Nine Questions About Investment Risk

During the five-year ascent from the trough of the 2000-2002 bear market to the market peak of October 2007, there seemed scant reason to worry about investment risk. But the market downturn brought about by the credit crunch and weakened economy has driven home the fact that the concept of risk is ignored at an investor's peril.

So how much do you know about measuring risk? Here is a nine-question investment quiz to test -- and possibly enhance -- your knowledge of the concepts of investment risk.

Feel free to use the many features available on to help you answer the questions. A great place to start your quest is the "Search" box at the top of

Another great resource available on our Website is a glossary of definitions and explanations of financial and investment terms. Just roll-over the "Portfolio Tools" tab at the top of the site and select "Glossary" (or simply click here).

This investment trivia quiz is a self-test, so keep your own score. Ready?

Good luck!

Question 1: What is the most basic measurement of investment risk?

Basic measure of risk can be applied to any number of different types of investments, such as individual stocks and bonds, a group of stocks, a combination of bonds, or a diversified portfolio of stocks and bonds.

When you have identified the most basic measurement of investment risk, what is the logic in using this measure and what do the values represent?

Question 2: What is a "Sharpe ratio" (and who is William F. Sharpe, after whom the gauge is named)?

This relates to the first question, but moves things in a direction of more interest to ordinary investors. Understanding the Sharpe ratio might get you to look at your investments a bit differently.

Question 3: If an investor is considering two stocks with exactly the same projected rates of return and identical standard deviations of returns, under what condition would it make sense to hold both of them rather than just one?

The answer to this can add new dimensions to your approach to portfolio construction.

Question 4: What does "drawdown" mean and in what markets is it most commonly used as a measure of risk?

A huge amount changes hands daily in markets where drawdown is a common risk metric. How do these markets impact the lives of ordinary people?

Question 5: What is the most common risk measurement for fixed-income investments?

An interesting measure is used to gauge the risk of fixed-income investments like bonds. But the more you get into the measurements of bond risks, the greater will be your appreciation that fixed-income investments are a lot more complex than you might have thought. The answer to this will contain some bonus information for those who are really into math.

Question 6: Is cash -- stored in a completely theft-proof, climate-resistant vault -- the least risky investment?

Economists and scholars who study risk have thoughts about the above the concept of risk-free "savings" that might surprise you. If cash stored in a completely secure vault isn't totally risk-free, then what is -- at least in the minds of those who study the subject of risk?

Question 7: What is "modern portfolio theory," the "beta coefficient," and what do they have to do with the measurement of investment risk?

This really gets you into the theory of risk. But a basic understanding of the principles behind "MPT" can help refine your approach to investing.

Question 8: What is the "alpha coefficient" and what is its significance?

There are mutual funds with names like Alpha Hedged Strategies ( APHCX), GMO Alpha Only III ( GGHEX) and Nuveen Symphony Optimized Alpha ( NOPAX). What do the references to alpha in their names mean?

Investment professionals will sometimes describe a manager as "someone who consistently achieves positive alphas." What is so important about the alpha coefficient?

Question 9: What is the equation for determining the beta coefficient of a mutual fund, given its monthly returns?

This one is likely to challenge anyone who breezed through all the preceding questions. If you now have a conceptual knowledge of investment risk measures, you are in good shape -- even without knowing the underlying equations. But math freaks who want to know "how the engine works" will want to try this one.

Your answer should include detailed descriptions of all the variables in the equation.

Ready for the answers to questions one through nine?

Answer to Question 1: Standard deviation of returns. This is arguably the most basic measure of investment risk.

The importance of standard deviation is underscored by the fact that it is one of several risk measured used by Ratings in the determination of our mutual fund ratings grades. We also use it in our articles to stress how differences in volatility impact the relative riskiness of investments.

For example, " Two Glaring Reasons to Be Wary of This ETF" stressed that the HOLDRS B2B Internet ( BHH) is relatively risky because its three-year annualized standard deviation of 29.38% is more than triple the 8.68% standard deviation of the S&P 500 total return index.

Standard deviation is defined in's glossary as follows:

Standard deviation is a statistical measurement of how far a variable quantity, such as the price of a stock, moves above or below its average value. The wider the range, which means the greater the standard deviation, the riskier an investment is considered to be.

Answer to Question 2: The Sharpe ratio, a measure of investment return adjusted for the portfolio's degree of risk.

For example, as of the end of March, the one-year return of the Dreyfus Premier Greater China B ( DPCBX) was 10.18% while that of the more conservative JP Morgan Treasury & Agency Fund ( OTABX) returned 7.76%. But the Sharpe ratio of the less volatile JP Morgan fund was 2.54% versus a Sharpe ratio of only 0.16% for the Dreyfus fund. So? That difference means that the less volatile bond fund was achieving more return per unit of risk than the more volatile China fund.

The Sharpe ratio is defined in's glossary as follows:

Using the Sharpe ratio is one way to compare the relationship of risk and reward in following different investment strategies, such as emphasizing growth or value investments, or in holding different combinations of investments.

To figure the ratio, the risk-free return (e.g., the return on Treasury bills) is subtracted from the average return of an investment portfolio over a period of time, and the result is divided by the standard deviation of the return.

A strategy with a higher ratio is less risky than one with a lower ratio.

This type of analysis is named for William F. Sharpe, who won the Nobel Prize in economics in 1990.

Answer to Question 3: Diversification is always helpful for spreading risk.

In the case of two investments with the same projected rates of return and identical standard deviations of returns, inclusion of each in a portfolio makes sense if one tends to show strength during periods when the other is subject to weakness and vise versa. The "zigs" of one will tend to cancel out the "zags" of the other, resulting in a smoother pattern of returns versus the "choppier" returns either would produce as an individual investment. So the standard deviation of the combined holding will be relatively low.

Statisticians call such a situation "low covariance" and have ways of measuring it. But an sharp investor can make careful observations and achieve the same result.

For example, a Chinese exchange-traded fund, such as the iShares FTSE/Xinhua China 25 Index Fund ( FXI) might tend to be strong during periods when a domestic small-company growth stock experiences weakness. So when combined, the series of returns will likely suffer less volatility than if just one of them is selected.

Answer to Question 4: Drawdown is the percentage change over a specified time period between an asset's peak value and its deepest subsequent trough. This risk metric considers only the depth of the decline and not the length of time between the peak and trough.

Drawdown is frequently used by commodity speculators but is becoming more widely applied to other types of investments. The prices we end up paying for most basic necessities are based on quotes from the commodity pits.

Drawdown, by the way, is one of several risk measures used to determine Ratings mutual fund grades.

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'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'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 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 Fund ( DEMSX), 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.

    Richard Widows is a senior financial analyst for Ratings. Prior to joining, Widows was senior product manager for quantitative analytics at Thomson Financial. After receiving an M.B.A. from Santa Clara University in California, his career included development of investment information systems at data firms, including the Lipper division of Reuters. His international experience includes assignments in the U.K. and East Asia.

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