# A bond

EIFM Seminar 2 – week commencing Oct 18th 2021

Question 1: A bond is a security that is issued in connection with a borrowing arrangement. The borrower issues (i.e., sells) a bond to the lender for some amount of cash and the bond is the “IOU” of the borrower. The contract between the issuer and the bondholder is called the bond indenture. The coupon rate, maturity date, and par value of the bond are part of the bond indenture.

Could you use the above terms to describe the following bond to a potential bond investor? The bond is issued by the UK Treasury, with a coupon rate of 5%, a maturity of 30 years, a par value of £1,000 and one coupon instalment per year.

If the bond in part a) is currently trading at £1,200, could you work out its yield to maturity (YTM) using Excel?

Could you explain the concept of YTM to a potential bond investor? How does the YTM calculated in part b) compare with the bond’s coupon rate?

The bond issued by the UK Treasury is an IOU of the UK Treasury. In this borrowing agreement, UK Treasury is the borrower and bond holder is the lender. The UK Treasury promises to pay bondholder an annual coupon payment of £50 (5% multiplied with £1,000) every year for 30 years and return the par value, £1,000 at the time of maturity, or 30 years from now.

Type “=YIELD(DATE(2021,10,18), DATE(2051,10,18), 0.05, 120, 100, 1)” into any cell and click “return” button

The answer is 0.038626 or 3.86%

The YTM measures the average return from holding a bond to maturity. It takes account of two forms of return: coupon and capital gain or loss. The bond in part b) has a coupon rate of 5% and a YTM of 3.86%. The YTM is lower than the coupon rate because the bond is trading at a price of £1,200, which is £200 above its par value. This built-in capital loss of £200 is reflected in the YTM, but not the coupon rate.

Question 2: When economists use the word “interest rate” they often mean the yield to maturity (YTM). So a rise in interest rate also means a rise in YTM, which is the average return from holding a bond to its maturity. However, when investors believe market interest rate is likely to rise in the near future, they often rush to sell bonds or stay away from bonds for the time being. What’s the rationale for this behaviour?

A rise of YTM is good news for potential bond investors, but bad news for existing bond investors. This is because a rise in YTM means future payments of bond must be discounted more heavily and bond price must fall. For an existing bond holder, this would mean a capital loss. Hence it is logical for existing bondholders to try to sell the bond before this scenario turns into reality. It is also rational for potential investors to wait until interest rate actually rises and then buy the bond at a much reduced price and enjoy a higher average return while holding the bond.

Question 3: Consider a bond with a par value of £1,000, a coupon rate of 10%, a maturity of 29 years and one coupon instalment per year. Suppose the market interest rate of this bond is 20%. Could you work out its market price using the following formula?

Question 4: A financial advisor has just given you the following advice: “Long-term bonds are a great investment because their interest rate is over 20%.” Is this financial advisor necessarily right?