Today is 1/1/2022. The YTM (yield to maturity) for a 10-year treasury bond is 1.5%. You are an analyst at S bank and it is your job to determine the investment of the deposit the bank just received. One option is to invest $10 billion in 10-year treasury bonds. The bond face value is $1,000. The coupon rate is 2% and the coupon is paid twice a year, on 6/30 and 12/31. The maturity date for the 10-year treasury bond is 12/31/2031.

1. What is the price of the bond today? How many bond contracts ($1,000 each contract) can you purchase using the deposit of $10 billion? (3 pts)

2. The bank cannot afford to lose the value of their investment by 25% (bond value becomes less than $7.5 billion). At what market interest rate would the bond price lose 25% of its value? (2 pts)

3. Given the possibility of interest rate increases, you are tasked with conducting a sensitivity analysis with potential interest rate changes. Using the average and standard deviation of the daily interest rate for 10-year treasury bonds from the attached file, you are asked to assess the probability that the bank will fail (lose over 25% of bond value). (15 pts)

a. At first, you decide to use the average and standard deviation values from the daily interest rate in 2021. What is the probability of bank failure after you run 1,000 simulations?

b. Then, you decide to use the data since 2000 (1/3/2000-12/31/2021). Does the result change?

c. Between a and b, which one makes more sense?