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Unformatted text preview: nal
Limited
1800 Contacts, Inc.
1800
FLOWERS.COM, Inc.
1800ATTORNEY,
Inc.
1st Constitution
Bancorp (NJ)
Intel Corporation
Juniper Networks, Inc.
Yahoo! Inc.
priceline.com
Incorporated security
symbol
OIIM current
shares short
2846753 prev. month change in shares % change in average daily
shares short
short
shares short
volume
713442
2133311
299
797977 CTAC
FLWS 3047592
466209 2571988
532703 475604
66494 18
12 190341
57857 ATTY 733 576 157 27 8646 FCCY 132 0 132 0 1099 INTC
JNPR
YHOO
PCLN 74613777
25482068
27236052
3748882 80023642
29421056
27338277
4417898 5409865
3938988
102225
669016 7
13
0
15 42550432
18507315
9687090
1842726 In general, stocks that lend themselves to some speculation and stocks around corporate events
(mergers and acquisition, dividend dates, etc.) with uncertain outcome will have a particular high
short interest.
It is theoretically possible to have short interest of more than 100%, because some market
participants (e.g., market makers) have the ability to short sell a stock without having a locate,
i.e., having someone who actually owns the stock and has agreed to lend it. 3 Question 1.12.
We are interested in borrowing the asset “money” to buy a house. Therefore, we go to an owner
of the asset, called Bank. The Bank provides the dollar amount, say $250,000, in digital form in
our mortgage account. As $250,000 is a large amount of money, the bank is subject to substantial
credit risk (e.g., we may loose our job) and demands a collateral. Although the money itself is
not subject to large variations in price (besides inflation risk, it is difficult to imagine a reason for
money to vary in value), the Bank knows that we want to buy a house, and real estate prices vary
substantially. Therefore, the Bank wants more collateral than the $250,000 they are lending.
In fact, as the Bank is only lending up to 80% of the value of the house, we could get a mortgage
of $250,000 for a house that is worth $250,000 ÷ 0.8 = $312,500 . We see that the bank factored
in a haircut of $312,500 − $250,000 = $62,500 to protect itself from credit risk and adverse
fluctuations in property prices.
We buy back the asset money over a long horizon of time by reducing our mortgage through
annuity payments. 4 Chapter 2
An Introduction to Forwards and Options
Question 2.2.
Since we sold the stock initially, our payoff at expiration from being short the stock is negative. In order to obtain the profit diagram at expiration, we have to lend out the money we received
from the short sale of the stock. We do so by buying a bond for $50. After one year we receive
from the investment in the bond: $50 × (1 + 0.1) = $55 . The second figure shows the graph of the
sold stock, of the money we receive from the investment in the bond, and of the sum of the two
positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at
expiration is indeed zero. 5 Part 1 Insurance, Hedging, and Simple Strategies Question 2.4. a) The payoff to a long forward at expiration is equal to:
Payoff to long forward = Spot price at expiration – forward price Therefore, we can construct the following table:
Price of asset in 6 months
40
45
50
55
60 b) agreed forward price
50
50
50
50
50 payoff to the long forward
10
5
0
5
10 The payoff to a purchased call option at expiration is:
Payoff to call option = max[0, spot price at expiration – strike price] 6 Chapter 2 An Introduction to Forwards and Options The strike is given: It is $50. Therefore, we can construct the following table:
Price of asset in 6 months
40
45
50
55
60 strike price
50
50
50
50
50 payoff to the call option
0
0
0
5
10 c)
If we compare the two contracts, we immediately see that the call option has a protection
for adverse movements in the price of the asset: If the spot price is below $50, the buyer of the
call option can walk away, and need not incur a loss. The buyer of the long forward incurs a loss,
while he has the same payoff as the buyer of the call option if the spot price is above $50.
Therefore, the call option should be more expensive. It is this attractive option to walk away that
we have to pay for.
Question 2.6. We need to solve the following equation to determine the effective annual interest rate:
$91 × (1 + r ) = $100 . We obtain r = 0.0989 , which means that the effective annual interest rate is
approximately 9.9 %
Remember that when we drew profit diagrams for the forward or call option, we drew the payoff
on the vertical axis, and the index price at the expiration of the contract on the horizontal axis. In
this case, the particularity is that the defaultfree zerocoupon bond will pay exactly $100, no
matter what the stock price is. Therefore, the payoff diagram is just a horizontal line, intersecting
the yaxis at $100.
The textbook provides the answer to the question concerning the profit diagram in the section
“ZeroCoupon Bonds in Payoff and Profit Diagrams”. When we were calculating profits, we saw
that we had to find the future value of the initial in...
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 Spring '14
 NguyenThiMaiLan
 Derivatives

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