Efficient Markets and the Portfolio Theorem

In the 1960's, economists developed a theory of efficient markets, also known as the "random walk" hypothesis. The efficient markets hypothesis states that the best information about a tradable security, such as a company's common stock, is always embedded in the security's price. Therefore, you cannot take advantage of any known information to get an excess return from trading stocks.

Suppose that on the basis of widely-known information it became possible to predict that stock X would earn an especially high rate of return. In that case, traders would sell other securities to buy X, causing the price of X to go up until the expected excess return disappears. In an efficient market, this adjustment would take place in an instant.

There is a joke about an economist walking down the street, and his friend tells him that there is a $20 bill on the sidewalk. "Can't be there," says the economist. In an efficient market, there are no $20 bills lying around waiting to be picked up.

The efficient markets hypothesis says that all new information arrives randomly. If it were predictable, it would not be new information! If new information arrives randomly, and stock prices only respond to new information, then stock prices will move randomly. Every instant, regardless of past behavior, a stock price has about a 50-50 chance of going up or going down. If someone predicts that a particular stock will go up, that prediction has a 50-50 chance of coming true.

A statistical process in which something has a 50-50 chance of going up or down is called a random walk. The efficient markets hypothesis says that stock prices will follow a random walk. Actually, there is a slight upward bias in stock prices, because over a long period of time, stocks earn a positive average return. This is called a "random walk with upward drift."

Individual investors and Wall Street analysts put a lot of effort and resources into picking stocks. They argue over whether a strategy of investing in "value" stocks works better than a strategy of investing in "growth" stocks. They argue about whether you should buy stocks with "momentum" (i.e., their prices have risen recently) or instead take a "contrarian" position (buying stocks whose prices have fallen recently).

According to the efficient markets hypothesis, all of this effort to come up with trading strategies is wasted. You can do just as well picking stocks by throwing a dart at the list of stocks on the financial page as you can be spending time and effort doing research or listening to a particular adviser, broker, or strategist.

The efficient markets hypothesis also says that there is no point in trying to time the market. Market timing means trying to guess when stocks are undervalued or overvalued, and to buy and sell accordingly. The "Fed model" to which we referred in the previous section is a formula for trying to time the market. If the efficient markets hypothesis holds, then the Fed model and other market timing formulas are of no value in predicting the future course of the market. When the model signals "buy," the stock market only has a 50-50 chance of going up. When the model signals "sell," the stock market still has a 50-50 chance of going up.

To test the efficient markets hypothesis, you have to compare it to an alternative. An alternative might be the hypothesis that the stock recommendations of the most highly-paid analysts will outperform the market. Another alternative might be the hypothesis that using the Fed model to trigger buying and selling decisions will outperform the market.

In almost all tests, the efficient markets hypothesis holds up well relative to the alternatives. There is no formula or strategy that can enable a trader to make excess profits reliably.

Markets tend to be efficient where there are many, well-informed traders. This would include anything traded on the major exchanges, including stocks, bonds, international currencies, and farm commodities (wheat, soybeans, etc.). The market for a particular type of used guitar might not be so efficient.

For each of the following markets, comment on whether you think it will be efficient. Explain your reasoning.

An economist gets into a traffic jam and says, "I'm not even going to try to change lanes." Explain the economist's behavior in terms of the theory of efficient markets.

In an efficient market, expected events are already factored into stock prices. Everyone knows that retail stores earn much of their profits during the Christmas season. You cannot make an excess return by buying stock in Circuit City in October. On the other hand, if Circuit City's sales are much higher (or lower) than expected this November, its share price will rise (or fall) as soon as investors become aware of the news.

Risk, Return, and the Portfolio Theorem

Bonds issued by the U.S. Treasury have a return that is essentially guaranteed. Other securities tend to be riskier. For example, corporate bonds suffer from the risk that a corporation could go bankrupt. As of July, 2002, the risk of bankruptcy appeared to be low for Freddie Mac, but it appeared to be high for WorldCom. The rate of interest on bonds issued by Freddie Mac was close to the rate on Treasuries. The rate of interest on Worldcom bonds was much higher.

Stocks also are risky securities. In any given year, some stocks will go up sharply while others will decline dramatically.

An economic measure of risk is based on the statistical concept of variance. The variance is the average squared deviation from the mean outcome. For example, if we flip two coins, we could get HH, HT, TH, or TT. If we score one point for each head, then on average we will get 4/4 = 1 point. The variance will be

variance = (1/4)[(2-1)2 + (1-1)2 + (1-1)2 + (0-1)2] = 1/2

Formulas aside, the issue is that you do not know ahead of time exactly what the rate of return will be when you invest in a stock. There are many plausible scenarios, some of which will be good for the company and some of which will be bad for the company. If you take an average across all of the plausible scenarios, that average is a measure of the mean return or expected return. If you look at how widely the scenarios differ from one another, that is a measure of the risk or the variance of the return.

For example, if you buy stock in a major utility, such as Pepco, you take relatively little risk. Pepco is unlikely to turn in a spectacular performance, and it is unlikely to go bankrupt. Pepco is a low-variance stock.

