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Bill is considering investing in a mining company whose stock is selling at $80 per share. After careful research he determines that there is a 60% chance the stock price will drop and only a 40% chance it will go up. He decides to buy it anyway. Should we lock him up where he cannot hurt himself?
If you said, “we don’t have enough information to answer the question,” go to the head of the class. In fact it may make perfect sense to make such an investment if:
a. The investor can afford the loss, and
b. The likely loss is small but the possible gain is large.
Suppose for example that the stock has a 60% probability of dropping by $10 per share and a 40% probability of rising by $20 per share. Bill may find it worth taking the risk of a $10 loss in order to have a chance at a $20 gain.
This brings us to a concept described by the technical term, “expectation.” Expectation includes probabilities of gain or loss and the likely result in each case. To calculate expectation we simply take the probability of each possible outcome and multiply it by the result of that outcome. Then we add up all those values to get the total expectation. In the case of Bill’s stock purchase, we have a 60% probability of losing $10 per share and a 40% probability of gaining $20 per share. Total expectation is then:
0.6 X (-$10/share) + 0.4 X (+ $20/share) = -$6/share + $8/share = +$2/share
(Note the minus signs in there.)
Bill’s expectation is a gain of two bucks a share. If he can afford the loss, he may decide that the risk is worth taking.
This adds more science to the question of when we should take a risk and when we should avoid the hazard. We’re seldom 100% confident of the outcome of any decision. However by considering both the likelihood of each outcome and the effects of that outcome we can give ourselves a better chance to get what we want. If you’re considering a new job you might think about how likely it is to work out the way you want it to. Then you can think about what you will gain if it does work out and what you will lose if it doesn’t.
If you’re mathematically inclined you might even put some numbers on those probabilities and outcomes. If not, you can make better decisions by just thinking about the different possibilities. How likely is each outcome and how desirable is it? You can do the same with many decisions such as buying a new home or car, where to go on your vacation etc.
Now returning to our mining stock example, that was oversimplified of course. Stock prices can change by almost any amount, not just $10 or $20. It might lose $2.13, gain $5.84, or lose or gain most any other amount. If Bill does a good analysis he will consider the probabilities of all possible changes in the price of that stock. Such an analysis is quite mathematical and beyond the scope of this blog, so I’ll let it rest there.
However the multiple possible outcome issue does have similarities with other types of decisions. Most have lots of possibilities to consider. The new job may not work out exactly as you expected, but it may still provide enough satisfaction and income to make it worth the change. Or the job may be bad enough to make you wish you had not made the change but still might provide enough income to support your family. You just need to be careful enough to consider the possibilities.
Such decisions may be about your work life, investing money, or supporting a government bailout plan for the economy. In almost all cases there are many possible outcomes, some good, some bad, some great and some terrible. For major decisions it can be valuable to actually calculate the expectations. Even if we don’t do the math, just thinking about it will help us make better decisions. That will help in our personal lives, our family lives, our work lives and our effectiveness as citizens.
“But wait!” you say. “It can’t be that cut and dried. Get out the calculator and determine which way to decide? I don’t think so.”
You’re right. There is another important aspect of this which I’ll discuss next time, one that depends heavily on individual situations, personalities, and temperaments. However the above is enough for today.