Hedging And Diversification

A portfolio that is invested in multiple instruments whose returns are uncorrelated will have an expected simple return which is the weighted average of the individual instruments’ returns. Its volatility will be less than the weighted average of the individual instruments’ volatilities. This is diversification. Diversification is the “free lunch” of finance. It means that an investor can reduce market risk simply by investing in many unrelated instruments. The risk reduction is “free” because expected returns are not affected. The concept is often explained with the age-old saying “don’t put all your eggs in one basket.”

Diversification should not be confused with hedging, which is the taking of offsetting risks. With diversification, risks are uncorrelated. With hedging, they have negative correlations.

A common misperception is the notion that the more uncorrelated risks a portfolio is exposed to, the lower that portfolio’s overall market risk will be. This is not true. If a portfolio is leveraged in order to take new risks, the net result is likely to be an increase in risk. Let’s consider a common example:

A salesman for a foreign exchange trading firm approaches the trustees of a pension plan and proposes that they add a currency overlay strategy to their existing portfolio of domestic stocks and bonds. The strategy will consist of an actively traded portfolio of currency forwards. Because forwards represent long/short positions, they require little or no up-front investment. Accordingly, the strategy could be implemented without changing any of the plan’s existing investments. That is why it is called an “overlay” strategy.

In addition to possibly generating positive returns, the salesman argues that the added exposure to currencies will have a diversifying effect on their portfolio—decreasing the portfolio’s total market risk.

Is the salesman right? Will the overlay strategy reduce the portfolio’s market risk? At first blush, it is difficult to say. Fluctuations in the value of the overlay portfolio should have little or no correlation with returns on the existing portfolio. On the other hand, the overlay strategy introduces a new risk in addition to the portfolio’s existing risks.

In fact, the salesman is wrong. Far from reducing market risk, the overlay strategy will increase the total market risk. The overlay strategy does diversify the portfolio’s risks, but it also leverages them. The diversification effect will reduce market risk, but this will be more than offset by the leveraging effect.

Let’s look at the situation in terms of eggs and baskets. Suppose you are carrying a basket of 12 eggs. To diversify your risk, you might obtain a second basket and place six of the eggs in it. Now, carrying one basket in each hand, you will have reduced risk. Suppose instead, you act under a misperception that risk is reduced by simply carrying more baskets of eggs. Instead of dividing your 12 eggs between two baskets, you instead offer to carry your friend’s basket of 12 egg as well as your own. Now you are carrying two baskets of 12 eggs each. In financial terminology, you have leveraged your position. The net result is an increase in risk. In effect, this is what the salesman’s overlay strategy will do to the pension portfolio.

For diversification to work, it is not sufficient to add risks to a portfolio. Instead, where there are concentrations of risk, these need to be reduced while other, unrelated risks are taken on.

The issue of how investors can use diversification to optimize their portfolios is a central concern of portfolio theory.

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