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simple-hedging

simple-hedging - Simple Hedging(Part 1 890-2011 STOR 890...

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Simple Hedging (Part 1) 890-2011 2/3/2011 STOR 890, 2011 simple hedging
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Introduction Hedging: to reduce the risk in an invested security by holding another security with possible “ opposite ” scenarios. Diversification between negatively correlated stocks is an example of hedging. not a free lunch, often at the expense of reduced returns, similar to buying an insurance ... more sophisticated examples: CDO, CDS (later). STOR 890, 2011 simple hedging
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Case 1 Consider investment options at a beach based on the following annual return table: umbrella maker ( U ) resort owner ( R ) probability rainy 50% -25% 0.5 sunny -25% 50% 0.5 Compare three portfolios: P 1 : all wealth invested in U P 2 : all wealth invested in R P 3 : wealth split equally between U and R STOR 890, 2011 simple hedging
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Case 1 (continued) Note: P 1 , P 2 and P 3 have the same expected return μ = 12 . 5 % . P 1 and P 2 have the same risk, i.e. their variance σ 2 = 0 . 5 ( 50 % - 12 . 5 %) 2 + 0 . 5 ( - 25 % - 12 . 5 %) 2 = 0 . 5 ( 37 . 5 %) 2 0 . 07 . However, P 3 has no risk (its variance equals zero) because it consists of equal shares of U and R , i.e. c 1 = c 2 = 1 / 2 , hence the return for P 3 is constant 1 2 ( 50 %) + 1 2 ( - 25 %) = 12 . 5 % regardless of the weather at the beach! STOR 890, 2011 simple hedging
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Case 1 (continued) Issues: Why Case 1 could be regarded as a caricature of “bull market”? In an opposite situation, if both P 1 and P 2 have negative expected returns, i.e. μ 1 < 0 and μ 2 < 0 (see Case 2 as an example), then no matter what proportions c 1 and c 2 between U and R we set, the resulting portfolio will always have a negative expected return. Why? In the above “bear market”, what could we do to come up with a profitable portfolio? STOR 890, 2011 simple hedging
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Case 2: Bear Market Consider a setting similar to Case 1 except ...
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