false

Class Notes
(862,778)

CA
(521,983)

York
(37,398)

ADMS
(3,404)

ADMS 4503
(13)

Nabil Tahani
(13)

Lecture

School

York University
Department

Administrative Studies

Course Code

ADMS 4503

Professor

Nabil Tahani

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

More
Less
Unlock Document

Subscribers Only

Related notes for ADMS 4503

Only page 1 are available for preview. Some parts have been intentionally blurred.

Unlock Document
Subscribers Only

Practice

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.