ECN603 Asset Pricing/PS2
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ECN603 Asset Pricing/PS2
(1) An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with a) annual compounding, b) semi- annual compounding, c) monthly compounding and d) continuous compounding.
(2) Zero interest rates with continuous compounding are listed in the table below.
a. Calculate forward interest rates
b. Value an FRA where you will pay 5% for the third year on $1million
|
Maturity (years) |
Rate (% per annum) |
|
1 |
2.0 |
|
2 |
3.0 |
|
3 |
3.7 |
|
4 |
4.2 |
|
5 |
4.5 |
(3) A five year bond with a yield of 11% continuously compounded pays an 8% coupon at the end of each year
a. What is the bond’s price?
b. What is the bond’s duration?
c. Use the duration to calculate the effect on the bond’s price of a 20 basis points decrease in its yield.
d. Recalculate the bond’s price if the yield is 10.8% continuously compounded and verify that the result is in agreement with your answer to (c)
(4) The cash prices of six-month and one year Treasury bills are 94.0 and 89.0. A 1.5 year bond that will pay coupons of 4 every six months currently sells at 94.84 . A two year bond that will pay coupon of 5 every six months currently sells for 97.12. Calculate the six month, one year, 1.5 year and two year zero rates.
(5) A futures contract is used for hedging. Explain why the marking to market of the contract can give rise to cash flow problems
(6) Only July 1, an investor holds 50,000 shares of a certain stock. The market price is
$30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index futures price is currently 1,500 one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow?
(7) The standard deviation of monthly changes in the spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk.
Each contract is for the delivery of 40,000 pounds of cattle. What strategy should the beef producer follow?
(8) The CEO of an airlines states: “There is no point in using oil futures. The is just as much chance that the price of oil in the future will be less than the futures price as there is that it will be greater than this price” . Discuss the CEO’s viewpoint.
(9) An interest rate is quoted as 5% per annum with semi-annual compounding. What is the equivalent rate with a) annual compounding, b) monthly compounding, c) continuous compounding?
(10) The 6-month, 12 month, 18 month, and 24 month zero rates are 4%, 4.5%, 4.75%
and 5% with semi-annual compounding.
a. What are the rates with continuous compounding
b. What is the forward rate for the six month period beginning in 18 months
c. What is the value for an FRA that promises to pay you 6% (compounded semi- annually) on a principal of $1 million for the six month period starting in 18 months?
(11) Explain what basis risk means and why it occurs.
(12) Explain why a short hedger’s position improves when the basis strengthens
unexpectedly and worsens when the basis weakens unexpectedly.
(13) A hedge fund has a $20 million portfolio with a beta of 1.2 (as measured against the
S&P500). The fund would like to use futures contracts to hedge its risk. The S&P500 index futures is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that would minimise risk? What should the fund do if it wants to reduce the beta of the portfolio to 0.6?
2023-05-22