TCS Daily

What's Your
Margin of Safety?

By Arnold Kling - October 15, 2002 12:00 AM

"The margin of safety is always dependent on the price paid. It will be large at one price, small at some higher price, non-existent at some still higher price."
Benjamin Graham, The Intelligent Investor

Are stocks cheap, or are they still overpriced? The answer depends on how large a margin of safety one requires between the intrinsic value of stocks and the price that one is willing to pay.

For an example of someone with a very high margin of safety, consider Pimco's Bill Gross. In Dow 5000, Gross uses a standard method for arriving at intrinsic value. The intrinsic value of the Dow Jones Industrial Average is the price for which the dividend yield plus the real dividend growth rate equals the real rate of interest.

Gross suggests that the real interest rate is the rate on ten-year inflation-indexed securities (TIPs) issued by the U.S. Treasury, which is 3.0 percent. That inflation-adjusted yield is a target for stocks. Furthermore, he assumes that real dividends will grow at 2.0 percent per year, which is reasonable, because this is a good estimate for the inflation-adjusted growth rate for the economy as a whole.

The required dividend yield for stocks is the difference between the real interest rate and the real dividend growth rate, or 3.0 - 2.0 = 1.0 percent. The ratio of the dividends on one unit of the Dow Jones Industrial Average to the level of the Dow should be one percent. Gross estimates that one unit of the Dow yields $185 in dividends. If the dividend yield were 1.0 percent, then the intrinsic value of the Dow should be 18,500.

Why is the Dow not at 18,500? Because of the margin of safety. Nobody wants to pay the intrinsic value for stocks. They want to pay less than that, in order to have a margin of safety. Graham himself sometimes spoke of a 50 percent margin of safety, meaning that if the intrinsic value is 18,500 one might be willing to pay 9,250.

Graham's "margin of safety" plays the role in stock market valuation that economists usually assign to something called "the risk premium." However, this is a case of bad economic jargon driving out a useful practitioner's concept. There is no way for most economists, much less ordinary investors, to have intuition about what is a reasonable risk premium. But anyone can grasp the concept of a margin of safety.

Gross expresses his argument for a Dow of 5,000 in terms of a risk premium. But it is easy to convert his risk premium to a margin of safety. Since he says that he would find the Dow a buy at 5000, and his own figures give an intrinsic value of 18,500, he is only willing to pay 27 percent of intrinsic value for the Dow. His margin of safety is 73 percent.

Incidentally, venture capitalists - who advertise themselves as the riverboat gamblers of the investment community - use a margin of safety of 90 percent. A venture capitalist wants a rate of return that is a "ten-bagger," or 1000 percent, which means that if they put $10 million into a company they think that the shares they are buying are really worth $100 million.

What Does the Market Think?

The market value of the Dow does not depend on any one individual's margin of safety. It depends on the margin of safety of the entire market of investors. Relative to the market, if you have a comparatively large margin of safety, stock prices will seem too high to you. If you have a relatively small margin of safety, then stocks will appear to be cheap.
If Bill Gross is serious about his 73 percent margin of safety, but most other investors are willing to live with a smaller margin of safety, then the Dow will never drop to his target level. He will miss out on earning a rate of return that is considerably higher than the 3 percent he could get by buying TIPs.

On the other hand, if you buy the Dow at 8000 and the market permanently adopts Gross' margin of safety, it would take you a very long time (several lifetimes, in fact), for your returns to outperform TIPs. In the less-than-very-long run, changes in the market margin of safety dominate changes in intrinsic value as a source of the variation in stock market returns. Or, as Gross puts it, over the past hundred years,

"Ninety percent of the market's real return then came from factors other than earnings growth."

Stocks will always be priced below intrinsic value. How much below depends on the market's margin of safety. If the margin of safety gets larger, then prices will fall and returns will be low. If the margin of safety gets smaller, then prices will rise and returns will be extra-ordinarily high.

What do Economists Know?

As an economist, I feel qualified to have an opinion about the elements that go into the calculation of intrinsic value. In fact, I think that the intrinsic value of the Dow is higher than 18,500, because I believe that Gross is using an unrealistic indicator of the real interest rate. The market for TIPs is very thin, and I suspect that they are underpriced. (Putting my money where my mouth is, I have a lot of TIPs in my portfolio.) If TIPs were priced higher, then their yield would be lower, and this indicator of the real interest rate would be lower. This would raise the intrinsic value of the Dow beyond 18,500.
I also think that there is some potential for real economic growth to exceed 2 percent, which also would boost one's estimate of intrinsic value. Nonetheless, I would be willing to use 18,500 as a benchmark.

On the other hand, I feel quite unqualified to predict what the market's margin of safety will be. If the Dow is at 7600, then the margin of safety is around 60 percent. Gross thinks that it belongs at 73 percent, so that you should be able to buy stocks for 27 cents per dollar of intrinsic value. My personal margin of safety is closer to 50 percent, but I cannot claim to speak for the market.

I cannot rule out the possibility that the market's margin of safety could reach 73 percent, or even go higher. However, the fact that the margin of safety might for a period of time get as large as 73 percent is not an argument against buying stocks today. Buying stocks is a mistake only if the margin of safety expands to 73 percent and remains stuck there. As long as the margin of safety does not increase permanently, buying stocks will pay off.

For what it's worth, my reading of the historical record is that the market margin of safety is very unlikely to get permanently stuck at the level that Gross is advocating. I use the ratio of nominal GDP (in billions of current dollars) to the Dow as a crude indicator of the margin of safety. Suppose that Gross is right, and that the right level for the Dow is 5000. In that case, the ratio of nominal GDP to the Dow would be just over two. That means that a ratio of two corresponds to Gross' margin of safety of 73 percent.

Since 1959, the ratio of nominal GDP to the Dow has been less than two from 1959-1974 and from 1992 to present, which suggests that the market margin of safety was lower than 73 percent. However, the ratio was more than two from 1975-1991, which suggests that during that period the market margin of safety was higher than 73 percent. Based on that, one might say that for the majority of the past forty years the market's margin of safety has been less than what Gross is recommending.

The way I read the data, the chance that the market will permanently adopt a margin of safety of 73 percent or higher is close to nil. In fact, I believe that the chances are remote that the market's margin of safety will always remain as large or larger than the current 60 percent. At some point, the market's margin of safety will recover to lower levels, and that would mean that investors who buy today will enjoy superior returns.

Editor's note: For another commentary on the issues raised by Pimco's Bill Gross, see Why Stocks Don't Stink. Also, here is a short biography of Benjamin Graham.

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