On the other hand, you buy stock in a young biotech firm, you take a large risk. If the firm can bring valuable drug treatments to market within ten years, it could be a big winner. If not, then you stand to lose every dollar that you invest. The biotech firm is a high-variance stock.

As investors, we prefer lower variance. That is, if we were given the choice between a sure $10,000 or a coin flip with a 50-50 chance of winning $20,000, we would take the sure $10,000.

Of course, we also prefer higher expected return. If we were offered a coin flip where the payoffs are $25,000 for heads and $5,000 for tails, we would prefer that to a coin flip where the payoffs are $20,000 for heads and $0 for tails.

The interesting decisions are where in order to get a higher return you need to take a larger risk. For example, would you prefer a sure $10,000 or a coin flip where you get $25,000 for heads and $1000 for tails?

If two stocks have the same expected rate of return, a portfolio consisting of both stocks will have the same return but a lower variance, as long as the stocks are not perfectly correlated with each other. If the stocks were perfectly correlated, then they would always move up or down together by the same amount. In reality, stocks are influenced by different factors, and their prices do not all move together. The lower the rate of correlation among stocks in a portfolio, the lower will be the variance of the portfolio compared with the variance of the individual stocks. Because the variance of a portfolio is less than the variance of an individual stock, diversification reduces the risk of a stock portfolio.

Many people understand that diversification reduces risk. However, some people interpret this as meaning that diversification deprives you of a chance of earning a large return. You will see financial journalists and others argue that the way to get the best return is to concentrate on a few stocks.

In fact, the portfolio theorem says that a diversified portfolio is optimal for any desired combination of risk and return. It is usually called the portfolio separation theorem, because it separates the decision about how much risk to take from the decision of which stocks to hold in a portfolio. The theorem states that everyone should have holdings that combine some amount of risk-free securities (short-term Treasuries) and some amount of the well-diversified stock market portfolio. People who prefer low risk should put relatively more of their wealth into the risk-free component; those who are willing to take more risk in order to achieve a higher return should hold relatively more of their wealth in the diversified stock portfolio, and not as much in the risk-free securities.

For example, suppose that the risk-free rate of return is 1 percent, and the expected rate of return on the diversified portfolio of risky stocks is 3 percent. If you put 50 percent of your wealth into the risk-free asset and the other 50 percent intothe diversified portfolio, then your expected rate of return is

(.5)1 + (.5)3 = 2 percent

Now,suppose that you are willing to take more risk to get a higher return. You could shift to having 20 percent of your wealth in the risk-free security and 80 percent of your wealth in the diversified portfolio. Thus, your expected return would be

(.2)1 + (.8)3 = 2.6 percent

The portfolio theorem says that of all the ways of increasing your return, shifting wealth from the risk-free asset to the diversified portfolio is the most efficient. Any other method, including buying a concentrated portfolio of just a few stocks, will produce more risk for the given level of expected return.

The portfolio theorem says that the best trade-off that you can get between risk and return is to exchange some of the riskless asset for shares in the broad market portfolio. An efficient market should ensure that this is the case.

Suppose that moving 10 percent of your portfolio from the riskless asset to the market portfolio increases your expected return by 0.2 percent and increases your risk by 5 percent. This says that the market ratio of risk to return is 0.2/5.0. Now, suppose that you could get a better trade-off by taking stock X out of the market portfolio. That would mean that by selling stock X and buying more of the other stocks, you could raise your expected return by more than 0.2 percent for every 5 percent increase in risk. If this were possible, then everyone would sell stock X and its price would fall until the expected return rose to the point where you no longer could get a good risk-return trade-off for taking X out of the market portfolio.

The portfolio theorem is really an elaboration of the theory of efficient markets. It says that in an efficient market, the trade-off between risk and return will always be equal to the trade-off that you would get from exchanging some of the risk-free asset for some of the market portfolio of risky securities. Each individual stock price will be bid up or down until this trade-off holds at the margin for every stock.

The portfolio theorem says that there is no reason for different people to hold different stock portfolios. Everyone's stock portfolio should consist of the same diversified basket of stocks. The only differences should be that individuals with high risk aversion will hold relatively more of the risk-free asset (short-term Treasury securities) and relatively less of the basket of stocks. Individuals with more tolerance for risk will hold relatively more stocks and relatively less of the risk-free asset.


Combining the efficient markets hypothesis with the portfolio theorem leads to a strategy known as Indexing. The concept of Indexing is to buy all stocks in proportion to their weights in a broad market index, such as the S&P 500 or the Russell 2000. This gives you a diversified portfolio, where you do not try to time the market or to select particular stocks. Indexing means that you "buy and hold" the stocks in the index, which means that you engage in relatively little active stock trading.

When economists developed these theories, they predicted that Indexing would outperform traditional mutual funds and other managed portfolios. Studies have borne out this prediction. As a result, a large share of investor wealth has been shifted into index funds, which use the Indexing strategy. However, there is still a lot of wealth invested in traditional managed funds, which continue to underperform the Index funds. This suggests that the portfolio theorem and the theory of efficient markets still are not sufficiently understood and accepted by investors.