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The Ira Harris Experience. Wilhelm's Warriors. No Hedgetation. The Gobs of Money Machine. Gamma Hedging. Critical Thinking. Good job overall Easy meter Today office hours: 4-6. The Hedge Tournament. Questions?. Price generation. SP500. NOT random!. beta + noise.

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## Gamma Hedging

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**The Ira Harris Experience**Wilhelm's Warriors No Hedgetation The Gobs of Money Machine Gamma Hedging**Critical Thinking**• Good job overall • Easy meter • Today office hours: 4-6**The Hedge Tournament**• Questions?**Price generation**SP500 NOT random! beta + noise real g,real volatility STOCKS Bids and Asks B.S.+ noise OPTIONSBids and Asks real initial prices real beta,real volatility**Confidential Peer Evaluation**May affect your grade**Hedging**Gamma, Vega, Theta & Rho**Gamma**• Delta (D) measures the changein portfolio valueas the underlier’s price S changes (~speed). • Gamma (G) measures the rate of change in portfolio value as S changes (~acceleration).**Meaning of Gamma**• If Gamma is small (abs.), small changes in S will not affect much Delta (and your portfolio value) ,sothere is less need to take immediate rebalancing action. • If Gamma is large, small changes in S will affect Delta (and your portfolio value) significantly, sothere is a stronger need to take immediate rebalancing action.**Using Gamma**• During small periods of time t2-t1 D Portfolio = ½ *G * (S2-S1)2 Example: If you do not rebalance and the underlier price dropsfrom $52 to $50, the change of value in a Delta-Neutral Portfolio is approximately = ½ *G * (S2-S1)2 = 0.5 * (-10,000) * (52-50)2 = -$20,000 ~**How to Calculate Gamma**• Gamma = N’(d1) SsÖ t • N’(d1) = e –(d1)2/2 Ö (2 p) • d1 as in Black Scholes Gamma Stock price S Strike**Gamma-Neutral Portfolio**• More stable than a delta neutral-only. • Cannot use the stock to reach Gamma neutrality because the stock has Gamma = 0 1) Gportfolio <> 0 2) Gportfolio+ Gxqtyx = 0 3) qtyx= -Gportfolio / Gx • Warning: Acquiringqtyx will disturb Delta neutrality. You will need to rebalance.**Delta Gamma Delta**It’s a strategy, not a sorority. • Find out what to acquire to achieve Delta neutrality. • Find out what to acquire to achieve Gamma neutrality. • Find out what to acquire to re-achieve Delta neutrality. Stock is ideal because it will not affect Gamma.**More Dark Horses**• Simultaneous Delta Gamma • Conditional Gamma • Extreme transaction costs minimization Come and see me – not on the last day!**Theta, Vega, and Rho**Conceptually similar to Delta • Theta = change in portfolio value when timechanges • Vega = change in portfolio value when the volatilitychanges • Rho = change in portfolio value whenthe rate of interestchanges**WINIT**What Is NewIn Technology?**Homework**Spartan Trader**Your Opinion Matters**• Name • A couple of things that you are learning from the class • Things that you like/that can be improved • Is the class getting you to thinkon your own? • Concerns about the HT

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