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York University

Administrative Studies

ADMS 4503

Nabil Tahani

Winter

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LIH TING JOYCE LI STUDENT# 211423803
ASSIGNMENT 1
Answer 1.
a. The present value of the dividends “I” , is
I = 2e;0.04 x 2/1+ 2e;0.04 x 8/12= 1.986711 + 1.947371 = 3.934082
rt
So that F0= ( S0- I )e
= (194.5 – 3.934082) e0.04 x 1
= 190.565918 x 1.408108
= 198.34
Theoretical 1 year future price: $198.34
b. Since the theoretical 1 year future price is $206.51, the market has overpriced the contract and there is an
arbitrage that consists of shorting the 1 year forward contract to sell 1 stock at the maturity date, borrow
the money at the risk free rate of 4% to buy the stock today at $ 194.5.
Today In 1 year
Short one 1 year forward 0 200
contract to sell 1 stock @ $200
Buy a stock -194.5
Dividend I = -$3.93 Receive $2 in 2 months and 8
months
Borrow: Excess = $194.5 - $3.93 Payback loan $198.34
=-$ 190.57
Total 0 $1.65
0.04 x 1
Loan amount to be paid back at the date of maturity = 190.57e = $198.34 which is also the
theoretical future price calculated in part a.
Note that, today we buy the stock at spot price of $ 194.5; we receive dividends of $2 in 2months and 8
months.As such the Present value of these dividends as calculated in part (a) is $3.93, we need a loan of
$194.5 - $3.93 = $ 190.57.
At the end of one year, we sell the stock at $200, and we have to pay the loan on $190.57 plus interest for
one year at 4% risk free rate, which gives $ 198.34
By doing this, we lock in a net profit of $1.65 for one contract
(Assumption: 1 contract has one IBM stock)
c. If future price 10 months from now is $204 that is the spot price. The value of the short futures
contract would be :
f = S − Ke ;rt
0 ;0.04 x 2/12
= 204 – 200 x e
= 204 – (200 x 0.993356)
= 204 – 198.671101 = $1.33 LIH TING JOYCE LI STUDENT# 211423803
Answer 2:
a. S 0 1472, q = 0.02, r = 0.04.
𝐓𝐡𝐞 𝐭𝐡𝐞𝐨𝐫𝐞𝐜𝐭𝐢𝐜𝐚𝐥 𝟏 𝐲𝐞𝐚𝐫 𝐟𝐮𝐭𝐮𝐫𝐞 𝐩𝐫𝐢𝐜𝐞:
r;q t
F 0 S e0
= 1472e 0.04;0.02 x 1
= 1472 x 1.020201
= $ 1501.74
b. Since the 1 year future price is $1490, the future contract is underpriced and therefore gives opportunity
for arbitrage in the following manner:
Today At maturity
Long in one future contract 0 -$1490
Short one S&P500 asset +$1472
Dividend paid out 1472 x 2% = -$29.44
Invest the proceeds @ 4% =$1472 -29.44 = -$1442.56 1442.56𝐞 𝟎.𝟎𝟒 𝐱 = $1501.43
Total 0 $11.43
Here, at time zero, we take a long position on one future contract and short one asset, investing the net
proceeds at the risk free rate of 4%. Here net proceeds would mean sales proceeds less dividend paid out
at 2% of asset price $29.44, thus investing $1442.56 at 4% compounded continuously, giving us $1501.43
at maturity, when we buy the future at $1490.
These steps would help give a profit of $11.43.
(Here, we have assumed that one contract has one stock)
Answer 3.
a. Convenience yield :
We input all information in the following formula and find y “yield”
yT r:u T
F 0 = 𝑆 0
710 e y x 0.5= 701 e(0.04;0.02 0.5
y x 0.5
e = 1.017392
Y = 0.034485
So the convenience yield: 3.4485%
b. If there is no arbitrage , convenience yield is zero
So that:
F 0 yT= 𝑆 0 r:u T
9
(710+5) e (0 12) = S e (0.04:0.02 9/12
0 LIH TING JOYCE LI STUDENT# 211423803
715
(0.04+0.02 9/12 S0
e
S = 715/ 1.0460279
0
= $683.54
So the spot price of palladium 9 months from now with no arbitrage = $683.54
Note: we added $5 the Future price because we take the $100,000 gain on 200x 100 oz = 20,000oz
Gain per oz = 100,000/ 20,000 = $5
Answer 4.
a. For 6 month future exchan

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