Haircut
Additional collateral set aside to compensate for risk which belongs to the short seller, held by the lender until position is closed
Short Rebate
Interest earned on the collateral in the stock market
Repo Rate
Interest earned on the collateral in the bond market
Shortsale
Believes that the price of the stock will decrease and profit can be made from this
Payoff
If one completely cashes out, does not consider cash flows on other dates
Profit
Considers cash flow on other dates with accumulated value at the given rate
Profit of Long Position
Payoff  AV(premium) at riskfree rate
Profit of Short Position
Payoff + AV(premium) at riskfree rate
Bull Spread
Long Call + Short Higher Strike Call
Long Put + Short Higher Strike Put
Bull Spread used when
belief price of asset will increase between two strike prices
Bear Spread
Short Call + Long Higher Strike Call
Short Put + Long Higher Strike Put
Bear Spread used when
price of asset decrease between two strike price
Box Spread
Long Bull (call) + LongBear (put)
Long Bull (put) + Long Bear (call)
Box Spread used when
lend or borrow money
Box Spread (lending money)
Long Bull (call) + Long Bear (put)
Box Spread (borrowing money)
Long Bull (put) + Long Bear (call)
Ratio Spread
Long M options (K1) + Short N options (K2)
Where K1 differs from K2
Collar
Long Put (K1) + Short Call (K2); where K2 > K1
Collar used when
wishes to benefit from underlying asset price decreasing
Collared Stock
Combination of purchased collar + long stock
Straddle
Long Call (K1) + Long Put (K1)
Straddle used when
price of underlying asset will have large movements in either direction
Strangle
Long put (K1) + Long call (K2); where K2 > K1
Strangle used when
price of underlying asset will have large movements in either direction but with low initial cost (however lower payoff)
Butterfly Spread used when
Underlying asset will stay close to its current price but protect against large losses
Asymmetric Butterfly Spread
Strike Price Unequally Spaced
Symmetric Butterfly Spread
Strike Price Equally Spaced
PutCall Parity Equation
C(S,K)  P(S,K) = F^{P}(S)  Ke^{rt}
Law Of One Price
Two portfolios with exact same payoffs must have the same cost
PutCall Parity Equation
C(S,K)  P(S,K) = F^{P}(S)  Ke^{rt}
Floor
Long Asset + Long Put
Floor useful for
guaranteeing a minimum price at which an asset can be sold with payoff of at least K
Caps
Short Asset + Long Call
Caps useful for
Insurance against short selling asset
Risk of price increasing
Buying asset for fixed price (k)
Capped the cost to close short position
Write a Covered Call
Short Call + Long Asset
Write a Covered Put
Short Put + Short Asset
Payoff of Call as K increases
The payoff will decrease and the cost decreases
Payoff of Put as K increases
Payoff of put will increase and the cost will also increase
Maximum Loss on Long Put
AV(Put Premium) at riskfree rate
Maximum Loss on Short Put
Limited to:
K  AV(Put Premium)
Assume you shortsell an asset and will have to buy the asset at a future date to close your short position. You wish to insure against an increase in the asset price.
Short Asset + Long Call = Cap
Assume you own an asset, and you wish to insure against a decrease in its price
Long Asset + Long Put = Floor
Identity: Floor
Long Asset + Long Put =
Long Call + Long risk free zero coupon Bond
Identity: Cap
Short Asset + Long Call
Long Put + Short riskfree rate zero coupon Bond
Long Put + Short riskfree rate zero coupon Bond
Identity for?
Identity: Cap
Short Asset + Long Call
Long Asset + Long Put =
Floor
Short Asset + Long Call =
Caps
Short Call + Long Asset =
Write a Covered Call
Short Put + Short Asset =
Write a Covered Put
AV(Put Premium) at riskfree rate;
Max Loss for?
Maximum Loss on Long Put
K  AV(Put Premium)
Max Loss on?
Maximum Loss on Short Put
Purpose of Covered Call?
Given Option Writer Shorts Call
Faces risk of asset price increases
Thus buys asset to offset
Long Call + Long risk free zero coupon Bond
Identity for?
