Time For Investings Fourletter Word

What four-letter word should pop into mind when the stock market takes a harrowing nose dive?

Risk is the potential for realizing low returns or even losing money, possibly preventing you from meeting important objectives, like sending your kids to the college of their choice or having the retirement lifestyle you crave.

But many financial advisers and other experts say that these days investors aren't taking the idea of risk as seriously as they should, and they are overexposing themselves to stocks.

"The market has been so good for years that investors no longer believe there's risk in investing," says Gary Schatsky, a financial adviser in New York.

So before the market goes down and stays down, be sure that you understand your tolerance for risk and that your portfolio is designed to match it.

Assessing your risk tolerance, however, can be tricky. You must consider not only how much risk you can afford to take but also how much risk you can stand to take.

Determining how much risk you can stand—your temperamental tolerance for risk—is more difficult. It isn't quantifiable.

To that end, many financial advisers, brokerage firms and mutual-fund companies have created risk quizzes to help people determine whether they are conservative, moderate or aggressive investors. Some firms that offer such quizzes include Merrill Lynch, T. Rowe Price Associates Inc., Baltimore, Zurich Group Inc.'s Scudder Kemper Investments Inc., New York, and Vanguard Group in Malvern, Pa.

Typically, risk questionnaires include seven to 10 questions about a person's investing experience, financial security and tendency to make risky or conservative choices.

The benefit of the questionnaires is that they are an objective resource people can use to get at least a rough idea of their risk tolerance. "It's impossible for someone to assess their risk tolerance alone," says Mr. Bernstein. "I may say I don't like risk, yet will take more risk than the average person."

Many experts warn, however, that the questionnaires should be used simply as a first step to assessing risk tolerance. "They are not precise," says Ron Meier, a certified public accountant.

The second step, many experts agree, is to ask yourself some difficult questions, such as: How much you can stand to lose over the long term?

"Most people can stand to lose a heck of a lot temporarily," says Mr. Schatsky. The real acid test, he says, is how much of your portfolio's value you can stand to lose over months or years.

As it turns out, most people rank as middle-of-the-road risk-takers, say several advisers. "Only about 10% to 15% of my clients are aggressive," says Mr. Roge.

What's Your Risk Tolerance?

Circle the letter that corresponds to your answer

1. Just 60 days after you put money into an investment, its price falls 20%. Assuming none of the fundamentals have changed, what would you do?

a. Sell to avoid further worry and try something else b. Do nothing and wait for the investment to come back c. Buy more. It was a good investment before; now it's a cheap investment, too

2. Now look at the previous question another way. Your investment fell 20%, but it's part of a portfolio being used to meet investment goals with three different time horizons.

Equation 6.1 is consistent with the notion that utility is enhanced by high expected returns and diminished by high risk. Whether variance is an adequate measure of portfolio risk is discussed in Appendix A. The extent to which variance lowers utility depends on A, the investor's degree of risk aversion. More risk-averse investors (who have the larger As) penalize risky investments more severely. Investors choosing among competing investment portfolios will select the one providing the highest utility level.

Risk aversion obviously will have a major impact on the investor's appropriate risk-return trade-off. The above box discusses some techniques that financial advisers use to gauge the risk aversion of their clients.

Notice in equation 6.1 that the utility provided by a risk-free portfolio is simply the rate of return on the portfolio, because there is no penalization for risk. This provides us with a

2A. What would you do if the goal were five years away?

2B. What would you do if the goal were 15 years away?

2C. What would you do if the goal were 30 years away?

3. The price of your retirement investment jumps 25% a month after you buy it. Again, the fundamentals haven't changed. After you finish gloating, what do you do?

a. Sell it and lock in your gains b. Stay put and hope for more gain c. Buy more; it could go higher

4. You're investing for retirement, which is 15 years away. Which would you rather do?

a. Invest in a money-market fund or guaranteed investment contract, giving up the possibility of major gains, but virtually assuring the safety of your principal b. Invest in a 50-50 mix of bond funds and stock funds, in hopes of getting some growth, but also giving yourself some protection in the form of steady income c. Invest in aggressive growth mutual funds whose value will probably fluctuate significantly during the year, but have the potential for impressive gains over five or 10 years

5. You just won a big prize! But which one? It's up to you.

6. A good investment opportunity just came along. But you have to borrow money to get in. Would you take out a loan?

a. Definitely not b. Perhaps c. Yes

7. Your company is selling stock to its employees. In three years, management plans to take the company public. Until then, you won't be able to sell your shares and you will get no dividends. But your investment could multiply as much as 10 times when the company goes public. How much money would you invest?

a. None b. Two months' salary c. Four months' salary

Scoring Your Risk Tolerance

To score the quiz, add up the number of answers you gave in each category a-c, then multiply as shown to find your score points points points











If you scored .

9-14 points 15-21 points 22-27 points

Conservative investor Moderate investor Aggressive investor

Source: Reprinted with permission from The Wall Street Journal. © 1998 by Dow Jones & Company. All Rights Reserved Worldwide.

convenient benchmark for evaluating portfolios. For example, recall the earlier investment problem, choosing between a portfolio with an expected return of 22% and a standard deviation ct = 34% and T-bills providing a risk-free return of 5%. Although the risk premium on the risky portfolio is large, 17%, the risk of the project is so great that an investor would not need to be very risk averse to choose the safe all-bills strategy. Even for A = 3, a moderate risk-aversion parameter, equation 6.1 shows the risky portfolio's utility value as 22 -(.005 X 3 X 342) = 4.66%, which is slightly lower than the risk-free rate. In this case, one would reject the portfolio in favor of T-bills.

