1. Algorithmic Trading
Portfolio-level Delta Hedging

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

3. 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!

4. Delta of a Position
Dposition = qtyi * di

5. Delta of a Portfolio Family
Dfamily = S qtyi * di

6. 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.

7. 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
= 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

8. 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

9. 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

10. 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…

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

12. 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

13. WINIT
What Is New In Technology?

14. Demo
(who else can do this?)

15. You do the talking Name, Major Things you like about the class
Things that can be improved
Attitude towards the tournament?