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
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
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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