Identity: Floor
Long Asset + Long Put =
Additional collateral set aside to compensate for risk which belongs to the short seller, held by the lender until position is closed
Haircut
Interest earned on the collateral in the stock market
Short Rebate
Interest earned on the collateral in the bond market
Repo Rate
Believes that the price of the stock will decrease and profit can be made from this
Shortsale
Long Call + Short Higher Strike Call
Long Put + Short Higher Strike Put
Bull Spread
Short Call + Long Higher Strike Call
Short Put + Long Higher Strike Put
Bear Spread
belief price of asset will increase between two strike prices
Bull Spread used when
price of asset decrease between two strike price
Bear Spread used when
Long Bull (call) + Long Bear (put)
Box Spread (lending money)
Long Bull (put) + Long Bear (call)
Box Spread (borrowing money)
Purpose of covered put?
Given Option Writer Shorts Puts
Faces risk of asset price decrease
Thus offsets with shorting the asset
Maximum Loss of Long Call
Accumulated Value of Cash OutFlow from purchasing the Call
Maximum Gain of Long Call
Infinite
Maximum Loss of Short Call
Infinite
Maximum Gain of Short Call
Accumulated Value of Cash InFlow from selling the Call
Maximum Loss of Long Put
Accumulated Value of Cash OutFlow from purchasing the Put
Maximum Gain of Long Put
Strike price to which you have the right to sell

Accumulated Value of Cash OutFlow used to purchase the Put
Maximum Loss of Short Put
Strike price at which you need to buy the asset

Accumulated Vaue of Cash InFlow from selling the Put
Maximum Gain from Short Put
Accumulated Value of Cash InFlow from selling the Put
How to hedge short position on underlying asset with Collar
Written Collared Stock
Short Put Strike Price + Long Call Higher Strike Price
Risk Premium for Security (i)
E[R_{i}]  r_{f}
Expected Market Risk Premium
E[_{market}]  r_{f}
Expected excess return of the Market
E[R_{market}]  r_{f}
Expected excess return for Security (i)
E[R_{i}]  r_{f}
CAPM Formula
E[Return on Investment]
= Riskfree rate + (Beta of investment security)*(Expected Market Risk Premium)
Enterprise Value
Which is the risk of the firm's underlying business operation that is seperate from its cash holdings.
Enterprise Value Formula:
Net Debt = Debt  Excess cash and shortterm investments
r_{U}=w_{E}⋅r_{E}+w_{D}⋅r_{D}
Unlevered Cost of Capital or Asset
If project is financed purely with equity, considered to be
unlevered
Project finanaced with Debt and Equity considered to be
levered
β_{U}=w_{E}⋅β_{E}+w_{D}⋅β_{D}
Unlevered Beta or Asset
Benefits from Tax Deduction
Reduces Debt Cost of Capital > more money to pay equity holders
Effective aftertax cost of debt
rD•(1−τC)
τC = coporate tax rate
rD = Cost of Debt
weightedaverage cost of capital (WACC)
r_{WACC }= w_{E}⋅r_{E }+ w_{D}⋅r_{D}⋅(1−τC)
WACC vs Unlevered Cost Of Capital (is based off of?)
WACC = based on firm's aftertax cost of debt
Unlevered Cost Of Capital = based on firm's pretax cost of debt
Beta is calculated as
B_{i }=
( Cov[R_{i},R_{Mkt}]
/
σ^{2}_{Mkt })
equation for the CAPM is
r_{i }= E[R_{i}] = r_{f }+ β_{i}(E[R_{Mkt}]−r_{f})
security market line (SML) represents
is a graphical representation of the CAPM
CML vs SML
CML vs SML
Uses Total Risk vs Systematic Risk
Uses Efficient Portfolios Only vs Any security/combination of securities
The difference between a security's expected return and the required return
alpha
Alpha equation
α_{i }= E[R_{i}]−r_{i }= E[R_{i}]−[r_{f }+ β_{i}(E[R_{Mkt}]−r_{f})]
ADDING A NEW INVESTMENT
r_{New}=r_{f}+β_{New},_{P}⋅(E[R_{P}]−r_{f})
market risk premium
E[R_{Mkt}] − r_{f}
Beta Formula in words
Change in an Asset's Return
/
Change in Market Return
What does Beta Meaasure?
