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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 A B r r 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 ˆ ˆ 0.72 IBM M M IBM r r r R α β ε ε δ β = + + = + + = = = 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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