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Fixed Income: HW 2

1) Suppose that a life insurance company has guaranteed a one-time payment of $14 million to a pension fund 4.5 years from now. If the life insurance company receives a premium of $10.4 million from the pension fund today, and can invest this entire premium in an asset that makes a one-time payment 4.5 years from now which grows at an annual interest rate of 6.25% compounded semi-annually, will it have sufficient funds from this investment to meet the $14 million obligation?

2) The portfolio manager of a tax-exempt fund is considering investing $500,000 in a debt instrument that makes a one-time payment four years from now that grows at an annual interest rate of 5.7%, compounded annually. At the end of four years, the portfolio manager plans to reinvest the proceeds into a security that will make a one-time payment three years after that, and expects that an annual interest rate of 7.2%, compounded annually, can be earned over this three year period. What is the seven-year expected future value of this investment?

3). Suppose that the portfolio manager in Question 2 has the opportunity to invest the $500,000 in a debt obligation that makes a one-time payment seven years from now, and that promises to pay an annual interest rate of 6.1% compounded semiannually. Is this investment alternative more attractive than the one in Question 2?

4) Calculate for each of the following bonds the price per $1,000 of par value assuming semiannual coupon payments.

Bond Coupon Rate (%) Years to Maturity Required Yield (%)

A 8 9 7

B 9 20 9

C 6 15 10

D 0 14 8

5) Suppose that you are reviewing a price sheet for bonds and see the following prices (per $100 par value) reported. You observe what seem to be several errors. Without calculating the price of each bond, indicate which bonds seem to be reported incorrectly, and explain why?

Bond Price Coupon Rate (%) Required Yield (%)

U 90 6 9

V 96 9 8

W 110 8 6

X 105 0 5

Y 107 7 9

Z 100 6 6

6) We will be running a portfolio competition throughout the course. There are four exchange-traded funds (ETFs) that you can invest in: SHY (short-maturity Treasuries), TLT (long-maturity Treasuries), LQD (investment-grade corporates) and HYG (high-yield corporates). In the spreadsheet: HW2_data.xlsx you can find the cum-dividend prices for these ETFs and for the SP500. Here we examine the historical returns of these five securities.

6a) Determine log-returns, which at date-t we define as the forward looking term Ln [ P_(t+1)/ P_(t) ] and not Ln [ P_(t)/ P_(t-1) ]. As in the previous HW, you will have one less row of returns than what you have with the levels!! Please do not include either the levels or the returns in your write up.

6b) Determine (and report) average annual historical log-returns. These are obtained by first determining average monthly returns, and then multiplying by 12.

6c) Determine (and report) the correlation matrix of log-returns. When we discuss defaultable debt in a few weeks, we will argue that holding a corporate bond is like holding a portfolio that is part risk-free bond, and part equity. Moreover, the higher the default risk, the more equity-like the corporate bond becomes. Do the observed correlations of the corporate bond ETFs seem in agreement with that story?

6d) Identify the annual variances for each asset class by multiplying the average monthly variance by 12. The take the square root to determine (and report) the annual volatility.

7) For the date 01/20/2023, download the 5Y, 7Y, 10Y, 20Y and 30Y nominal Treasury yields from https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/textview.aspx?data=yield

Then for the same date, download the 5Y, 7Y, 10Y, 20Y and 30Y real Treasury yields (i.e., TIPS) from https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/TextView.aspx?data=realyield

Determine the breakeven inflation rate for each maturity, and then report a plot of i) nominal yield, ii) real yields, and iii) breakeven inflation rates as functions of maturity. Do investors believe that the US is on a path of approximately 2% inflation per year over the long run?