Joi Chatman recently received her finance degree and has decided to enter the mo
ID: 2709673 • Letter: J
Question
Joi Chatman recently received her finance degree and has decided to enter the mortgage broker business. Rather than working for someone else, she will open her own shop. Her cousin Mike has approached her about a mortgage for a house he is building. The house will be completed in three months, and he will need the mortgage at that time. Mike wants a 15-year, fixed-rate mortgage in the amount of $500,000 with monthly payments. Joi has agreed to lend Mike the money in three months at the current market rate of 4 percent. Because Joi is just starting out, she does not have $500,000 available for the loan; she approaches Ian Turnbell, the president of IT Insurance Corporation, about purchasing the mortgage from her in three months. Ian has agreed to purchase the mortgage in three months, but he is unwilling to set a price on the mortgage. Instead, he has agreed in writing to purchase the mortgage at the market rate in three months. There are Treasury bond futures contracts available for delivery in three months. A Treasury bond contract is for $100,000 in face value of Treasury bonds.
Suppose that in the next three months the market rate of interest rises to 6 percent.
How much will Ian be willing to pay for the mortgage?
What will happen to the value of Treasury bond futures contracts? Will a long or short position increase in value?
Suppose that in the next three months the market rate of interest falls to 3 percent.
How much will Ian be willing to pay for the mortgage?
What will happen to the value of T-bond futures contracts? Will a long or short position increase in value?
Are there any possible risks Joi faces in using Treasury bond futures contracts to hedge her interest rate risk?
Explanation / Answer
Let MB0 =Present Value of Mortgage in 3 months, MP=monthly pay=500,000, r be the current market rate of interest=6%/12 or 6/12%=.5% per month, T be time to maturity=15*12=180 months
MB0=(MP/r){(1-1/(1+r)T)}
MB0=(500,000/.005)(1-1/(1.005)180)=(100000000)(1-1/(1.005)180)=$59251757.33
Thus Ian be willing to pay $59,251,757.33 for the mortgage.
Treasury bond futures contracts are futures contracts on Treasury bond,with the market rate of interest rise to 6 percent the value of underlying Treasury bond shall decrease thus as one with a long position in futures is also long on underlying Treasury bond shall also see decrease in the value in the position whereas a short position in futures on underlying Treasury bond shall see increase in the value in the position as short profits when long is in losses and short losses when long is in profits.
If in the next three months the market rate of interest falls to 3 percent.
Let MB0 =Present Value of Mortgage in 3 months, MP=monthly pay=500,000, r be the current market rate of interest= 3/12%=.25% per month, T be time to maturity=15*12=180 months
MB0=(MP/r){(1-1/(1+r)T)}
MB0=(500,000/.0025)(1-1/(1.0025)180)=(200000000)(1-1/(1.0025)180)=$72402735.73
Thus Ian be willing to pay $72,402,735.73 for the mortgage.
Treasury bond futures contracts are futures contracts on Treasury bond,with the market rate of interest falling to 3 percent the value of underlying Treasury bond shall increase thus as one with a long position in futures is also long on underlying Treasury bond shall also see increase in the value in the position whereas a short position in futures on underlying Treasury bond shall see decrease in the value in the position as short profits when long is in losses and short losses when long is in profits.
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