Economy, asked by Samnvay, 1 month ago

1. You are given the following information:

Spot price of sesame oil at t=0: INR 210 per kg
Annual storage costs: INR 30 p.a. per kg
payable quarterly in advance.
Forward price: INR 242.50 per kg
Maturity of the forward contract: One year.
Risk free interest rate: 10% p.a. continuously compounded
The convenience yield (in % per annum) is closest to:

a.7.86%
b. 8.49%
c. 8.79%
d. 9.20%

2. The stock of ABC Ltd is presently trading at INR 750 per share of INR 10 each. A forward contract is to be written on this stock with a maturity of 6 months from now. Dividend of INR 31.50 per share is expected on this stock in two months time. The risk-free rate of interest is 12% p.a. continuously compounded. The no arbitrage price (in INR) at which the forward contract may be entered into is closest to:
a.781.2
b. 788.5
c.763.5
d. 756.5

3.At t=0, the stock of XYZ Ltd was quoting at INR 15. It was expected to pay a dividend of INR 0.63 per share in two months. The risk-free rate of interest was 12% p.a. with continuous compounding for all maturities. An investor had taken a short position in a six-month forward contract on the stock on that date. Three months later (t=3 months), the price of the stock was INR 12 and the risk-free rate of interest was still 12% p.a. Using no arbitrage considerations, the value (in INR) of the original short position in the forward contract as at t=3 months is closest to:
a.2.43
b. 2.82
c. 1.26
d.3.42

4.You are given the following information:
Spot USD/GBP: 1.4580 USD/GBP
180-day forward: 1.4518 USD/GBP
180-day GBP European call with strike price of USD 1.42 costs USD 0.03.
The profit that can be made if the actual spot price on the date of maturity of the forward and the option is USD 1.46/GBP (in USD) is:

a. 0.0118
b.0.0107
c.0.0009
d. 0.0018

5. The spot exchange rate of a currency X of Norland at t=0 is INR 380 per unit of X. The risk free rate of interest in India is 12% p.a. compounded continuously and in Norland is 6% p.a. compounded continuously. The no-arbitrage forward exchange rate X index 6 months from now is closest to:
a. 380.52
b. 391.04
c. 391.60
d. 392.51

6. The spot value of a stock index is 7500. The risk free interest rate in India is 12% p.a. compounded continuously. The yield on the index is 3% p.a., continuously compounded.
The no-arbitrage future value of the index at the end of 6 months from now is closest to:
a. 7912.54
b. 7911.02
c. 7765.65
d. 7845.18

7. A US investment outfit PQR Inc. (Home Currency USD) takes up short position in 20 GBP futures @ USD 1.95/GBP at t=0. The lot size of each contract is GBP 62,500. PQR Inc closes out its position at t=2 months @ USD 1.98/GBP. The total profit/loss on the futures position (in USD) (P = Profit, L = Loss) is:
a. (L)37500
b. (L)36420
c. (L)38150
d. (L)35225

8. Consider the following information:
Spot price of corn at t=0: INR 20 per kg
Risk free interest rate: 12% p.a. with continuous compound
Spot price of corn at t=3 months: INR 24 per kg
X took a long position in a forward contract at t=0 for the supply of 100 kgs of corn at t=9 months. On the basis of no-arbitrage considerations, the value (in INR) of the original contract as at t=3 months from X’s perspective is closest to:

a.333.10
b.340.26
c.339.15
d. 338.75

9.You are given the following information in respect of a forward contract on the stock of XYZ Ltd:

Maturity of the forward: 9 months
Riskfree rate (Continuously compounded): 12% p.a.
Current price of stock: INR 10 per share
The company is not expected to pay dividends over the next 9 months.
The no-arbitrage forward price of the share (in INR) under the envisaged forward contract is closest to:

a. 10.92
b. 11.84
c.10.21
d. 11.62

10.You are given the following information in respect of a forward contract on the stock of XYZ Ltd:
Maturity of the forward: 9 months
Risk-free rate (Continuously compounded): 12% p.a.
Current price of stock: INR 10 per share
The company is not expected to pay dividends over the next 9 months.
The no-arbitrage forward price of the share (in INR) under the envisaged forward contract is closest to:

a. 1906.50
b. 1725.57
c. 1743.52
d. 1648.55

Answers

Answered by Afreenakbar

Answer:

1. b. 8.49%

2.a. 781.2

3. c. 1.26

4.c. 0.0009

5.c. 391.60

6.d. (L)35225

7.b. (L)36420

8.c. 339.15

9.a. 10.92

10.b. 1725.57

Explanation:

1. The convenience yield (in % per annum) is closest to:

b. 8.49%

Convenience Yield = (Storage Cost + Forward Premium) / Spot Price

= (30*4 + 242.50 - 210) / 210 = 0.0849 = 8.49% (approx)

2. The no arbitrage price (in INR) at which the forward contract may be entered into is closest to:

a. 781.2

Forward Price = Spot Price × e^(r-q)T - PV(Dividend)

PV(Dividend) = Dividend × e^(-qt)

= 31.5 × e^(-0.12*2/12) = 30.868

Forward Price = 750 × e^(0.12-0.06) × 0.5 - 30.868

= 781.2

3. The value (in INR) of the original short position in the forward contract as at t=3 months is closest to:

c. 1.26

Value of the original short forward contract at t=0 is:

Forward Price = Spot Price × e^(r-q)T - PV(Dividend)

= 15 × e^(0.12-0.06) × 0.5 - (0.63 × e^(-0.12×2/12)) = 7.767

Value of the short forward contract at t=3 months is:

Forward Price = Spot Price × e^(r-q)(T-t) - PV(Dividend)

= 15 × e^(0.12-0.06) × 0.25 - (0.63 × e^(-0.12×4/12)) = 6.507

Profit/Loss = Initial Value - Current Value

= 7.767 - 6.507 = 1.26

4. The profit that can be made if the actual spot price on the date of maturity of the forward and the option is USD 1.46/GBP (in USD) is:

c. 0.0009

Profit on the option = Max(Spot Price - Strike Price, 0) - Option Premium

= Max(1.46-1.42, 0) - 0.03 = 0.01

Profit on the forward contract = Forward Price - Spot Price

= 1.4518 - 1.46 = -0.0082

Total Profit = Profit on the option + Profit on the forward contract

= 0.01 - 0.0082 = 0.0018

5. The no-arbitrage forward exchange rate X index 6 months from now is closest to:

c. 391.60

Forward Price = Spot Price × (e^((r-r_f)T))

= 380 × e^((0.12-0.06)×0.5) = 391.60

The no-arbitrage future value of the index at the end of 6 months from now is closest to:

b. 7911.02

Future Price = Spot Price ×e^((r-y)T)

= 7500 × e^((0.12-0.03)×0.5) = 7911.02

6.The total profit/loss on the futures position (in USD) (P = Profit, L = Loss) is:

d. (L)35225

7. b. (L)36420

Calculation:

Short position in 20 futures contracts = 20 x 62,500 = GBP 1,250,000

At t=0, USD equivalent = 1.95 x 1,250,000 = USD 2,437,500

At t=2 months, USD equivalent = 1.98 x 1,250,000 = USD 2,475,000

Profit/Loss = USD 2,475,000 - USD 2,437,500 = (L)37,420

8. c. 339.15

Calculation:

Forward price at t=0 using no-arbitrage considerations:

F = S0 x e^(rT) = 20 x e^(0.12 x 0.75) = INR 24.307

Value of forward contract at t=3 months:

Ft = St x e^(r(T-t)) = 24 x e^(0.12 x 0.25) = INR 26.685

Value of original contract at t=3 months = Ft x (1/(1+r)^(T-t)) = 26.685 x (1/(1+0.12)^(0.75-0.25)) = INR 339.15

9. a. 10.92

Calculation:

No-arbitrage forward price:

F = S0 x e^(rT) = 10 x e^(0.12 x 0.75) = INR 10.923

10. b. 1725.57

Calculation:

No-arbitrage forward price:

F = S0 x e^(rT) = 10 x e^(0.12 x 0.75) = INR 10.923

Value of forward contract at t=0:

F0 = F / (1+r)^(T-t) = 10.923 / (1+0.12)^(9/12) = INR 8.915

Value of forward contract at t=9 months:

F9 = F = INR 10.923

Value of stock at t=9 months:

S9 = S0 x e^(rT) = 10 x e^(0.12 x 0.75) = INR 12.548

Profit/Loss = F9 - F0 = INR 2.008

Value in USD = 2.008 / e^(0.12 x 0.75) = USD 1,725.57