Systematic Risk of an asset by calculating the sensitivity of the Asset's return to the Market return
Statisitical term of Beta defined as:
COV[Asset_{i}, Market]
/
Variance of Market Return
Linear Regression estimate of Beta
R_{i}  r_{f} = a_{i} + B_{i }(R_{mkt}  r_{f}) + e_{i}
Delta
Change in option cost per $1 of underlying asset movement
Gamma
Measures Delta's expected rate of change
If Delta is 0.40 and Gamma is .05 then first $1 dollar change is 0.40 of option's price, second $1 dollar change is 0.45
How Gamma works
Vega
How much option cost may change with each 0.01 change in implied volatility
Option with Delta of .40 is also interpreted
as 40% chance of expiring in the money
IRR
Internal Rate of Return
What is IRR
Rate at which the Present Value of cash Inflow
=
Present Value of cash Outflow
Geometric Series Finite
(First Term  First Omitted Term)
/
(1  Common Ratio)
Geometric Series Infinite
(First Term)
/
(1  Common Ratio)
Present Value Annuity one period before the first payment date
1  v^{n}
/
i
Present Value Annuity on the date of the first payment
1  v^{n}
/
d
Present Value Annuity with payments one period after the comparison date and continuing forever
1
/
i
Present Value Annuity with payments on the comparison date continuing forever
1
/
d
Sensitivity Analysis
changing the input variable one at a time to see how sensitive NPV is to each variable
Scenario Analysis
Changing several input variables at a time
SemiVariance
= E [ min( 0, R  E[R] )^{2 }]
SemiVariance can be estimated by the sample semi  variance
What is the Formula?
(1/n) * Summation_{i}^{n} (min ( 0, R_{i}  E[R] )^{2}
VaR (ValueatRisk) of a Random Variable
Simply its Percentile
When riskneutral probabilities are given, Calculate NPV with
riskfree rate
Black Schole Call Price Formula
C = F^{p}(S)•N(d_{1})  F^{p}(K)•N(d2)
= (Prepaid Forward Price Stock)*N(d_{1})  (Prepaid Forward Price Strike)*N(d_{2})
What is a Forward Contract
Agreement between two parties, the buyer and seller, to exchange an asset on specified date AND specified price
Agreement between two parties, the buyer and seller, to exchange an asset on specified date AND specified price
Forward Contract
Long Forward makes investor
obligated to buy the underlying asset at the forward price
Payoff Long Forward
Spot Price at Expiration  Forward Price
Also equals the Profit of Long Forward
Profit Long Forward
Payoff_{long forward}
Forward Price should equal?
AV
of the Prepaid Forward Price
at riskfree rate  compounded cont.
F_{0,T} = (AVprepaid forward price)
(F^{P})(e^{rt})
r = risk free rate
Prepaid forward price = Stock's Price at
Stock's Price at T=0
Notional Value means
Size
Liquidity
How easy is it to buy and sell an asset
Black Scholes price for Put Option
P = F^{p}(K)•N(d_{2})  F^{p}(S)•N(d_{1})
Call Option Price Min Boundary
C(S,K,T) >= max [0, F^{P}(S)  Ke^{rt}
Put Option Price Min Boundary
P(S,K,T) >= max [0, Ke^{r}^{T}  F^{P}(S) ]
Call Option Price Max Boundary
S >= C(S,K,T)
Put Option Price Max Boundary
K >= P(S,K,T)
Strike Price Proposition 1
C(K_{1}) >= C(K_{2}) >= C(K_{3})
P(K_{1}) <= P(K_{2}) <= P(K_{3})
Strike Price Proposition 2
C(K_{1})  C(K_{2}) <= (K_{2}  K_{1})e^{rT}
P(K2)  P(K1) <= (K_{2}  K_{1})e^{rT}
d_{1 }=
ln ( (F^{P}(S) / F^{P}(K) ) + (0.5)(σ^{2})(T)
/
σ • sqrt(T)
d_{2} =
d_{1}  (σ • sqrt(T))