Assume that today is July 1, 2020.

A corporate bond rated BB has a YTM of 7%/yr and a maturity date of June 30, 2030. It has a DV01 of $711 per $1,000,000 face value.

A Treasury has a YTM of 2.5%/yr and a maturity date of June 30, 2030. It has a DV01 of $880 per $1,000,000 face value.

Both bonds are priced at par on July 1, 2020. The repo rate is 0.35%/yr.

The typical spread between BB bonds and Treasuries is 300 basis points.

You wish to enter a long/short trade that will be profitable if the spread returns to its typical level, and you want to spend as little of your own cash as possible so you will use repurchase agreements on both sides of the trade, similar to the LTCM problem we did in class. There is a 1% haircut on the repos.

You want to hedge this trade against general movements in interest rates.

You are going to fund this trade for exactly 1 year (which is June 30, 2021). You will close out the trade on June 30, 2021.

Hint: Therefore, you do not need to worry about day count.

In addition to the initial cash flow, this trade will generate cash flows (could be positive or negative) at December 30, 2020 and at June 30, 2021.

On December 30, 2020, if your cash flow is positive, you will invest it at the risk free rate of 0.40%/yr until June 30, 2021.

If the cash flow is negative on December 30, 2020, you will borrow at the risk free rate of 0.40%/yr so that you can pay it. You will pay back this loan on June 30, 2021.

a. Set up this trade on July 1, 2020. Show each position in the trade and show each position’s cash flow as well as the net cash flow.

if you have a net positive net cash flow on July 1 2020, assume that you will invest it at the risk-free rate of 0.40%/yr until June 30, 2021. If you have a negative cash flow July 1 2020, you may ignore it.

Assume that you will invest $1,000,000 in the long position. Label each position clearly. Round bond and repo prices to the nearest dollar. If you are using a calculator, round your DV01 ratio to 4 decimal places. If using a spreadsheet, do not round the DV01 ratio.

b. Close out this trade at 6/30/2021, assuming that the corporate bond’s YTM is 7.5% and the Treasury YTM is 5.5%.

Show all cash flows that arise from closing out this trade (including the effect of any cash flows that occurred at 12/30/20), including your dollar profit or loss. Actually reprice the two bonds at 6/30/21 (do not use DV01 to estimate).