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ADMS 4503 (13)
Lecture

Assignment 1.docx

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Department
Administrative Studies
Course Code
ADMS 4503
Professor
Nabil Tahani

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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 2/12 + 2e;0.04 x 8/12 = 1.986711 + 1.947371 = 3.934082
So that F0 = ( S0 - I )ert
= (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
contract to sell 1 stock @ $200
0
200
Buy a stock
-194.5
Dividend
I = -$3.93
Receive $2 in 2 months and 8
months
Borrow:
Excess = $194.5 - $3.93
=-$ 190.57
Payback loan $198.34
Total
0
$1.65
Loan amount to be paid back at the date of maturity = 190.57e0.04 x 1 = $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 = S0Ke;rt
= 204 200 x e;0.04 x 2/12
= 204 (200 x 0.993356)
= 204 198.671101 = $1.33

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Description
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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