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.

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 15SEP10 327.00 327.50 327.75DEC10 331.25 331.75 330.65MAR11 342.75 343.00 342.10MAY11 347.25 346.75 348.00JUL11 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

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

Q3. 3.1The 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 commodity’s

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 -$1.00delivery at T. Ft,T

k Sell commodity for Sk Long a futures for -$1.00delivery 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.

Q4. I agree with the statement.

PROOF: In case of a long hedge we have:

A LONG HEDGE

TIME SPOT FUTURES Bt 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 Bt Contract to sell SHORT Ft,T Bt

Do nothing

k SELL Sk LONG Fk,T Bk

T Delivery

Actual selling price:

= Sk + Ft,T - Fk,T = Ft,T + [Sk - Fk,T] = Ft,T + BASISk

So in either hedge the actual price consists of the known futures price on date t plus the unknown and hence, risky, basis value on date k. In conclusion, opening a hedge implies that the original spot price risk is exchanged with the basis risk .

This completes the proof that the statement is correct.

Q5. A speculator observe the following futures prices on FEB 3:

FFEB3, JUL = $3.25/bushel; FFEB3, OCT = $3.95/bushelThe 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.

Q6.6.1DATE SPOT MARKET FUTURES

MARKETMAR 15 Contracts to: Long 50 OCT WTI F =

$53.90/barrelBuy 50,000 barrels WTISell 840,000 gallons GAS Short 20 OCT GAS F = $1.57/

gallonon SEP 20Do 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) = 59.00Long 20 OCT GAS F =

$1.47/gallon

Sell 840,000 gallonsof 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.

Q7.

7.1Calculate 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.

RefineryZZZ

1.48 – 1.47 = .01

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.

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:

$25,000[1+.1/365]365(5) = $25,000[1+R4/4]4(5)

R4 = 4([1+.1/365]365/4 – 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 = $25,000[1+.1/365]365(5)

rC = 365ln[1 + .1/365]

rC = .099986

or 9.9986%