Financial Information Management
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
NOT random!
SP500
real g,
real volatility
STOCKS
Bids and
Asks
real initial prices
real beta,
real volatility
OPTIONS
Bids and
Asks
Confidential Peer Evaluation
May affect your grade
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OVERALL CONTRIBUTION
TEAM RAPPORT
TEAM WORK
TO TEAM SUCCESS
QUALITY OF WORK
AMOUNT OF WORK
KNOWLEDGE
OF THE PROJECT AREA
IDEAS CONTRIBUTED
TO THE PROJECT
ORGANIZATION OF TEAM WORK
(ADMIN.)
LEADERSHIP
ENTHUSIASM,
ATTITUDE, INITIATIVE
RESPECT FOR OTHERS
DEPENDABILITY,
GOOD TEAM PLAYER
MEETING ATTENDANCE,
PUNCTUALITY
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Financial Information Management
Hedging
Gamma, Vega, Theta & Rho
Gamma


Delta (D) measures the change in portfolio value
as 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) ,
so
there is less need to take immediate rebalancing
action.
 If Gamma is large, small changes in S will affect Delta
(and your portfolio value) significantly,
so
there is a stronger need to take immediate
rebalancing action.
Using Gamma

During small periods of time t2-t1
2
D Portfolio =
~ ½ * G * (S2-S1)
Example:
If you do not rebalance and the underlier price drops from $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)
Ss t
2
–(d1)
/2
 N’(d1) = e
 (2 p)
 d1 as in Black Scholes
Gamma
Strike
Stock price S
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)
2)
3)

Gportfolio <> 0
Gportfolio + Gx qtyx = 0
qtyx = -Gportfolio / Gx
Warning: Acquiring qtyx will disturb Delta neutrality. You will
need to rebalance.
Delta Gamma Delta
It’s a strategy, not a sorority.
1. Find out what to acquire to achieve Delta
neutrality.
2. Find out what to acquire to achieve Gamma
neutrality.
3. 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 time
changes
 Vega = change in portfolio value when the
volatility changes
 Rho = change in portfolio value when the rate
of interest changes
Financial Information Management
WINIT
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Financial Information Management
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 think
on your own?
 Concerns about the HT