FIN4520
Practice Exam 1
Dr. Lucy Ackert
100 possible points
Formula sheet permitted (oneside of a sheet of paper, only formulas)
Part 1: Multiple Choice (3 points each)
Circle the correct answer. If more than one answer is circled, the answer is incorrec
Valuing Stock Options:
The BlackScholesMerton
Model
Chapter 13
1
The BlackScholesMerton Model
The
option pricing model is derived by
constructing a riskless hedged portfolio
consisting of European options and stock
of nondividend paying firms.
The
Mechanics of Futures
Markets
Chapter 2
1
Futures Contracts
An
agreement between a buyer and a seller
to buy or sell something at a future date for
a specified price. Profits and losses are
computed on a daily basis.
Available on a wide range of underlyi
Introduction
Chapter 1
1
All I can say is beware of geeks
bearing formulas.
Derivative securities are financial
weapons of mass destruction.
Warren Buffett
2
The Nature of Derivatives
A derivative is an instrument whose value
depends on the values of othe
Example
January: An investor enters into a long
futures contract to buy 100 oz of gold @
$1050 in April.
April: the price of gold $1065 per oz
What is the investors profit assuming he
holds to maturity?
1
Answer
(1065 1050) * 100 = $1,500
2
Overthe Count
Estimating Volatility from
Historical Data (page 295298)
1.
2.
Take observations S0, S1, . . . , Sn on the
variable at end of each trading day
Define the continuously compounded
daily return as:
Si
ui = ln
S i 1
3.
4.
Calculate the standard deviation
Duration
Duration is a measure of the average life of a debt
instrument on a PV basis.
A zero coupon bond that matures in n years has a
duration of n.
A coupon bond has duration < n because payments are
made before maturity.
Financial institutions often t
Delivery
If a futures contract is not closed out before maturity, it is
usually settled by delivering the assets underlying the
contract. When there are alternatives about what is
delivered, where it is delivered, and when it is delivered,
the party with
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Futures
Price
Spot
Price
Time
t1
t2
1
What is the cause of basis risk?
1.
2.
3.
You dont know exactly when you will
receive or sell the asset.
There may not be a futures
Hedging Strategies Using
Futures
Chapter 3
1
Long & Short Hedges
A
hedge is a transaction designed to
reduce risk.
A long futures hedge is appropriate when
you know you will purchase an asset in
the future and want to lock in the price
A short futures h
Interest Rates
Chapter 4
1
Types of Rates
Treasury rate rate earned on Tbills and Tbonds
LIBOR (London Interbank Offer Rate)  rate at which a
bank is willing to loan funds to another bank.
Commonly used as riskfree rate in textbooks
This is financial
Determination of Forward
and Futures Prices
Chapter 5
1
Consumption vs Investment Assets
Investment
assets are assets held by
significant numbers of people purely for
investment purposes (Examples: gold,
silver).
Consumption assets are assets held
prima
Interest Rate Futures
Chapter 6
1
Interest Rate Futures
These
contracts are offered on many
assets whose prices are determined by
interest rates.
Tbonds (and notes)
Tbills
Eurodollars
2
Day Count Conventions
There are 3 day count conventions used in
Swaps
Chapter 7
1
Nature of Swaps
A swap is an agreement to exchange cash
flows at specified future times according to
certain specified rules.
Interest rate swap Two parties agree to
swap interest rate payments on a notional
principal denominated in th
Securitization and the
Credit Crisis of 2007
Chapter 8
1
Definitions
Collateralized Debt Obligation (CDO)
AssetBacked Security (ABS)
An ABS where the underlying asset is a portfolio of
bonds
A security created from a portfolio of loans, bonds,
credit car
Mechanics of Options
Markets
Chapter 9
1
Types of Options
A
call is an option to buy
A put is an option to sell
A European option can be exercised only
at the end of its life
An American option can be exercised at
any time
2
Option Positions
Long
call
Properties of Stock
Options
Chapter 10
1
Notation
c : European call
option price
p : European put
option price
S0 : Stock price today
K : Strike price
T : Life of option
: Volatility of stock
price
C : American Call option
price
P : American Put option
pr
Trading Strategies
Involving Options
Chapter 11
1
Three Alternative Strategies
Take
a position in the option and
the underlying
Take a position in 2 or more
options of the same type (A
spread)
Combination: Take a position in a
mixture of calls & puts (
Call is underpriced
Today
ST < 18
ST > 18
3

ST 18
Sell stock
+20
ST
ST
Buy bond
17
18.79
18.79
0
18.79  ST
.79
Buy call
Total
1
Puts: An Arbitrage
Opportunity?
Suppose that
p =1
T = 0.5
K = 40
S0 = 37
r =5%
D =0
Is there an arbitrage opportunity?
U
Calculation of Delta
Delta is the rate of change in option price
over the rate of change in the price of the
underlying asset.
Delta is calculated using nodes at time t.
An estimate of delta at time t is
2.16 6.96
Delta =
= 0.41
56.12 44.55
1
Trees and Di
Binomial Trees in
Practice
Chapter 18
1
Binomial Trees
Binomial trees are frequently used to approximate the
movements in the price of a stock or other asset.
In each small interval of time the stock price is
assumed to move up by a proportional amount u
Forward Rate Agreement
A forward rate agreement (FRA) is an
agreement that a certain rate will apply to
a certain principal during a certain future
time period
1
Forward Rate Agreement
continued
An FRA is equivalent to an agreement
where interest at a pre
Futures for Lean Hogs on Aug
4, 2009
1
Regulation of Futures
Regulation is designed to protect the public
interest
Regulators try to prevent questionable trading
practices on the floor of the exchange or by
outside groups
Four key regulators:
Broker
Excha
Hedge Funds
Hedge funds are not subject to the same rules as
mutual funds and cannot offer their securities publicly.
Mutual funds must
makes shares redeemable at any time,
limit use of leverage
disclose investment policies,
take no short positions.
Hedge
Key Mistakes Made By the
Market
Misperception of risks
Default correlation (tendency for
borrowers to default at the same time)
goes up in stressed market conditions
Assuming that housing prices only go
up
1
Need to Align Interests of Originators
and Inve
Optimal Hedge Ratio
Proportion of the exposure that should optimally be
hedged is
S
h =
F
where
S is the standard deviation of S, the change in the
spot price during the hedging period,
F is the standard deviation of F, the change in the
futures price dur
When Interest Rates are Measured
with Continuous Compounding
F0 = S0erT
This equation relates the forward price
and the spot price for any investment
asset that provides no income and has no
storage costs.
1
If Short Sales Are Not Possible.
Formula works
Arbitrage Opportunities
Suppose that
c =3
S0 = 31
T = 0.25
K =30
r = 10%
D=0
What are the arbitrage
possibilities when
p=3?
3 =? 3+3130e.1(.25)=4.74
1
Violation of putcall parity
Today
ST < K
ST > K
Buy call
3

ST  30
Sell put
+3
ST  30

Sell stock
RiskNeutral Valuation
The variable does not appear in the BlackScholes equation.
The equation is independent of all variables
affected by risk preference.
This is consistent with the riskneutral
valuation principle.
1
Implied Volatility
The implied vola