Question

# 1a) The spot exchange rate is \$0.75 US/CAD. The U.S. interest rate is 2%, the interest...

1a) The spot exchange rate is \$0.75 US/CAD. The U.S. interest rate is 2%, the interest rate in Canada is 3%. A futures contract on 1,000,000 CAD, with one year to delivery, settles at 0.77 US/CAD. Calculate the amount of U.S. dollars that you need for the arbitrage strategy.

 Borrow \$978,874 U.S. Borrow \$728,155 U.S. Invest \$978,874 U.S. Invest \$728,155 U.S.

1b) A futures contract on S&P 500 with the maturity 3 months has settled at 2,510 today. The underlying index value is \$2,500 now and is going to pay a \$10 dividend in 3 months. The discount factor (present value of \$1) is 0.997. Calculate your arbitrage profit in 3 months from the strategy in the table below (per unit of the index).

 Position Cash Flow, t=0 Cash Flow, in 3 months Buy S&P 500 -2,500 Borrow at the risk-free rate +2,500 Short Futures 0 Total 0 Arbitrage profit = ?

1c) Cash price of the bond is 116.978. The next coupon of \$6 will be paid in 122 days (0.3342 years). The term structure is flat, and the interest rate is 10%. Using the parity equation for T-bond futures, find the cash futures price for delivery in 250 days (0.6849 years). Round to the nearest integer.

 110 115 120 125

1d) Quoted price of the bond is \$105. Coupon is 10% per year, paid twice a year. Par value is \$100. The most recent coupon was paid 50 days ago, and the next coupon will be paid 132 days from now. Find the cash price of the bond. Round to the nearest integer.

 100 106 111 115

1e) Cash futures price is 119.67. The bond pays coupons of \$6. At the time of delivery, the most recent coupon would be paid 128 days prior to delivery, and the next coupon would be paid 55 days following delivery. Conversion factor is 1.65. Find the quoted (settlement) futures price. Round to the nearest integer.

 65 70 75 80

1a)

As per Interest Rate Parity,

Theoretical Forward Rate \$/C\$ = Spot \$/C\$*(1+Interest Rate on \$)/(1+Interest Rate on C\$)

= 0.75*[1+0.02]/[1+0.03]

= 0.7427

Actual Forward Rate > Theoretical Forward Rate

Actual Forward Rate of C\$ is Overvalued

To make an Arbitrage Gain, Buy C\$ in Spot and Sell in Forward

To Buy C\$ in Spot, we need \$. Therefore, we need to Borrow \$.

Futures Contract is of C\$1000000. Therefore, we need to invest C\$, so that it will yield C\$1000000 after 1 year. Therefore, C\$ to be invested = 1000000/1.03 = C\$970873.79

To Buy C\$ 970873.79 today, we need 970873.79*0.75 = \$728155.34

Therefore, Borrow \$728155 U.S.

Note: Given questions are 5 DIFFERENT QUESTIONS and NOT SUB QUESTIONS. And, as per Guidelines, we are supposed to answer ONLY 1 QUESTION.