Donald Schlesinger and Robert Krause of Morgan Stanley explain the intricacies of...

Hedging Imperfect Baskets

Often an institutional investor will fashion a basket of stocks that does not replicate any exchange-traded index. This is called an "imperfect basket." By contrast, a "perfect basket" does match an exchange-traded index. While imperfect baskets have their benefits, they can present problems when it comes to hedging.

Where there is no tradable index that comes close to matching the particular basket that an investor holds, he or she can devise a hedging vehicle by purchasing from an investment bank an over-the-counter put option whose underlying asset matches the portfolio in question. In designing this OTC product the investor may also select a wide array of features using exotic options (for example, average rate, knock-in, knock-out, compound and lookback options, etc.) that structure the risk/reward ratio in a variety of different forms.

One advantage of this approach is that there is no basis risk as long as the portfolio remains intact and the derivative security is held to maturity. (Usually, basis is the difference between the spot market and the futures market. In this instance the term expresses the difference between the basket and the underlying derivative instrument used.) Of course, as a purchaser of over-the-counter options, the investor must accept the creditworthiness of the counterparty. Also, OTC trades can have tax, accounting, liquidity or regulatory implications that the investor needs to investigate in advance. For these reasons many portfolio managers actually prefer hedging using listed products on a regulated exchange. With this choice, however, other problems can arise.

Matching an imperfect basket to a particular market index can be a little tricky. First, the investor has to search for an index with a high correlation to his or her basket. Second, there is the need to consider the liquidity of the futures or options of that index. For example, if the Russell 2000 index is the closest matching index to the basket, but the basket is sufficiently large, the investor may not feel comfortable giving up a wide bid­ask spread just for the privilege of a "close" hedge. Practically speaking, the investor may need to use the far more liquid S&P 500 to transact in the size required. Now, however, the investor has created a hedge that is even less perfect than the previous less-than-perfect hedge.

Closer to perfect

Correlation is one measure of the amount by which a basket will outperform or underperform the index. The correlation statistic attempts to define how closely one item's movements are linked to another item's movements. A +100 percent correlation implies that the movement of one item is always in the same direction as the other item, but not necessarily with the same magnitude; a value of ­100 percent means that the movement of one item is always in the opposite direction as the other (again, not necessarily with the same magnitude). A value of zero means that the two move independently of each other. For instance, is the price of rice in Tokyo related to the number of people who visit the Eiffel Tower in Paris every day? No. So correlation is zero. How about the movement of the S&P 100 and the movement of the S&P 500? The correlation is near +100 percent (but not quite). How about the movement of the S&P 500 with short-term interest rates? Answer: the correlation is negative, but not near ­100 percent.

A word of caution: just because two assets have been highly correlated does not necessarily mean that the correlation will continue. For instance, years ago traders noticed an unusually high correlation between the price of silver and the price of cattle. Intuitively, this made little sense. However, it did not stop traders from thinking there was a relationship. Then, too, even if there has been a high correlation in the past, and there is a strong logical reason for it, it is still possible that it will be weakened at some time in the future.

Compromise plan

When an investor tries to hedge, he or she often has to compromise between absolute price risk and basis risk. Theoretically, therefore, as the correlation between spot and futures increases, then the basis risk will diminish. Thus the investor first determines the correlation of the basket to the futures contract chosen as a potential hedging vehicle. Next the investor should have confidence that the correlation for the period studied is likely to continue, and then decides to accept the basis risk.

Let's look at an actual portfolio, which began on March 21, 1995. It was created in the hope of outperforming the S&P 500 index. So far it has not performed as expected. Exhibit One shows the performance of the S&P 500 and this basket composed of 77 stocks (all of which are, or were, in the S&P 500 index). One would not expect this basket to track the index exactly, because of differences in portfolio composition. But they should track closely, because they are highly correlated.

Exhibit Two shows the magnitude of the underperformance of the basket relative to the S&P 500 index. This is the performance this hypothetical portfolio would have received if the investor who created this basket had also sold an equal dollar amount of S&P 500 futures at fair value.

Another approach is possible: the investor decides to hedge, only this time using a vehicle that is likely to underperform his or her basket. Very likely one of the reasons that an investor lacks a perfect basket is that he or she thinks their stock selection is superior to any listed index. This time the investor chooses as a hedge an index that is expected to be the worst-performing index. The risk will probably increase compared to the previous example, but it will probably be less than holding just an outright long position.

In this instance the investor, instead of hoping that the basis risk won't hurt the portfolio, actively searches for some change in basis, which hopefully is achieved by the index's underperforming the basket. If this viewpoint is ultimately correct, the investor probably will have reduced the portfolio's risk and profited from the outperformance of the basket.

Closer lines

Let's return to our original basket and compare its performance to the S&P MidCap 400. Just as before, we would expect the lines to be different (because they represent different portfolios), but still fairly close together (because they are positively correlated).

Originally, when we bought these 77 stocks, we felt that they would outperform the "large cap" S&P 500. Then, we took our analysis a step further, by projecting an underperformance of the S&P MidCap 400 relative to the S&P 500. Therefore, we chose to take the basis risk and hedge our basket with S&P MidCap 400 futures. Exhibit Three shows how our expectation turned out. It can be seen that over this time frame our basket underperformed in the beginning, but then proved us right, and outperformed the MidCap by the end.

While investors can create a "perfect" hedge for most baskets using OTC products, it may be desirable to use publicly traded markets for credit risk, liquidity, tax, accounting or regulatory reasons. However, these publicly traded securities may provide "imperfect" hedges. Another alternative that tries to turn these disadvantages into advantages is to seek out an "imperfect" hedge. Here the investor may be able to turn hedging into an opportunity by performing better than a "perfect" hedge. Seeking an "imperfect" hedge may be more risky than hedging in the other two manners described, but it would probably be less risky than an outright long market position-though this assertion would depend on the degree of future correlation. Therefore, while a "perfect" hedge will not incur basis risk, an "imperfect" hedge can reduce risk and may provide new opportunities for profit.

At the request of the Morgan Stanley lawyers, we include the following observation. "OTC derivatives are not suitable for all investors. A potential user should conduct due diligence before investing in them."