One of the central elements in modern finance theory is that of a risk-return tradeoff.
The idea is simply that investors are risk averse, and accordingly must be paid to incur risk. There is, then, a constant trade-off in the investment world: safe investments carry low return, high-return investments aren’t so safe. Fortunately, this conforms with almost everyone’s intuitions.
What exactly is risk, though? Yes, we have an intuitive idea. The guy jumping out of an airplane is taking a risk that the appreciative audience standing on firm ground below is not. Further, if he has neglected to check his gear properly he is taking an extra, unwarranted, risk.
But we can be a good deal more
specific about what the word means in the world of investments. It means the
size of the standard deviation of return. It means the width of that bell curve we've discussed in earlier posts.
Standard Deviation
A standard deviation is the “average
distance from the average” here’s a simple example: there are five dogs in your
neighborhood, and you weigh them. They are each conveniently named with a
single letter. It turns out that the pooches weigh:
Name pounds
A 5
B 7
C 10
D 13
E 15
The average weigh of a neighborhood
dog then, is 10 lbs.
The distance of each dog from that
average is as follows:
Name distance
A 5
B 3
C 0
D 3
E 5
The average of those numbers is 3.2, so that would be the standard deviation of
dog poundage.
In a neighborhood with a wider range
of dog types, and so of dog sizes, you’d expect the standard deviation to be
wider. At any rate, as you can see from the bell curve portrayed earlier this week, the curve is getting close to zero by the time it gets out to two
standard deviations [or two “sigma"] from the mean. In our (small) neighborhood
sample, then, it is unsurprising there are no dogs whose weight is two sigma, or in this case 6.4 lbs.
away from the mean.
In a large population, randomly
chosen so that the bell curve should apply, we would expect that 68 percent of
the dogs would fall within one sigma of the mean, 95 percent within two sigma,
and 99.7 percent within three.
It may not be intuitively clear why we should call standard deviation a good proxy for risk. One doesn’t normally speak of the “risk” of encountering a
smaller-than-usual dog, after all. And only trespassers need worry about the risk of
encountering a larger-than-usual dog. Even there, the size of the dog is a
rather unsatisfactory proxy for what the trespasser ought to be worried about.
So why would Harry
Markowitz, one of the founders of modern portfolio theory, write that “if … ‘risk’
[were replaced] by ‘variance of return,’ then little change of apparent meaning
would result”?
Chiefly, because investments differ from each other according to the predictability of their return from one period to another. Those we call low-risk are designed precisely to
deliver boringly consistent (but low) returns from one period to another.
Corporate bonds deliver a steady contracted-for stream of interest payments.
They have a variation in return (thus, a standard deviation, or risk) only to
the extent that the corporation might go bust and default on the payments. The
chancier the future of this corporation, the wider the standard deviation will
be.
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