Optimal Hedge Ratio2

Optimal Hedge Ratio2 - ( K F ) e rT 5 Valuing a Forward...

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When Interest Rates are Measured with Continuous Compounding F 0 = S 0 erT This equation relates the forward price and the spot price for any investment asset that provides no income and has no storage costs. 1
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If Short Sales Are Not Possible. . Formula works for an investment asset because investors who hold the asset will sell it and buy forward contracts when the forward price is too low. 2
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When an Investment Asset Provides a Known Dollar Income F 0 = ( S 0 I ) erT where I is the present value of the income during life of forward contract. 3
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When an Investment Asset Provides a Known Yield F 0 = S 0 e ( r q ) T where q is the average yield during the life of the contract (expressed with continuous compounding) or q is income as a % of asset price. 4
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Valuing a Forward Contract Suppose that K is delivery price in a forward contract & F 0 is forward price that would apply to the contract today. The value of a long forward contract, ƒ , is ƒ = ( F 0 – K ) e rT Similarly, the value of a short forward contract is
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Unformatted text preview: ( K F ) e rT 5 Valuing a Forward Contract: Intuition When a forward contract is entered into its value is zero (f=0). The delivery price (K) equals the forward price (F). Suppose I wish to buy a forward contract that will lead to delivery of an asset in the future. I could buy an existing contract or I could buy a new contract. The value of the existing contract is the difference between the delivery prices of the new (F0) and existing (K) contracts --- but remember this difference is realized in the future so we must discount to take into account the time value of money. 6 Forward vs Futures Prices Forward and futures prices are usually assumed to be the same. It can be shown that if the risk-free interest rate is constant and equal for all maturities, the forward and futures price are exactly the same. When interest rates are uncertain they are, in theory, slightly different. 7...
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Optimal Hedge Ratio2 - ( K F ) e rT 5 Valuing a Forward...

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