The Capital Asset Pricing Model
The Risk Return Relation
Formalized
Summary
As we discussed, the market pays
investors for two services they provide: (1)
surrendering their capital and forgoing
current consumption and
(2) sharing in the total risk of the

Futures Contract
Forward contracts have two limitations:
(a) illiquidity
(b) counter-party risk.
Futures contracts are designed to address these two limitations.
Definition: A futures contract is an exchange-traded, standardized, forward-like
contract tha

Hedging using Futures
Basis and basis risk
Perfect hedge does not always exist
The asset we are trying to hedge may not be
exactly the same as the asset underlying the
futures.
The time at which we sell the asset (which
could be random)might not be exa

Covered Calls
(A) the portfolio consists of a long position in a stock plus a short position in a call option. This is
known as writing a covered call. The long stock position "covers" or protects the investor
from the payoff on the short call that become

Uses
1. Suppose we are given a financial derivative.
What is the fair" price for such a contract?
[Pricing]
2. Suppose we are managing a large portfolio.
How can we control the exposure to financial
risks? [Hedging]
3. Suppose that you have to achieve

Long put position (buying a put option)
Profit from Strategy
3,000
Exercise price
Put premium
2,500
= Rs.70
= Rs.6.13
2,000
1,500
1,000
500
Profit up to Rs.6,387
[100x(Rs.70-Rs.6.13)]
0
(500)
(1,000)
40
Limited loss
Break-even price
Put premium
50
60
70
8

Long put position (buying a put option)
Position taken in the expectation that price will decline.
Example:
For a put buyer with
an exercise price = Rs.70
option premium (option price) paid by the put buyer =
Rs.6.13
The following diagram shows diffe

Options can be either sold (written) or purchased, thus
giving rise to four possible basic option positions
Long call position (holder of a call option)
Short call position (writer or seller of a call option)
Long put position (holder of a put option)

Basis Risk - Intuition
At time of origination of contract (initial basis)
B0,T = S0 F0,T
At time of Closure of contract (cover basis)
Bt,T = St Ft,T
Price risk is
St- S0
Basis risk is Bt,T B0,T = (St Ft,T ) (S0 F0,T )
The investor is swapping the price ri

Using Options instead of stocks
Suppose you have a choice of two investment strategies. The first is to
invest Rs.100 in a stock. The second strategy involves investing Rs.90 in
6 month T-bills and Rs.10 in 6 month calls. If the call is priced at Rs.5,
t

Protective Puts
Strike Price X = Rs. 100; Stock Price S = Rs. 97 (at the expiration
date)
Value of Put = X-St = 100 97 = 3
Protective Put means holding stock and put options. If the
price of the stock moves down you have protection on value
loss. Used as

Arbitrage Bounds
Lower Bound on an American Put Option
PA >= max(0, X-S)
Lower Bound on a European Call Option
CE >= max(0, S-X(1+r)-T)
Lower Bound on a European Put Option
PE >= max[0, X(1+r)-T - S]
However, Exercise Price is set based on an
unknown futu

Commodity hedging
Hedging on Commodities
If I have 100 tonnes of coconut Oil, I want to lock in the price. I am
Long on the commodity. A short position in a forward contract
based on the same commodity would provide the desired negative
price correlatio

Bond Hedges
Find Yield Beta by correlating the 10 year yield to the 15 year
yield. If it follows expectations hypothesis, the yield beta = 1.
Find Modified Durations of A and B and current price
(Modified Duration and prices are 6.4036 years and 87.71 f

NOB
Mid feb prices for a june expiry
Contract
Settlement price
Implied Yield
20 yr, 6% T bond
103.0625
5.74
10 yr 6% T note
104.0625
5.47
You expect a flattening yield curve the existing 27 bp
yield difference will disappear
Strategy
Go long in one Tre

Put Call Parity
Is Parity Violated?
17+105/(1.05) = 110 +5 = 2 YES!
Arbitrage Strategy
Position
Cash Flow
Now
ST< 105
ST>105
Buy Stock
-110
ST
ST
Borrow
(equals to the
exercise price
= 105/1.05
100
-105
-105
Sell Call
17
0
-(ST-105)
Buy Put
-5
105-ST
0
To

Index Arbitrage
If Futures Price > Spot Price - Short futures and buy
stocks (Negative Arbitrage)
If Futures Price< Spot price Long Futures and sell
stock (Positive Arbitrage)
Stock current price is $100, one year rf is 6%, One
year future price is 104. H

Long call position (buying a call option)
Position taken in the expectation that price will
rise.
Example:
For a call buyer with
an exercise price = Rs.70
option premium (option price) paid by the call buyer =
Rs.6.13
The following diagram shows dif

Pricing of Options: Arbitrage Bounds
Options are priced based on arbitrage principle
(as they are redundant securities)
For example: Suppose that an American call option on
Mahindra Satyam with an exercise price of Rs.70 is selling for Rs.3
and that the M

Put Call Parity
Consider a combination of Call plus bond (where the value of
the bond is equal to the strike price of the stock) payoff
ST <= X
ST > X
Call
0
St-X
Bond
X
X
Total
X
ST
The Payoff is similar to Protective put! Hence:
C+X/(1+Rf)T = So +P
P =

ANALYSIS OF FS
The Firm, Its Claimants, and the Capital market
The Capital Market: Trading
Value
The Investors:
The claimants on value
The Firm: The Value generator
Cash from Loans
Operating
Activities
Investing
Activities
Financing
Activities
Debt h

BINOMINAL BASIC
Three step Binomial Tree
call Pricing
Strike
100
U
1.2
D
0.9
Riskfree Ra
0.01 per each period
Replication Method
(0,0)
S
Delta
Bond
Call
100
0.639008
-53.079
10.82201
(3,3)
S
172.8
Delta
Bond
(2,2)
Call
72.8
S
144 172.*delta+1.01B=72.8
Del

Futures Prices
Dr A Vinay Kumar
Agenda
Cost of Carry Models
Full carry markets
Expectations Hypothesis
Transaction costs
Risk Aversion
Future Prices
Basis
Cash Price minus Futures Price
Spread
Is the relationship between the two futures
prices se

where hedging and underinvestment are our main variables of interest and the control
variables include size, managerial risk aversion, access to capital markets, likelihood of
financial distress, return on assets, and concave tax function. All variables w

We also define a variable that captures the relationship between cash holdings and hedging in
firms with large investment opportunities, which is our proxy for possible underinvestment
problems. This variable is created by multiplying the previously prese

3. METHODOLOGY
_
The chapter describes the methodological approach applied in this research. The sampling
method and variables are described in detail, and an in-depth discussion regarding the
econometric technique is presented.
_
3.1 Methodological appro

approximately linear, which is also consistent with previous research (Bolton et al, 2011).
This regressand will be used in Model 1 and 2.
= ln (
)
A consequence with the definition of the dependent variable that can disrupt the results is that
cash