Question

A. You have a client who is interested in reducing the risk in their investment portfolio and is looking at including some US government bonds in that portfolio. In doing your research as to what to recommend you note the following: a. There is one set of bonds with 1 years remaining to maturity – with a coupon rate of 4.6% and face value of $1,000. They have a market price of $1,027 b. A second bond has 5 years to maturity, has a coupon rate of 6.4% and face value of $1,000 – with a current market price of $925 c. A third bond has 10 years to maturity and has a coupon rate of 4.5% and a face value of $1,000. It has a current market price of $1200 These bonds pay interest semi-annually. If your client buys these bonds and holds them to maturity, what yield could they expect? Suggest an interpretation of the implied yield curve?

Answer 1

The three bonds on offer with semi-annual coupon payments, if and when held to maturity would give their respective YTM's as returns. Hence, one needs to calculate their respective YTMs.

(a) Bond Par Value = $ 1000, Market Value = $ 1027, Coupon Rate =4.6% per annum , Maturity = 1 year

Let bond yield be R1 per half year

Therefore, 1027 = 23 / (1+R1) + 1023 / (1+R1)^(2)

Using EXCEL goal seek to solve the above equation we get

R1 = 0.93 % per half year or 1.86% per annum

(b)

Bond Par Value = $ 1000, Market Value = $ 925, Coupon Rate = 6.4% per annum , Maturity = 5 year

Let bond yield be R2 per half year

Therefore, 925 = 32 x (1/R2) x [1-{1/(1+R2)^(10)}] + 1000 / (1+R2)^(10)

Using EXCEL goal seek to solve the above equation we get

R2 = 4.13 % per half year or 8.26 % per annum

(c)

Bond Par Value = $ 1000, Market Value = $ 1200, Coupon Rate =4.5% per annum , Maturity = 10 year

Let bond yield be R3 per half year

Therefore, 1200 = 22.5 x (1/R3) x [1-{1/(1+R3)^(20)}] + 1000 / (1+R3)^(20)

Using EXCEL goal seek to solve the above equation we get

R3 = 1.13 % per half year or 2,26 % per annum

The implied yield curve (or expected YTMs of bonds with differing maturities) is found to show an initial rise with an increase in maturity, followed by a gradual decline as maturity goes beyond a certain range. This shows that near-term interest rates are expected to be low, followed by a sharp rise in the medium term followed by a decline again in the very long term. It also implies that near term and long term bond investment is considered very safe, hence higher prices and low-interest rates for the same. The opposite is true about medium-term bond investments.