point change in the interest rate.

Duration is defined in TheStreet.com's glossary as follows:

In simplified terms, a bond's duration measures the effect that each 1% change in interest rates will have on the bond's market value.

Unlike the maturity date, which tells you when the issuer has promised to repay your principal, duration, which takes the bond's interest payments into account, helps you to evaluate how volatile the bond's price will be over time.

Basically, the longer the duration -- expressed in years -- the more volatile the price. So a 1% change in interest rates will have less effect on the price of a bond with a duration of 2 than it will on the price of a bond with a duration of 5.

Answer to Question 6: There is no way of escaping risk. Even cash stored in a perfectly secure vault exposes its owner (you) to an "opportunity risk" -- meaning the return that would have been achieved by investing the money (capital ) rather than storing it as cash.

Most academics and quantitative investment professionals would agree with the definition of "risk-free return" from TheStreet.com's glossary that follows:

When you buy a U.S. Treasury bill that matures in 13 weeks, you're making a risk-free investment in the sense that there's virtually no chance of losing your principal (since the bill is backed by the U.S. government) and no threat from inflation (since the term is so short).

Your yield, or the amount you earn on that investment, is described as risk-free return. By subtracting the risk-free return from the return on an investment that has the potential to lose value, you can figure out the risk premium, which is one measure of the risk of choosing an investment other than the 13-week bill.

Because we always want to offer users of TheStreet.com Ratings information to be computed via the most precise data and the most quantitatively rigorous methodology, our standard deviations, beta coefficients, alpha coefficients, Sharpe ratios and Treynor ratios all use what financial scholars call "excess returns." These are rates of returns of funds and indices adjusted to reflect their ratio to short-term Treasury bill returns. Thus, our statistical data is based on the underlying investment vehicle's returns in excess of a true "risk-free" level.

Answer to Question 7: The analytical methodology known as "modern portfolio theory" (MPT) began in the early 1950s by Harry Markowitz, who eventually received a Nobel Prize for his work.

MPT theorists developed metrics for measuring risk, with an emphasis on the benefits of portfolio diversification. They determined that for diversified equity portfolios, "market risk" -- meaning movements in the overall stock market -- influenced fluctuations more than other "flavors" of risk, such as "sector risk" and risk that's specific to an individual company.

They developed a measure for correlating the amplitude of a portfolio's fluctuations with corresponding movements in the market. It is the slope of a line on a set of coordinates, determined by a statistical technique known as "regression analysis," which measures the sensitivity of an asset to movements in the overall market. A steep slope indicates a "riskier" investment that will tend to experience greater fluctuations than the market. The "regression line" is essentially defined by the well-known linear equation of Y = a + bX. In the equation, "Y" represents movements in the investment, "a" is a constant, "b" is the slope of the line and "X" represents movements in the market.

The DFA Emerging Markets Small Cap FundDEMSX, for example, has a three-year beta coefficient of 1.50. This means that if the general stock market should experience an advance of 10%, the DFA fund would be expected move up 1.50 times that rate for a gain of 15%.

So the relative volatility of an investment relative to the market could have been called the "b measure" after the "b" in the above equation. But using a Greek letter sounds more academic, so this common risk measure became known as the "beta coefficient."

Answer to Question 8: The value of "a" in the linear equation (Y = a + bX) in the answer to question 8 is called the "alpha coefficient."

"Alpha" is a measure of an investment's positive or negative performance relative to its expected return at any level of "market risk." So a manager who is said to consistently produce "positive alpha" is achieving investment returns greater than what would be expected, given the portfolio's degree of risk. The same is implied in mutual funds with "Alpha" embedded in their names.

The three-year annualized alpha coefficient of the Russell Diversified Equity Fund RDESX, for example, is 1.20%. This means the funds three-year annualized return of 10.19% through the end of April was 1.20 percentage points higher per year than would be expected from a fund with the Russell's degree of risk.

Like the beta coefficient, this could have accurately been called the "a value" but instead, adopted the more scientific name of "alpha coefficient."

Answer to Question 9: The equation for determining the beta coefficient of a mutual fund, given monthly returns, is:

Beta = (N * sigma(X * Y) - (sigmaX * sigmaY)) / (N * sigma(X ^ 2) - (sigmaX) ^ 2)

Now here's a breakdown of the equation:

"Beta" is the beta coefficient.

"N" is the number of monthly or weekly observations.

"X" values represent the logarithms of individual weekly or monthly relative values of the "excess" total returns (meaning all distributions are assumed to be reinvested) of the market.

"Y" values represent the logarithms of individual weekly or monthly relative values of the "excess" total returns (meaning all distributions are assumed to be reinvested) of "the fund".

Please note: "Excess" returns are total reinvested returns relative to risk-free returns (like Treasury bill returns) for the corresponding time periods.