Question

You hold a portfolio of US Treasuries with a roughly even split between 1 year, 5 year and 10-year bonds (these are the years to maturity as of now). Assume that all US Treasury yields would have a similar outlook (obviously different yields, but the same trends for 1, 5 and 10-year bonds). Further, assume that your thoughts were in line with most of the market, that is, bond yields would continue to increase through all of 2019.

1)     Back in June of 2019, under the assumptions above, which Treasuries would you sell first? Your 1, 5 or 10-year bonds and why – I want to see your thinking on maturity and price effects related to interest rate changes.

2)   Explain why changes in bond yield (required returns) and bond prices are inversely related.

3)     Discuss how price risk may differ for investors that intend to hold their bills/bonds to maturity vs. those that are more likely to churn or turn over their bond portfolios. This is not a big “investment class” discussion, this is about the basics that you should understand from the course material. As a hint, think about holding period return and yield to maturity as well as the value of a bond when you sell it vs. the value at maturity.

Answer 1

(1) All the treasury yields have similar outlook i.e. the trend. Therefore, all the treasuries are similar as far as return requirement is concerned as it shows a similar trend whether upward or downward. Under the assumptions, one would first sell the treasury with longer maturity. The simple logic being the longer the maturity period the higher is the fluctuation in interest rate risk as it serves a longer period in existence. So, its convenient to have bonds with shorter maturities among treasuries having similar outlook. The treasuries shall be sold in the order of 10 year, 5 year and 1 year bonds.

(2) Bond yield is the required rate of return of an investor. Bond price is the price an investor is willing to pay in order to earn such income. This inverses relationship between bond yield and price can be understood effectively with an example.

Suppose an investors required rate of return is 10% and a bond has a face value of 1,000 with coupon rate being 6%

So, the price which investor shall be willing to pay for a 6% coupon/ interest rate for a bond having face value of 1,000 will be (1,000 * 6%)/10% = 600.

This shows that bond current price for a required rate of return of 10% is 600. Similarly, when the required rate of return is 12%, investor's willingness to pay = (1,000 * 6%) / 12% = 500.

If the required rate of return falls to 8%, investor's willingness to pay = (1,000 * 6%) / 8% = 750.

Trend: Bond yield = 10% Bond price = 600

Bond yield = 12% Bond price = 500

Bond yield = 8% Bond price = 750

Therefore, it can be clearly seen that as the bond yield or the required rate of return is inversely proportional to the bond price and vice versa.

(3) Price risk differs among various classes of investors mainly dependent on their risk appetite. The investors holding their investments till maturity are more of the type which holds on to a certain decision and go all the away through it without taking the course of any alternate investment opportunities whereas investors who are willing to opt to any opportunity that arises during the course of the investment are the other type with more active participation.