October 13, 2006 Letters to the Editor

Updated: October 13, 2006.

Article on Capitalization-Weighted Stock/Bond Allocations

I received this letter from Rob Bennett.

I am going to bring forward here a question/comment about the Efficient Market Hypothesis that I have had in my head for years, but that never seems to come up in discussions of it. It comes up in a tangential way in your article.

The idea behind the EMH seems to be that you want to participate in the economic growth of humankind and you don't want to guess where it is going to come from. So you invest in everything, sure that that way you will get your share of the entire pie.

You point to several problems with how the theory is executed in the real world. One is your focus, how allocations between stocks and bonds are set. You make reference to another problem, that to pull this off properly you would need to be invested in all the corporations of the world, not just those of the United States (and there are all sorts of complications that arise when trying to do that).

I have a concern that I believe is even more fundamental.

Why is the cash asset class not included in the mix?

Cash is not the same thing as stocks or bonds. Cash has economic value. It should be included in the mix.

My sense is that cash was very low on peoples' priority lists at the time this theory was developed. That's just a prejudice. Cash has pros and cons of its own, just as stocks and bonds do. There are times when stocks are superior, there are times when bonds are superior, there are times when cash is superior (and there are times when other asset classes are superior).

This has become an especially important point since the introduction of TIPS and IBonds, which I think of as Super-Cash (because of the inflation protection offered). Even cash without inflation protection offers some value, though. I do not understand on a theoretical basis why it was not included.

This theory seems to me to have been developed by people who had a pro-stock bias. They seem to have not even considered the possibility that there are circumstances in which non-stock asset classes rise to the top. This flaw is so fundamental to the EMH construct that everything generated from it shares the flaw.

HERE IS MY RESPONSE

Thank you.

To be more precise about “the idea behind the EMH:”

Dr. Harry Markowitz established an overall structure and definitions.

From pages 399 and 400 of David Dreman’s “Contrarian Investment Strategies: The Next Generation.”

“..According to Markowitz, rational investors should be risk-averse. This means they should not be willing to take higher risk without receiving larger returns. Risk was defined by Markowitz, as by all subsequent efficient market researchers, in terms of short-term market fluctuations. The greater the volatility of the security or portfolio, the greater the risk..”
“..”
“..An efficient portfolio would produce the highest level of return for a given level of risk..”

Later researchers (Sharpe-Lintner-Mossin) introduced simplifying assumptions (known as the Capital Asset Pricing Model CAPM) which, in essence, equate the optimal portfolio to the market as a whole.

That is, Dr. Markowitz set the structure for “An Efficient Something-Or-Other That Is Hard-To-Calculate Hypothesis.” Simplifying assumptions converted this into the “Efficient Market Hypothesis.”

The “Hard-To-Calculate” problem has disappeared. There remains a much more difficult problem: making such calculations meaningful.

From page 401 of David Dreman’s “Contrarian Investment Strategies: The Next Generation” regarding this later research:

“The important concept is that the market or its surrogate stock price index is seen as the optimal risk portfolio. No other combination of securities can produce a better trade-off between risk and reward..”
“..”
“In order to receive an above market return, according to the theorists, the investor is assumed to be able to borrow at the T-bill rate (the risk free rate), and then leverage the portfolio, reinvesting the borrowed funds into the market..The more one borrows, of course, the greater the risk, but if the market behaves itself, the larger the return..”

From the first footnote: "This is theoretically defined as the complete universe of risky investments available for purchase, with each weighted for its share of the total market value..As noted, the S&P500 is frequently used, although there are certainly other choices."

Advocates of the Efficient Market Hypothesis "don't to guess where it is going to come from." They assert, as a matter of faith, that it is impossible to improve their odds in any meaningful way.

Concerning Cash:

I have a concern that I believe is even more fundamental.

Why is the cash asset class not included in the mix?

Cash is not the same thing as stocks or bonds. Cash has economic value. It should be included in the mix.

In one sense, cash is included. We don’t see it explicitly because it causes a “divide by zero” problem.

The Sharpe ratio of an investment is (the average return of an investment in excess to the risk free return) divided by the standard deviation of that investment.

Cash is the risk free investment.

The mathematics is set up so that cash has no variation at all. Or, at least, that is the approximation.

Cash has a standard deviation of zero. To calculate the Sharpe ratio of cash, you have to divide by zero.

Mathematicians took care of this kind of issue a long time ago. If a calculation has a “divide by zero” problem at a single point and if there is an obvious answer that makes sense, you use the obvious answer. For example, if you divide the formula x=3*t by the formula y=4*t, the ratio (x/y) = 3/4 unless t=0. If t=0, there is a “divide by zero” problem. Your computer (or calculator) will be unhappy. It makes sense to report the ratio as 3/4 even when t=0. Mathematicians do this. They refer to this special value as a LIMIT.

Since the market is assumed to allocate everything else efficiently, the obvious answer is that the best cash allocation equals that of the overall market.

However, the Efficient Market mathematics is set up so that an investor varies his cash allocation only according to his tolerance for volatility.

Concerning Timing:

There are times when stocks are superior, there are times when bonds are superior, there are times when cash is superior (and there are times when other asset classes are superior).

It is not a prejudice against cash so much that it is a prejudice against any kind of market timing whatsoever. The theory is set up so that only changes in your personal situation, such as your age or marital situation, are relevant to your cash allocation.

The fundamental flaw:

This theory seems to me to have been developed by people who had a pro-stock bias. They seem to have not even considered the possibility that there are circumstances in which non-stock asset classes rise to the top. This flaw is so fundamental to the EMH construct that everything generated from it shares the flaw.

The theory was developed for the purpose of defining the best way to invest in the stock market.

The theory was simplified by assuming that the best way to invest in the stock market is to invest in the market as a whole. This leads to the conclusion that the best way to invest in the stock market is to invest in the market as a whole.

The theory was structured for a fixed allocation between a cash equivalent and stocks. The risk free component was short-term treasuries (T-Bills), a cash equivalent. Other securities, such as bonds, were introduced later.

We accept theories that have internal inconsistencies so long as they give us meaningful answers. We make refinements to fill in the gaps. Very often, there is a hope that a relationship will be stable enough to produce good projections for a few decades as opposed to centuries. We have not seen this kind of stability with Efficient Market approaches.

The Efficient Market Hypothesis provided supporting rationale for capitalization weighted, broad market index funds. Yet, it is the cost efficiency of such funds that endures.

Attempts to build upon the Efficient Market Hypothesis have to come back to capitalization weighted allocations and special circumstances (temporarily inefficient markets). This conflicts with other approaches by the same researchers such as slice-dice-and-rebalance. The same people tell you that you can’t beat the market. Then they offer to do better nonetheless.

Capitalization Weighted Stock-Bond Allocations

Letters to the Editor in 2006

Letters to the Editor in 2005