FINA7351EXAM I ANS

1
FINA7351 EXAM I ANS Q1. 1.1 The
clearinghouse gives every trader of futures an
absolute guarantee that the contract will be
honored at delivery if he/she goes to delivery.
That is, the long (short) is guaranteed to be
able to take delivery and pay the contract price
(deliver and receive the contract price) if
he/she gets to delivery. 1.2 Liquidity is
defined to be the ease (speed) witch with traders
can enter and exit the market. The easier it is,
the more liquid the market is said to be. The
guarantee implies no default at delivery. Thus,
no credit risk nor completion risk exists. Hence,
the market is anonymous - It makes no difference
whatsoever who is the counterparty to any trade.
So, a trader with any position, long or short,
may exit the market instantly by opening a
position that exactly offsets his/hers current
position. With two offsetting position, a trader
commits to buy and at the same time sell the same
commodity on the same delivery date and thus, the
trader is simply out of the market. Clearly, the
offsetting position is opened at the current
market price and profit or loss may occur. It
follows that entry and exit from the futures
market can be achieved instantly. Thus, the
clearinghouse guaranty provides high liquidity in
the futures market.
2
Q2. Observe the following wheat futures prices
for three consecutive days AUG 13, 2010, AUG
14, 2010 and AUG 15, 2010 Prices are given in
cents per bushel. Wheat contract 5,000
bushels. Delivery _____ Settlement
Prices Month AUG 13 AUG 14 AUG
15 SEP10 327.00 327.50 327.75 DEC10 331.25 331
.75 330.65 MAR11 342.75 343.00 342.10 MAY11 34
7.25 346.75 348.00 JUL11 351.50 351.00 351.50
Your positions at the opening of trading on AUG
14 were 10 long SEP10 30 long MAR11 10 long
JUL11 20 short DEC10 20 short MAY11 You
did not trade on AUG14 and not on AUG 15.
Explain the cash flows into and out of your
margin account by the end of trading on AUG 14
and AUG15 and calculate the net effect of these
cash flows on the amount of capital in your
margin account.
Position Margin account Margin account
Position AUG 14 AUG 15
10 long SEP 10 (.005)50,000 250 (.0025)50,000 125
20 short DEC 10 -(.005)100,000 -500 (.011)100,000 1,100
30 long MAR 11 (.0025)150,000 375 -(.009)150,000 -1,350
20 short MAY 11 (.005)100,000 500 -(0.0125)100,000 -1,250
10 long JUL 11 -(.005)50,000 -250 (.005)50,000 250
Total change 375 -1,125
3
Q3. 3.1 The Basis on date j for a futures
contract with delivery date T, Bj,T for j T, is
defined to be the difference between the
commoditys spot price on date j, Sj, minus the
date j futures price for delivery on date T,
Fj,T Bj,T Sj Fj,T 3.2 Suppose that when a
hedger opens a short hedge at time t, and the
basis is - 1/unit. Later, on date k, the hedge
is closed and the basis is -1/unit. Date Spot
Market Futures Market Basis t St Short a
futures for -1.00 delivery at T.
Ft,T k Sell commodity for Sk Long a futures
for -1.00 delivery at T. Fk,T The actual
selling price is Sk Ft,T Fk,T Ft,T
Bk,T Ft,T 1 Ft,T Bt,T Ft,T St -
Ft,T St. Alternatively, we showed in class
that the selling price is Sk Ft,T Fk,T
St St Rearranging the terms in the last
equation yields St Bk Bt. In our case
the result is that the actual selling price is
the initial spot price because Bk Bt -1.
4

• Q4. I agree with the statement.
• PROOF In case of a long hedge we have
• A LONG HEDGE
• TIME SPOT FUTURES B
• t Contract to buy LONG Ft,T Bt
• Do nothing
• k BUY Sk SHORT Fk,T Bk
• T Delivery
• Actual purchase price
• Sk Ft,T - Fk,T Ft,T Sk - Fk,T
  Ft,T BASISk
• In the case of a short hedge we have
• A SHORT HEDGE
• TIME SPOT FUTURES B
• t Contract to sell SHORT Ft,T Bt
• Do nothing
• k SELL Sk LONG Fk,T Bk
• T Delivery

5
Q5. A speculator observe the following futures
prices on FEB 3 FFEB3, JUL 3.25/bushel
FFEB3, OCT 3.95/bushel The speculator expects
the spread to narrow. 5.1 Sell the spread
Short the OCT futures and Long the JUL
futures. 5.2 On JUN 1 the market futures prices
are FJUN1, JUL 2.85/bushel FJUN1, OCT
3.15/bushel, Close the spread Long the OCT
futures and Short the JUL futures. The speculator
Profit per unit 3.95 - 3.25 - 3.15 2.85
.40.
6
Q6. 6.1 DATE SPOT MARKET FUTURES MARKET MAR
15 Contracts to Long 50 OCT WTI F
53.90/barrel Buy 50,000 barrels WTI Sell
840,000 gallons GAS Short 20 OCT GAS F 1.57/
gallon on SEP 20 Do Nothing 6.2 DATE SPOT
MARKET FUTURES MARKET SEP 20 Buy 50,000 barrels
Short 50 OCT WTI F 62.34/barrel WTI
S(WTI) 59.00 Long 20 OCT GAS F
1.47/gallon Sell 840,000 gallons of G
S(GAS) 1.48 WTI purchase price 53.90
59.00 62.34 50.56/barrel. GAS selling
price 1.57 1.48 1.47
1.58/gallon.
7
Q7. 7.1 Calculate the cash flow associated with
this agreement on SEP 20. The payments are
according to the contract between the refinery
and ZZZ 7.2 In the previous question
we found that The refinery sells the GAS for
1.57/gallon. Now, together with the
agreement with ZZZ, the refinery receives
1.58 - .08 1.50/gallon. Notice that this
selling price is the original spot price of
1.50/gallon on MAR 15.
ZZZ
1.48 1.47 .01
Refinery
1.50 1.57 -.07
Thus, the CF to the Refinery is -.01 (-.07)
-.08, which implies that the refinery pays ZZZ
eight cents per gallon.
8
Q8. 8.1 The interest is paid out on a
quarterly basis thus, we first, must make sure
that the annual rate with quarterly compounding
is equivalent to the annual rate of 10 with
daily compounding. This ensures that at the end
of five years the total amount in the account
will be the same, regardless of the way the
interest was paid out. Thus, by the definition
of equivalent annual rates we have 25,0001.1/3
65365(5) 25,0001R4/44(5) R4
4(1.1/365365/4 1) R4 .101246 or
10.1246 The quarterly interest paid out by the
account is 25,000.101246/4
632.7875. 8.2 rC, the annual rate with
continuous compounding that is equivalent to the
given 10 annual rate with daily compounding is
defined by the following equality 25,000e5rC
25,0001.1/365365(5) rC 365ln1 .1/365 rC
.099986 or 9.9986