The Myth of Time Diversification

Something my Financial Risk Analysis professor mentioned last week:

A common argument is that stocks are safe investments in the long run because of “time diversification.” Buy-and-hold advocates argue that if you hold a stock over a long period of time, the “good” and “bad” returns will tend to cancel each other out, so time will diversify a portfolio just like how investing in multiple assets diversifies a portfolio.

The time diversification argument is only valid if there is a mean-reversion in stock returns – ie there is a negative serial correlation of returns. (In non-academic speak, this means that if returns are high today, they will be low tomorrow on average). Let’s examine the three cases of stock returns (positive correlation, no correlation, and negative correlation) and see why buy-and-hold fails in each case:

Positive correlation
Research has shown that in the short run, stock returns are positively serially correlated. This makes sense: if the S&P closed high today, it will most likely be higher tomorrow, as long as there isn’t a huge piece of bad news. Conversely, if the market closed lower, it will most likely follow its downward trend. This is how trend-followers make money. So time diversification doesn’t work in the short run.

No correlation
Even if you follow traditional academic thought and claim that stock prices follow a random walk, ie stock returns are serially uncorrelated, time diversification still does not work here. Investing over a long horizon may increase your returns over a long time, but it also increases your risk relative to expected returns. The saying “markets can remain irrational longer than you can remain liquid” holds true here – if prices follow a random walk and drift downwards for 10 years and upwards for 12 years, your return might be positive but your variance remains huge.

Negative correlation
Now let’s move on to the situation that DOES favor time diversification – when stock returns are negatively correlated. Academic research shows that stock returns do exhibit this tendency in the long run, which is nice. So time diversification does help to lower your risk relative to expected return over the long run. However, it’s easy to see that buy-and-hold is the WRONG strategy for such a situation.

Let’s say that stock returns are negatively correlated and stock prices are mean-reverting. This means that if prices were higher than a certain mean, they will eventually come down. If they were lower than the mean, they would rise. The optimal way to make money would be to then buy when prices were below the mean, and sell them when they were above the mean – a surefire way to make money if stock prices were truly mean-reverting. This strategy is known as swing-trading, and is practiced by many traders.

In any of the three cases I highlighted, buy-and-hold falls flat on its face, and yet there is an entire industry of long-only mutual funds, pension funds, “value” investors etcetc that subscribe to the buy-and-hold mantra.

That one schpiel from my professor convinced me that I should be taking his class. Now who says that all academics live in an ivory tower?


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