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Chpt,r 31: Index Spreading 581
J!"<>r example, if one index sells for twice the price of the other, and if both indices
have similar volatilities, then a one-to-one spread gives too much weight to the
higher-priced index. A two-to-one ratio would be better, for that would give equal
weighting to the spread between the indices.
Example: UVX is an index of stock prices that is currently priced at 100.00. ZYX,
another index, is priced at 200.00. The two indices have some similarities and, there­
fore, a spreader might want to trade one against the other. They also display similar
volatilities.
If one were to buy one UVX future and sell one ZYX future, his spread would
be too heavily oriented to ZYX price movement. The following table displays that,
showing that if both indices have similar percentage movements, the profit of the
one-by-one spread is dominated by the profit or loss in the ZYX future. Assume both
fi1tures are worth $500 per point.
Market ZYX ZYX uvx uvx Total
Direction Price Profit Price Profit Profit
up 20% 240 -$20,000 120 +$10,000 -$10,000
up 10% 220 - 10,000 110 + 5,000 - 5,000
down 10% 180 + 10,000 90 - 5,000 + 5,000
down 20% 160 + 20,000 80 - 10,000 + 10,000
This is not much of a hedge. If one wanted a position that reflected the movement
of the ZYX index, he could merely trade the ZYX futures and not bother with a
spread.
If, however, one had used the ratio of the indices to decide how many futures
to buy and sell, he would have a more neutral position. In this example, he would buy
two UVX futures and sell one ZYX future.
Proponents of using the ratio of indices are attempting strictly to capture any
performance difference between the two indices. They are not trying to predict the
overall direction of the stock market.
Technically, the proper ratio should also include the volatility of the two indices,
because that is also a factor in determining how fast they move in relationship to each
other.