Efficient Frontier
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William J. Bernstein

The Duration of Stocks

Location: Pearly Gates

Cast of Characters: 1) Hy Defees, fund manager, late of the Churnum, Burnum, & Spurnum Group, and 2) Saint Peter

Apologies: to Charles Ellis (Investment Policy)

SP: Clue me in, Hy. No one ever told you that snowboarding and Margaritas don’t mix? Too bad, such a promising young man.

Defees: You’re telling me. The buzz is my American Hubris Capital Depreciation Fund was in line for its fifth star. Life’s cruel.

SP: The news at this end ain't good either. The tally looks pretty even, can't tell you if it’s yea or nay. (Scratches his beard thoughtfully.) OK, here’s the deal. You either go to the place where prices are permanently high, or to the other place where there will soon be an 80% fall in the market, with prices staying permanently depressed.

Defees: Pretty easy choice, I’m going to the realm of everlasting high valuations.

SP: You got it. That’s the first set of stairs to the left, then down. (chuckles to self) I lose more money managers that way . . . . .

Sad but true. You see, Mr. Deffes is indeed condemned to an Eternity of low returns—he forgot that he was managing his assets for the Hereafter, and not just the next quarter. Had he thought about it a little, he’d have realized that high prices mean low dividends, and vice versa. Since over very long periods most equity return is due to generations of reinvested dividends, he’d have been much better off with lower prices and higher yields.

If you're having trouble following this, let's start with something more basic. Like a one-year Treasury Bill. A bill is in reality a zero coupon bond, bought at a discount. For example, a 5% bill will sell for $0.9524 and be redeemed at par. If someone purchases this 5% bill, and a few seconds after it is issued yields suddenly rise to 10%, it falls in price to $0.9091, with an immediate loss of 4.55%.

But, if our investor holds the bill to maturity he will receive the full 5% return, the same as if there had been no yield rise/price fall. And beyond one year, it's all gravy—our investor can now reinvest the entire proceeds at double the yield. His "point of indifference" is thus the one-year maturity of the bill; before one year he is worse off because of the yield rise/price fall, after one year he is better off.

Now consider a holder of a 30-year 5% treasury bond. If soon after purchase at par we see the same rise in yield to 10%, our hapless investor has received a financial kick in the solar plexus—the bond is now worth less than 53 cents on the dollar. (And, in fact, this is precisely what happened to bondholders between 1967 and 1979.) . However, a bond is a very different beast, as it throws off coupons that can be reinvested at the higher yield. Because of this the recovery from disaster takes considerably less than 30 years. In fact, it only takes our hapless bondholder 10.96 years to break even. This 10.96 year period is known in financial circles as the duration of the security, and for a coupon-bearing bond is always less than the maturity, sometimes considerably so. (For a zero-coupon bond, maturity and duration are the same.)

There are lots of other definitions of duration, some dizzyingly complex, but "point of indifference" is the simplest and most intuitive. (The other useful definition is the ratio of price to yield change. That is, our 30-year bond will decrease 10.96% in price with each 1% increase in yield.)

To reiterate, after 10.96 years, our unlucky bondholder is better off for the fall in price because of the rise in yield.

Duration is almost always used to describe bonds, but there is no reason why you can't apply the same concept to stocks, as well. It's a simple matter to model the "duration" of the stock market. For example, stocks are currently yielding 1.4%. If they decline 75%, the absolute amount of the dividend remains the same, but you are now investing those dividends at a yield that is four times higher—5.6%. Eventually this will redound to your benefit, and you will wind up better off than at the lower yield/higher price. How long does it take to catch up? It depends on the beginning yield and the magnitude of the decline. My model shows that with today's 1.4% stock yield, a 25% decline would have a duration of 62 years, a 50% decline 50 years, a 75% decline 33 years, and a 90% decline only 19 years.

Skeptics will point out that a 90% stock decline would likely be associated with a decrease in the absolute dividend amount, but even during the Great Depression the real dividend stream of the Dow decreased by only 25%. In fact, the 1929-33 bear market provides a superb reality check of the above paradigm. One dollar invested in stocks on Labor Day 1929 declined in value to 16.6 cents by July 1, 1932 and increased back to par by the end of January 1945—less than 13 years after the bottom.

The dividend yield was 2.6% in September 1929, and for the 30 years after that earnings growth was only 1.8%. Thus, had the crash not occurred then stocks would have returned 4.4% per year, resulting in a "break-even" point with what actually occurred of January 1952, or 22 years, almost exactly the same period predicted by the duration model. Viewed from this perspective, today's market is a good deal more frightening than that of 1929, since a 75% stock decline produces a duration of 19 years at the 2.6% 1929 yield, versus 33 years at the current 1.4% yield.

Certainly, such a wrenching market decline today would wreak havoc on the financial and social structure of the republic, as it did 70 years ago. But at the same time, today's high prices and resultant low yields are no great blessing either.

Is there a way that an individual can shorten the duration of her stock portfolio? Yes. Since the size of the yield influences duration (the greater the yield, the shorter the duration), you can effectively increase the "yield" of your portfolio by adding to it every month. Let's start with the 75% price fall/1.4% yield/33 year duration scenario referred to above. If you start with $10,000 and neither add nor withdraw from your account, you will break even at the 33 year duration. But add in $200 per month and you break even at just over 11 years.

For the truly long-term investor, the results of a prolonged bear or bull market may very well prove of little consequence, or even produce surprisingly paradoxical results. But in reality, equanimity to market declines depends on time horizon. If you’re retired and living off savings, you will neither have enough time to get over the duration hump nor be able to make the contributions to shorten it. If you’re a boomer who is still adding to a decent-sized nest egg, then you will likely have plenty of time. And if you’re a twenty-something just beginning to save, then get down on your knees and pray for the Crash of 1999.

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copyright (c) 1999, William J. Bernstein