The Future Price

We have already mentioned in part (a), the lots of futures we cannot short frictional lots of future contracts. It is not a perfect hedge. Beta hedging can only help get close to a perfect hedge. There are other reasons for this as well.

First, the future price is not directly tied to the underlying index, except for the final settlement price on the expiration date (Figlewski, 1984). Day to day fluctuations in the difference between them induces fluctuations in the returns on the hedge position. The magnitude of this risk is limited by the possibility of arbitrage between cash and future markets. In market where transaction costs are small, and arbitrage is straightforward, basis risk may be negligible. But for stock index futures, a perfect arbitrage appears to be infeasible. It is impossible for the arbitrager to assemble such a portfolio in a reasonable size and to buy or sell all of the stocks simultaneously to capitalize on short-run, mispricing of index future price. Because the trade is not risk-free and there are sizable transaction costs, the range within which the future prices can move fairly freely without inducing arbitrage trading is broad enough to allow substantial basis risk.

Secondly, one key factor affecting basis risk is the choice of the futures contract to be used for hedging. Although fund managers have necessarily carried out a careful analysis to determine which of the available future contract has future prices that are most closely correlated with the price of the portfolio being hedged, this correlation is not perfect. Portfolio managers tend to hold a variety of diversified portfolios, examples being index tracking funds and growth funds. Hence the portfolio to be hedged tends not to match that of the underlying futures contract. Normally, the future market tends to be more volatile than the spot market. In addition, the optimal hedge ratio may not be stationary. Time-varying hedge ratios require frequent updating of the hedge ration, in this case the transaction costs need to be taken into account.

Thirdly, the hedger may not be exactly certain of when the asset will be bought or sold. There is a potential risk of early unwinding of position. Also, the closer the future is to maturity, the smaller its deviations from the equilibrium value it will be. However, there is a potential risk of greater need to close out early at a time when the basis is not in a favourable position.

Finally, returns to the index portfolio include dividends, while the index and the index future only track the capital value of the portfolio. Any risk associated with dividends on the portfolio will become a basis risk in a hedge position. However, dividends are fairly low and also quite stable, so this may not be a terribly important shortcoming.