Risk and time

Irving Fisher, the Yale economics professor most widely remembered for his unfortunate prediction a few days before the crash of 1929 that “stock prices have reached what looks like a permanently high plateau,” published a classic the following year. In today’s post I’m going to look at the relationship between risk and time as described in The Theory of Interest as Determined by Impatience to Spend Income and Opportunity to Invest It (Macmillan, 1930). Don’t start yawning; this is weird psychological stuff! Richard Thaler wrote a short paper, “Irving Fisher: Modern Behavioral Economist," touching on some of these themes.

Fisher equates time preference with human impatience. The impatient man wants income now; the patient man is willing to wait for deferred income. The degree of a person’s impatience depends on four factors: (1) the size of his expected real income stream, (2) its time shape (constant, increasing, decreasing, fluctuating), (3) its composition (food, shelter, education, amusement), and (4) its probability, or degree of risk or uncertainty.

The first factor, size, is fairly straightforward. “In general, it may be said that, other things being equal, the smaller the income, the higher the preference for present over future income; that is, the greater the impatience to acquire income as early as possible.” (p. 72) The time shape of a person’s projected income stream cannot be easily quantified, but here’s the gist. A person who is poor and has no obvious prospects for a change in his situation, one for whom “poverty bears down heavily on all portions of [his] expected life,” wants immediate income even more than future income. A person who has a meager income but expects to double it in ten years is impatient to realize these future earnings. “He may, in fact, borrow money to eke out this year’s income and promise repayments out of his supposedly more abundant income ten years later.” On the other hand, a person approaching retirement may want “to save from his present abundance in order to provide for coming needs.” (p. 74) The third factor, composition, is not critical to Fisher’s theory, so he passes over it quickly. But then there is risk.

Most people view risk or uncertainty as greater in the distant future than in the immediate future, damping down impatience; they save for a rainy day. Occasionally risk is higher in the near term than in the perceived distant future—during a strike, for instance, thus enhancing a person’s impatience. But what if risk applies to all periods alike, from the immediate to the remote? Fisher writes: “Such a general risk . . . explains why the bondholder is content with a lower average return than the stockholder. The bondholder chooses fixed and certain income rather than a variable and uncertain one, even if the latter is, on the average, larger. In short, a risky income, if the risk applies evenly to all parts of the income stream, is equivalent to a low income. And, since a low income, as we have seen, tends to create a high impatience, risk, if distributed in time, uniformly or fairly so, tends to raise impatience.” (p. 78). I assume he means that the investor faced with a risky income (minimally) withdraws his dividends as they are issued and reinvests none of them.

Fisher acknowledges that there are “exceptional individuals of the gambler type in whom caution is absent or perverted. Upon these, risk will have quite the opposite effects. Some persons who like to take great speculative chances are likely to treat the future as though it were especially well endowed, and are willing to sacrifice a large amount of their exaggerated expectations for the sake of a relatively small addition to their present income. In other words, they will have a high degree of impatience. The same individuals, if receiving an income which is risky for all periods of time alike, might, contrary to the rule, have, as a result, a low instead of a high degree of impatience.” (p. 79)

Admittedly, by the time this book appeared Fisher might not have been in the best of moods. And after this week’s market correction perhaps many long-only investors are starting to become impatient. Is this the start of a major breakdown? I have no idea. Whatever the case, I find Fisher’s description of investment income as similar to the income of the fated pauper decidedly downbeat.