The downward adjustment of the expected return as a penalty for risk is .005 X 3 X 342 = 17.34%. If the investor were less risk averse (more risk tolerant), for example, with A = 2, she would adjust the expected rate of return downward by only 11.56%. In that case the utility level of the portfolio would be 10.44%, higher than the risk-free rate, leading her to accept the prospect.


A portfolio has an expected rate of return of 20% and standard deviation of 20%. Bills offer a sure rate of return of 7%. Which investment alternative will be chosen by an investor whose A = 4? What if A = 8?

Because we can compare utility values to the rate offered on risk-free investments when choosing between a risky portfolio and a safe one, we may interpret a portfolio's utility value as its "certainty equivalent" rate of return to an investor. That is, the certainty equivalent rate of a portfolio is the rate that risk-free investments would need to offer with certainty to be considered equally attractive as the risky portfolio.

Now we can say that a portfolio is desirable only if its certainty equivalent return exceeds that of the risk-free alternative. A sufficiently risk-averse investor may assign any risky portfolio, even one with a positive risk premium, a certainty equivalent rate of return that is below the risk-free rate, which will cause the investor to reject the portfolio. At the same time, a less risk-averse (more risk-tolerant) investor may assign the same portfolio a certainty equivalent rate that exceeds the risk-free rate and thus will prefer the portfolio to the risk-free alternative. If the risk premium is zero or negative to begin with, any downward adjustment to utility only makes the portfolio look worse. Its certainty equivalent rate will be below that of the risk-free alternative for all risk-averse investors.

In contrast to risk-averse investors, risk-neutral investors judge risky prospects solely by their expected rates of return. The level of risk is irrelevant to the risk-neutral investor, meaning that there is no penalization for risk. For this investor a portfolio's certainty equivalent rate is simply its expected rate of return.

A risk lover is willing to engage in fair games and gambles; this investor adjusts the expected return upward to take into account the "fun" of confronting the prospect's risk. Risk lovers will always take a fair game because their upward adjustment of utility for risk gives the fair game a certainty equivalent that exceeds the alternative of the risk-free investment.

We can depict the individual's trade-off between risk and return by plotting the characteristics of potential investment portfolios that the individual would view as equally

Figure 6.1 The trade-off between risk and return of a potential investment portfolio.

Figure 6.1 The trade-off between risk and return of a potential investment portfolio.

Standard Deviation Return Quadrants

CHAPTER 6 Risk and Risk Aversion 161

attractive on a graph with axes measuring the expected value and standard deviation of portfolio returns. Figure 6.1 plots the characteristics of one portfolio.

Portfolio P, which has expected return E(rP) and standard deviation o>, is preferred by risk-averse investors to any portfolio in quadrant IV because it has an expected return equal to or greater than any portfolio in that quadrant and a standard deviation equal to or smaller than any portfolio in that quadrant. Conversely, any portfolio in quadrant I is preferable to portfolio P because its expected return is equal to or greater than P's and its standard deviation is equal to or smaller than P's.

This is the mean-standard deviation, or equivalently, mean-variance (M-V) criterion. It can be stated as: A dominates B if

and and at least one inequality is strict (rules out the equality).

In the expected return-standard deviation plane in Figure 6.1, the preferred direction is northwest, because in this direction we simultaneously increase the expected return and decrease the variance of the rate of return. This means that any portfolio that lies northwest of P is superior to P.

What can be said about portfolios in the quadrants II and III? Their desirability, compared with P, depends on the exact nature of the investor's risk aversion. Suppose an investor identifies all portfolios that are equally attractive as portfolio P. Starting at P, an increase in standard deviation lowers utility; it must be compensated for by an increase in expected return. Thus point Q in Figure 6.2 is equally desirable to this investor as P. Investors will be equally attracted to portfolios with high risk and high expected returns compared with other portfolios with lower risk but lower expected returns. These equally preferred portfolios will lie in the mean-standard deviation plane on a curve that connects all portfolio points with the same utility value (Figure 6.2), called the indifference curve.

To determine some of the points that appear on the indifference curve, examine the utility values of several possible portfolios for an investor with A = 4, presented in Table 6.1.

Figure 6.2

The indifference curve.

Figure 6.2

The indifference curve.

Risk Averse Indifference Curve
Table 6.1 Utility Values of Possible Portfolios for Investor with Risk Aversion, A = 4

Expected Return, E(r )

Standard Deviation, a

Utility = E(r) - .005Aa2



10 - .005 X 4 X 400 = 2



15 - .005 X 4 X 650 = 2



20 - .005 X 4 X 900 = 2



25 - .005 X 4 X 1,150 = 2

Note that each portfolio offers identical utility, because the high-return portfolios also have high risk.


a. How will the indifference curve of a less risk-averse investor compare to the indifference curve drawn in Figure 6.2?

b. Draw both indifference curves passing through point P.

Lessons From The Intelligent Investor

Lessons From The Intelligent Investor

If you're like a lot of people watching the recession unfold, you have likely started to look at your finances under a microscope. Perhaps you have started saving the annual savings rate by people has started to recover a bit.

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  • Jo Hurdle
    Which investment alternative will be chosen by investor whose A=4?
    3 years ago

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