Question

In: Finance

Problem 1 Assume the T-bill maturity and futures delivery are on the same day. Ignore transactions...

Problem 1

Assume the T-bill maturity and futures delivery are on the same day. Ignore transactions costs.

Treasury Bill

Maturity          DTM               Bid                  Asked                                    

Mar                 90                    1.18                 1.17                                        

Index Futures

S&P 500 Index (CME)

                        Open               High                Low                 Settle

Mar                 1,905.00          1,911.00          1,901.00            1,907.70

S&P 500 closed at $1,910.00 on the same day.

  1. Find the discount factor using the T-bill data. Please use the “Bid” yield for the calculation.
  1. Suppose that if you buy one unit of S&P 500 index today, you will be entitled to a $10.00 dividend on the delivery day. Consider the following zero-net-investment strategy: buy S&P 500 index spot, borrow at the risk-free rate, and short the S&P 500 futures. Make sure your positions add up to zero at t=0. Show the cash flows from all your positions in the following table, per unit.

Position

Cash Flow, t=0

Cash Flow, Maturity

Buy S&P 500

Borrow

Short Futures

TOTAL CASH FLOW

0
  1. Considering that each S&P 500 futures contract is for 250 units of the index, what is your total arbitrage profit per 1000 contracts?

Solutions

Expert Solution

a.

Calculation of discount factor by using the Treasury-bill data:

Formula to calculate the discount factor:

Substituting Equation (1) with $100 for FV, $98.82 (100-1.18) for PP and 90 days for M to calculate the value of discount factor.

Hence, the value of discount factor is 0.295%.

Where,

FV is face value of bond

PP is price of bond

M is the date to maturity

b.

Completing the table:

Hence, profit per unit is $4.

c.

Calculation of Total Arbitrage Profit:

Formula to calculate total arbitrage profit:

Substituting Equation (2) with $4 for profit per unit, 250 for total units in contract and 1000 for total contracts to calculate the value of total arbitrage profit.

Hence, the value of total arbitrage profit is $1,000,000.

jeff jeffy answered 4 months ago
Next > < Previous

Related Solutions

A T-bill that is 275 days from maturity is selling for $96,010. The T-bill has a...
A T-bill that is 275 days from maturity is selling for $96,010. The T-bill has a face value of $100,000. a. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill. b. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill if it matures in 350 days.    Calculate the discount yield, bond equivalent yield, and EAR on the T-bill. (Use 360 days for discount yield and 365 days in a year for bond equivalent...
A T-bill that is 275 days from maturity is selling for $96,010. The T-bill has a...
A T-bill that is 275 days from maturity is selling for $96,010. The T-bill has a face value of $100,000. a. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill. b. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill if it matures in 350 days. Calculate the discount yield, bond equivalent yield, and EAR on the T-bill. (Use 360 days for discount yield and 365 days in a year for bond equivalent yield...
2-4 You can purchase a T-bill that is 73 days from maturity for $16,965. The T-bill...
2-4 You can purchase a T-bill that is 73 days from maturity for $16,965. The T-bill has a face value of $17,000. a. Calculate the T-bill’s quoted yield. (Use 360 days in a year. Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) T-bill’s quoted yield % b. Calculate the T-bill’s bond equivalent yield. (Use 365 days in a year. Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) T-bill’s...
1-Assume that a currency’s spot and futures price are the same, and the currency’s interest rate...
1-Assume that a currency’s spot and futures price are the same, and the currency’s interest rate is higher than the U.S. rate. If US investors wish to lock in the higher foreign return (and limit risk), what effect will the actions of U.S. investors have on the currency’s spot rate? the currency’s futures price? 2- Your company expects to receive 5,000,000 Japanese yen 60 days from now. You decide to hedge your position by selling Japanese yen forward. The current...
You purchase a 182 day T-bill when it is issued.  The bill has a par value of...
You purchase a 182 day T-bill when it is issued.  The bill has a par value of $1,000, and you paid $990 for it. 1. What is the T-bill discount when you purchased the bill? 2. What is the T-bill yield expected to be if you hold the bill until maturity? 3. If you hold the bill for 60 days and sell it in the secondary market for $995, what is the T-bill yield on your investment?
Assume the following spot prices and that they equal the futures prices for September delivery. Soybeans           ...
Assume the following spot prices and that they equal the futures prices for September delivery. Soybeans            $10.625 per bushel Soybean Meal    $319.90 per ton Soybean Oil        $.3798 per pound a.       Calculate the gross profit margin (GPM) in dollars and percentage from crushing one bushel of soybeans. b.       Does a bushel of soybean produce a greater amount of soy meal or soy oil? Quantify your answer. c.       In looking at the prices above, note that the soybeans are substantially higher (about 3...
Question 2 (8 marks) A T-bill quote sheet has 98-day T-bill (Face value: $10,000) quotes with...
Question 2 A T-bill quote sheet has 98-day T-bill (Face value: $10,000) quotes with a 3.86% bid and a 3.83% ask rates. (a) Calculate purchase price of the bill. (b) Calculate the corresponding bond equivalent yield. (c) Prices of zero-coupon bonds reveal the following pattern of interest rates: Years from now 1-year interest rate 0 5.2% 1 7.3% 2 8.6% Calculate: i) 2-year interest rate on today and 3-year interest rate on today. ii) 1-year forward rate 3 years from...
Write the correct answer using a decimal form. 1.A T-bill with 41 days to maturity has...
Write the correct answer using a decimal form. 1.A T-bill with 41 days to maturity has a $10,000 par value, a bid price of $9,995 and an asked price of $9,997. What is the asked yield? 2. A T-bill has 247 days to maturity. The T-bill par value is $1,000 and has an asked of 1.785%. What is the T-bill asked price in dollars?
The discount rate for a T-Bill with a maturity date of December30, 2020 (80 days...
The discount rate for a T-Bill with a maturity date of December 30, 2020 (80 days from its settlement date) and an even value of $100,000 is 0.225%. The price for this T-Bill isa. $90,950b. $19,950c. $9,950d. $99,950
A T-bill that is 180 days from maturity with a face value of $100,000 is selling...
A T-bill that is 180 days from maturity with a face value of $100,000 is selling for $98,850. (A) Calculate the discount yield, bond equivalent yield, and EAR on the T-bill. (B) Calculate the discount yield, bond equivalent yield, and EAR on the T-bill if it matures in 150 days.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT