Time diversification (Investments)

The Fallacy of Time Diversification:

Paul Samuelson and others have argued that the notion of time diversification is fallacious. Even though the uncertainty about the average rate of return diminishes over a long time period, it also compounds over a longer time period. Unfortunately the latter effect dominates. Hence the total return becomes more uncertain as the investment horizon lengthens.

An example will illustrate this point. Suppose the expected one year return on a stock is 15 percent with a standard deviation of 30 percent. If you hold the stock for 5 years, the expected annual return over 5 years remains at 15 percent, but the standard deviation of the average return over 5 years declines from 30 percent to 13.42 percent (30/√5)3. Even though the standard deviation of the 5 year return is now significantly lower at 0.1342 (or 13.42 percent) a disappointment of one standard deviation will affect the terminal wealth by a factor of (1—0.1342)5 = 0.487. This certainly has a larger impact than a swing of 30 percent in one year. While the confidence band around the expected rate of return narrows with investments life; the dollar confidence band widens.

The above result has an important implication: although an investor is less likely to lose money over a longer horizon, as compared to a shorter horizon, the magnitude of his potential loss clearly increases with the length of his investment horizon. Hence the critics of time diversification argue that if you prefer a risk less investment over a shorter investment horizon, you should prefer a risk less investment for over a longer investment horizon as well. Put differently, your risk exposure should not depend on your investment horizon.

Resurrection of Time Diversification:

Although the above critique of time diversification is mathematically correct, all is not lost for those who believe in the principle of time diversification. There remain some valid reasons why you should still condition your risk posture on your investment horizon. Two of them deserve a particular mention.

1. There is some evidence that stock returns are not serially independent but tend to mean revert over long intervals. This means that it is more likely that a below average return may be followed by an above average return than another below average return. Given this tendency of stock returns to mean revert, the dispersion of terminal wealth increases at a slower return than what is implied by serially independent returns. (Remember that the critics of time diversification assume a perfectly efficient market in which stock returns are serially independent).
2. You may be inclined to accept more risk over a longer horizon as you have greater scope to adjust your consumption and work habits. If a risky investment performs poorly at the beginning of a short horizon, there is little you can do to compensate for loss of wealth. Over a long horizon, however, you can postpone consumption and work harder to achieve your financial goals.

Benjamin Graham on Asset Allocation:

Benjamin Graham, the most revered investment guru, suggested that the investor should never have less than 25 percent or more than 75 percent of his funds in common stocks, with a consequent inverse range of between 75 percent and 25 percent in bonds. According to him the standard distribution should be 50:50 between the two major investment mediums. As he put it, we are convinced that our 50:50 version of this approach makes good sense for the defensive investor. It is extremely simple; it aims unquestionably in the right direction; it gives the follower the feeling that he is at least making some moves in response to market developments; more important of all, it will restrain him from being drawn more and more heavily into common stocks as the market rises to more and more dizzy heights.

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