Hedging Financial Risk EZ

Hedging Financial Risk EZ - Hedging and Insuring Hedging...

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Hedging Financial Risk Econ 422 Summer 2005 Hedging and Insuring Both hedging and insuring are methods to manage or reduce financial risk. Insuring involves the payment of a premium (a small certain loss) for the reduction or elimination of the possibility of a larger loss. Hedging involves a transaction that reduces the risk of financial loss by giving up the possibility of a gain. Hedging often involves the use of derivative securities. General Principles of Hedging Assume that you own risky asset A and want to reduce your risk exposure. Find an asset B whose price is (highly) correlated with that of A, i.e., there is a linear relationship between A’s price and B’s. Estimate the parameters of this relationship by running a regression of A’s price on B’s price: p A = α + δ p B + ε , δ = cov(p A ,p B )/var(p B ) Delta measures the sensitivity of expected changes in A’s price to expected changes in B’s price: E[p A ] = α + δ E[ p B ] Delta is referred to as the hedge ratio. General Principles of Hedging, Cont. If the prices of A and B are perfectly correlated , with a hedge ratio of δ , then ε = 0 and you could construct a perfect hedge by selling (short) δ units of B. Thus, your portfolio would have a long position of one unit of A and a short position of δ units of B. If the price of A rises by $1, the price of B (in this case) rises by ($1/ δ ). The value of your portfolio changes by: $1 - δ ($1/ δ ) = 0 You have eliminated the risk
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General Principles of Hedging, Cont. If the prices of A and B are not perfectly correlated , then ε≠ 0 and you could still construct a hedge by selling (short) δ units of B, but the hedge would not be perfect. Your portfolio would have a long position of one unit of A and a short position of δ units of B. If the price of A rises by $1, the price of B (in this case) rises by ($1/ δ ) on average, but not always. The value of your portfolio changes on average by: $1 - δ ($1/ δ ) = 0 but not always You have eliminated the risk on average, but not always. Hedging Using Returns • In practice, hedging using regression is usually done with returns instead of prices, for certain statistical reasons: error AB rr α δ = ++ The interpretation of δ remains the same: it is an estimate of the hedge ratio General Principles of Hedging (Example) XYZ Corp holds $12.5 million of IBM stock. It wants to reduce the risk associated with this asset, using a market index as a hedge instrument. We know based on the CAPM, that IBM’s return is correlated with the market return and the relationship is 2 ˆ 0.78 0.72 , 0.4 ˆˆ 0.72 IBM M M IBM r R αβ ε δβ =+ += + + = == To construct a hedge, sell 0.72 * $12.5 million = $9 million of the market index. • Q: Is the hedge perfect?
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This note was uploaded on 12/21/2011 for the course ECON 422 taught by Professor Staff during the Fall '08 term at University of Washington.

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Hedging Financial Risk EZ - Hedging and Insuring Hedging...

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