Risk Aversion

Risk Aversion

One of the key concepts in finance is the fact that a safe dollar is worth more than a risky dollar.

This important principle compares one safe dollar with one risk dollar. Any one who invests in the stock market is exchanging bird –in-the-hand safe dollars for a chance at a greater number of future dollars.

It is wrong to say that a risk-averse person will not take a risk. We are all risk averse, yet we take risks all the time.

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Risk Aversion and Rational People

Suppose a person is given a choice between the following two alternatives:

Alternative A $100 for certain
Alternative B 50% chance of $100, 50% chance of $0

No rational person would select B. Its average payoff is $50, only half what A offers with certainty.

Now consider another set of choices:

Alternative C $100 for certain
Alternative D 50% chance of $0, 50% chance of $200

D has an average payoff of $100, the same as C.
C, however, is safer than D.
People do not like a risk, and a rational person will choose the certain $100 over the risky $100.

Let’s now consider a more complicated example.

On a television game show, a contestant wins the right to spin a lottery wheel once. The wheel shows numbers 1 through 100, and a pinter selcts one number when the wheel stops. Which payoff schedule should the contestant choose from the four choices listed below.

Choice 1
Resulting Number….Payoff
1-50….$110
51-100….$90
Avg….$100
Choice 2
Resulting Number….Payoff
1-50….$200
51-100….$0
Avg….$100
Choice 3
Resulting Number….Payoff
1-90….$50
91-100….$550
Avg….$100
Choice 4
Resulting Number….Payoff
1-99….$1000
100….-$89,000
Avg….$100

Each of the choices has the same average payoff, but the consequences of the two possible outcomes with each choice vary widely.

Choice 1 is the safest alternative in the minds of many people.

Choice 2 offers a reasonable shot at $200. People who select this option reasons, “If my number doesn’t come up, at least I haven’t lost anything.” From an economic point of view, this logic is faulty. The person did lose something: the certain minimum payoff of $90 associated with Choice 1; this loss is an opportunity cost.
In other words, by choosing 1, a contestant will get at least $90. But the contestant gives up at least $90 in exchange for a try at a bigger return with the other choices.

Choice 3 offers a much higher possible return than 2 but ensures a payoff of at least $50. Some people select this option partly because of the entertainment value of the game.

What about Choice 4, with its high likelihood of a $1,000 payout? If the lottery wheel stops on the number 100, however, the contestant suffers a huge loss. Some people (and some investment portfolios) cannot tolerate any chance of such a loss and consequently could not seriously consider an option such as Choice 4.

Each of these alternatives has analogies in the investment world.

Choice 1 is much like buying shares of a conservative electric utility stock.

Choice 2 is akin to purchasing a stock option.

Choice 3 might be a convertible bond, with its assurance of steady interest income, and a chance for large gains if the underlying stock rises sharply.

Choice 4 is similar to a program of writing naked, out-of-the-money call options. With such a program the likelihood is high that the options will expire worthless (to the call writer’s benefit), but there is also a small chance that the options will become extremely valuable, in which case the call writer is in deep trouble.

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Risk and Time

Peter L. Bernstein, founder of the Journal of Portfolio Management and well respected on Wall Street, said, “Risk and time are dancing partners in an eternal dance.” It is easy to overlook this important point. Probability theory deals with HOW MUCH and HOW LIKELY but says nothing about WHEN. The market crashed in 1929 and in 1987. It is likely to do so again.

Bernstein also said, “Risk and time are opposite sides of the same coin.” How likely is the market to crash tomorrow? A betting person (which investment analysts and advisors typically will not admit to being) is more likely to put money on NO CRASH tomorrow.

On the other hand, how likely is a market crash sometime in the next 50 years? This time frame puts a different light on the situation; most people certainly would agree that the probability of a crash anytime in the next 50 years is greater than the probability of a crash tomorrow.

In finance, we typically measure risk by the variance or standard deviation of returns. Daily returns are different from weekly, monthly, or annual returns. For returns to be comparable, we must measure them over consistent time intervals. The dispersion of a forecast (such as a future stock price) increases indefinitely as the length of the forecast (or holding period) approaches infinity. Logically speaking, the standard deviation of daily stock returns is smaller than the standard deviation of annual returns.

It is important to note that while the returns over a long horizon may be more uncertain, history suggests that over long periods of time there is also less likelihood that the investment will lose money.

Consider the information in Table below:
http://spreadsheets.google.com/ccc?key=pJV5vBExPQ_AehxWIo5vCRA&hl=en

These figures are the result of a 2,500 trial simulation of a $1,000 stock investment assuming an average annual return of 12%, but with a 20% annual standard deviation.

The longer the term of the investment, the greater is the mean return - but the greater the range between the minimum and maximum values.

Note also the longer the term of the investment, the less the likelihood of losing money and the greater the likelihood that the investment will at least keep up with an assumed average inflation rate of 3%.

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Summary:

It is wrong to say that a risk averse person will not take a risk.

People have different degrees of risk aversion; some people are more willing to take a chance than are others.

An opportunity cost is what is given up in exchange for a chance at something better.

"Risk and time are dancing partners in an eternal dance." - Peter Bernstein

Forecast variance increases indefinitely as the length of the forecast period approaches infinity.