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re there is a loss on the hedge and a gain on the underlying can be difficult 5 Convergence of Futures to Spot Time Time (a) (b) Futures Price Futures Price Spot Price Spot Price 6 Basis Risk ? Basis is the difference between spot amp。P 500 hundred futures ? Sell 1,000,000/250,000 = 4 contracts 19 Hedging Using Index Futures ? Remember total risk can divided up into systematic and unsystematic risk ? Systematic risk is measured by the portfolio beta ? Hedging with futures allows us to change the systematic risk ? But not the unsystematic risk 20 Hedging Using Index Futures ? To hedge the risk in a portfolio the number of contracts that should be shorted is ? where P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract b PA21 Hedging Stock Portfolios ? Hedge reduces systematic not unsystematic risk ? b is puted with respect to the index underlying the futures contract ? Futures should be chosen on underlying index that most closely matches the investor’s portfolio 22 Changing Beta ? Let b* = desired beta ? Let b = portfolio beta ? Then N = (b* b)(P/A) (N 0: sell) ? N 0: buy ? If we adopt the above convention, this formula textbook generalizes 23 Reasons for Hedgi