Question

Andy Lancaster works as a fixed income analyst in Brandy mutual fund that invests in both equities and fixed income securities. His supervisor Tim Howard requires him to prepare his expectations regarding the yield curve. He prepared a memo stating that the 1-year interest rate in UK is expected to remain stable at its current level of 3.25%. Andy also prepared the yield curve, which is derived from the spot rates on UK Treasury securities. His yield curve shows the following data:

Maturity Spot Rate 1 year 3.25% 2 years 4.00% 5 years 6.80% 10 years 7.20%

The medium term portion of the Brandy mutual fund fixed income portfolio contains the following securities: A 6% coupon corporate bond maturing in ten years, A 6% coupon corporate bond maturing in five years, A 6% coupon UK government bond maturing in ten years. On November 15, 2015 the Treasury yield curve experienced an upward parallel shift equal to 112 basis points. Further increases in yields are expected as rate reverts to its long term mean. To reduce the impact on the portfolio Stanley proposed to sell some of the corporate bonds maturing after 5 years and to use the cash to buy more of the 10 year government and corporate bonds. Two years later, the 1-year, 2-year, and 3 year spot rates are 4.0%, 4.5%, and 4.75%, respectively. Tim Howard wants to diversify the medium term portion of the fixed income portfolio across more maturities. He asked Andy to look for cheap bonds for investment that matures in three years. S Andy believes that there is a good opportunity to purchase an under-valued 4% annual pay corporate bond with three years left until maturity and a par value of £1000. The bond is offered at a market price of £990. Wilma Green works as a stock investment manager in Brandy mutual fund. He has been following the stock price movements of Bakery supply international (BSI) and Hull Petrochemical Company (HPC). Green is convinced that the price of BSI stock is going to dramatically increase from its current price of $53.60 and that the price of HPC stock is going to dramatically decrease from its current price of $9.80. She has decided to buy/sell options to take advantage of the situation and has thus gathered the following data on three month put and call options for the two stocks:

BSI Call 8.5, 4.4, 1.1 Strike 45, 50, 55, Put 0.2, 0.5, 2.75

HPC Call 2.5 , 0.55, 0.1 Strike 7.5 , 10, 12.5 Put 0.15, 0.75 , 2.75

Task: 1. Discuss which of the three theories of the term structure of interest rates is least consistent with Stanley’s data in the table above? (3 Marks)

2. Indicate whether Andy’s proposal on buying and selling bonds is sound or not? Justify your answer. (2 Marks)

3. Indicate the maximum price that Howard is willing to pay for the bond investment proposed by Andy? (2 Marks)

4. Suppose that 3 months later, the price of BSI stock is $54.60 and the price of HPC stock is $8.13. Based on the table above, propose a strategy that would yield Green the greatest profit. (3 Marks)

Answer 1

1. Liquidity preference theory is least consistent because this theory assumes that investor prefers short term bond to long term bond. In the given case above Stanley however prefers long term bond when he says to increase exposure to 10 years bond (which is of highest maturity)instead of 5 year mid term bond.

2. No, Andy's proposal is not sound. The bond which should have been trading at 979.93(PV of bond) is trading at 990. It is over priced. Rather Andy should have suggested to short the bond instead of going long.

3.

Coupon 4%, FV 1000, Cash flow in year 1= 40, year=40, year 3= 040. Spot rate for year 1= 4%, year 2= 4.5%, year 3=4.75%

PV of Year 1 cash flow= 40/(1+4%)^1 = 38.46

PV of Year 2 cash flow= 40/(1+ 4.5%)^2 = 36.63

PV of Year 3 cash flow= 1040/(1+ 4.75%)^3 = 904.84

PV of bond= 38.46 + 36.63 + 904.84

= 979.93

4. Buy 3 month Call option on BSI with strike price of 55. Premium paid 1.1. At maturity price is 54.60 so call option expires out of money and is not exercised. Only loss is premium paid 1.1

Buy 3 month Put option on HPC with strike price of 12.5. Premium paid 2.75. at maturity stock price is 8.13 so put option is in the money and will be exercised.Buy HPC in spot market at price 8.13 and sell at strike price .

payoff from put option=(12.5 - 8.13)

= 4.37

Profit from put option = (Pay Off - Premium Paid)

= 4.37 - 2.75

= 1.62

Net profit = 1.62 - 1.1

= .52