Financial Information Management FINANCIAL INFORMATION MANAGEMENT Stefano Grazioli
Financial Information Management FINANCIAL INFORMATION MANAGEMENT Stefano Grazioli.
Dec 24, 2015
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FINANCIAL INFORMATION MANAGEMENT
Stefano Grazioli
Critical Thinking Team submission possible from H17 email me with team name, members
(userids) and get the team # on collab.
Easy meter
The Hedge Tournament Questions? Team formation / paper / opting
out
Fin
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Suggestions Give yourself plenty of time Audit the numbers!
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FinancialStrategies:
BasicsStefano Grazioli
Payoff Curves
Profit & Loss
Going long / short =flipping horizontally the payoff curve
Profit & Loss
Stock price
Stock price
short
$10
long
$10
price at which you bought it
Call and Put Payoffs
Stock price
Profit & Loss
long call
Stock price
short call
Profit & Loss
strike strike
Stock price
Profit & Loss
long put
Stock price
Profit & Loss
strike
short put
strike
Transaction Costs (constant)
Stock price
Profit & Loss
TCs always lower your payoff curve
TC
long - TC
$10
Stock price
short - TC
Profit & Loss
TC $10
Transaction Costs (variable)
Stock price
Profit & Loss
long - TC
TCs always lower your payoff curve
Stock price
short - TC
Profit & Loss
TC TC $10 $10
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In Technology?
Financial Strategies: Key idea Combine different types of
positions to obtain custom payoff curves.
Payoff curves can be designed to achieve many different objectives. Hedging is just one of them.
Hedging Strategies1. Offsetting the position (not applicable to the HT)
2. One to one3. One to many4. Dynamic approaches5. Synthetics (based on put/call parity)
6. Delta hedging (based on Black Scholes)
7. Delta + Gamma hedging (complex refinement)
Strategy #1: Offset the Position
Stock price
Long positionto hedge
Total Payoff
Profit & Loss
Short position
Perfect hedge, but guaranteed to lose money.Impossible do to when a position is illiquid
(i.e., you cannot do it in the HT)
Strategy #2 1:1 (e.g., Covered Calls)
Stock price
Profit & Losses
Total Payoff
long Stock
short call
strike
Very popular - Neutral to moderately bullish
Example 1:1 Strategies Table
A short call Go long on the stock
A long call Go short on the stock
A short put ...
A long put ...
A short stock ...
A long stock ...
If our position is... ...this is what we (the system) should do
…work well BUT are expensive
Strategy #3: Multiple options (e.g., collars)
Stock price
Profit & Losses
short call
long Stock
Way out of the money – Inexpensive means to protect wealth from sharp downturns
long put
Total Payoff
Strategy #4: Dynamic Approaches (e.g., “Stop Loss”)
Stock price
Profit & Losses
short call
Total Payoff
long on Stock
Buy the stockif its price raises above strike,and sell it back if falls below. Yes, there is a
catch....
Yes, there is a catch....
These were the Basics.... Typically useful for manually
managing your portfolio In the past:
Most teams did Delta Hedging Some of the better teams did their own mix of
Delta and Gamma hedging There is a dark horse…
Strategy #5: Offset the Positionwith a Synthetic Security
Stock price
Long positionto hedge
Total Payoff
Profit & Loss
Synthetic Short position
Perfect hedge, but costly.
Put-Call ParityFor European Ps and Cs that have the same strike K, and expire by the same time t:
P + S = C + K e-rt thus, we can solve for S, P, or C, effectively synthesizing a security with a combination of the other two and some interest-earning cash.
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Delta Hedging Objective: obtain the right
type and quantity of securities to counterbalance the movements of a security that we own.
DeltaNeutralPortfolio
What is Delta? Delta is a parameter. Roughly, it is the change in an option price
when the underlying stock price changes by a unit (e.g., one dollar).
O2 – O1
U2 – U1
Example1: a call option price goes down by $1.60 when a stock goes down by $2.Delta = -1.60 / -2.00 = +0.8
Example2: a put option is up by $0.5, when the stock is down by $1. Delta = 0.50 / -1.00 = -0.5
Delta =
Balancing a Position
I own 100,000 IBM stocks.
I am bearish - I think that the Stock price
may go down.
What kind andhow many options do I need, in order to counter-balance possible price changes and preserve my portfolio value?
Delta Hedging Example We want to hedge 100,000 long IBM stocks that we found in our IPs. First, we need to find a security with the appropriate hedging behavior
Stock price
long Stock
Current Price
Hedging a Long Stock
Stock price
Profit & Loss long call
Stock price
short call
Profit & Loss
strike strike
Stock price
Profit & Loss
long put
Stock price
Profit & Loss
strike
short put
strike
Delta Hedging Example- Short calls have the right behavior (also long puts)- How many short calls?
Stock price
short call
long Stock
Strike
Current Price
How many calls are needed to make our position price-neutral?gain/loss from options = - gain/loss from stocks
Noptions * (O2-O1) = - Nstocks * (U2-U1)
Noptions = - Nstocks * (U2-U1)/(O2-O1)
Noptions = - Nstocks * 1/Deltacall
Noptions = - 100,000 * 1/0.8
Noptions = - 125,000 i.e., we need 125,000 short calls.
Numeric CheckSuppose that the IBM stock price decreases by $10. What happens to my portfolio?
by assumption:
Option price change / Underlier price change = 0.8
so: Option price change = 0.8 * (-$10) = -$8
Change in Portfolio value = 100,000 * (-$10) + (-125,000) * (-$8) =
= -1,000,000 + 1,000,000 = $0
We have a Delta neutral portfolio
Computing Delta Delta of a Call Option = N(d1)
Delta of a Put Option = N(d1) -1
d1 = {ln(S/X) + (r + s 2/2) t} s t
What Hedges What
1 Short call Delta long stock
1 Long call Delta short stock
1 Short put |Delta-1| short stock
1 Long put |Delta-1| long stock
1 Short stock 1/Delta long call or 1/|Delta-1| short put
1 Long stock 1/Delta short call or 1/|Delta-1| long put
If your position is... ...this is what you need
Need for Recalibration
There is a catch.Delta changes with time....
Dynamic Delta Hedging Delta changes with S, r, s and t. Since they all change in
time, the hedge needs to be periodically readjusted – a practice called rebalancing (r, s are fixed in the HT).
Example:Yesterday we wanted to hedge 100,000 long stock and so we shorted 125,000 calls. But now the delta is 0.9.
100,000 = - Noptions * 0.9
Noptions = - 111,111 so, we need to buy 13,889 calls
(=125,000-111,111) to maintain delta neutrality.
Next Time Balancing a whole portfolio Other types of hedging
Fin
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In Technology?
Fin
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form
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M
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t HomeworkThe Spartan Trader
Suggestions Give yourself plenty of time Test the numbers!
Critical Thinking Teams! Collab Why APPL_COCTB crashed your system After sunday posting, no more late credit.
Easy meter
The Hedge Tournament Questions? Team formation
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