Algorithmic Trading Portfolio-level Delta Hedging

Critical Thinking Easy meter Need a TeamId for next homework (h21)

Delta of a Portfolio Family What if I have more than one type of derivative with the same underlier in my portfolio? Delta hedging still applies... and it can be made even better!

Delta of a Position Dposition = qtyi * di

Delta of a Portfolio Family Dfamily = S qtyi * di

Delta Neutral Portfolio Perfectly hedged portfolio family has Family Delta = 0 This means that the sum of the values of the positions in the family does not change as the stock price changes.

Delta of a Portfolio of Related Securities Assume that the underlier is GOOG Dfamily = S qtyi * di 1000 * 0.53 – 2000 * 0.46 – 500 * (-0.51) = -135 -135 + 135 = 0 long call short call (different strike) short put Initial Delta Delta that is necessary to make the portfolio delta neutral “Family” Delta for the portfolio

Key Portfolio Decisions I need +135 delta on my GOOG portfolio, how do I get it? Buy stocks Buyback short stocks Buy calls (delta > 0) Buyback short calls Sell puts (delta < 0) Sell short puts

In summary - to determine a recommendation, consider: date (hedging today?) size of portfolio delta imbalance (do we need to hedge?) price of security and available cash (do we have the money?) closeness to max margins (can we borrow more?) delta of security (how many?) transaction costs (can we afford it?) quality of hedge effect on AP portfolio and CAccount (grows/shrinks?) risk of going out of the money or grow out of control

Delta for the portfolio of GOOGLE positions: +2,420 Example Delta for the portfolio of GOOGLE positions: +2,420 Capital account: $ 5m Margin: $ 6m (max. $ 10m) Pros/cons: cash, horizon, price, tc, stability…

Portfolio-level Delta hedging Dfamily = S qtyi * di 0 = S qtyi * di + qtyx * dx qtyx = - (S qtyi * di ) / dx

Scoring an alternative - Example: do not follow it! PRICE QUALITY A-E PRICE A-E JULY EXPIRA-TION TC COEFF. CASH IMPACT MARGIN SCORE Buy stock HI n/a LOW OUT NO 100 Buyback stock YES (-) 200 Buy calls A > E July cheaper MEDIUM 600 Buyback calls 800 Sell puts E > A IN 900 Sell short puts YES (+) 400

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Demo (who else can do this?)

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