Question

Price a 5-year 1.625% annual coupon bond with a face value of $100 on the basis

of daily treasury yield curve data for relevant rates as of July 9, 2018 available on

https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/textview.aspx?data=yield

Now assume that you forecast that an upward parallel shift of 15 basis points will occur in the term structure at t=1. Work out P1, the price of the bond at t=1, and h1, the one-yearholding period return. Was this bond a good investment? Explain

Answer 1

Annual Coupon is 1.625%, Face Value (Maturity Value) - $100 and the YTM (relevant yield curve info) is 2.75%. The current price of this bond will be the future cash flows discounted at 2.75%, as below:

Price = 1.625/(1+2.75%) + 1.625/(1+2.75%)² + ... + (100+1.625)/(1+2.75%)⁵ = 94.81

After 1 year, if the market rate increase by 15 bps, then the yield will become 2.90% and now the residual maturity of the bond is only 4 years. Hence, we have :

Price = 1.625/(1+2.75%) + 1.625/(1+2.75%)² + ... + (100+1.625)/(1+2.75%)⁴ = 95.79

1 year holding period return = (1.625 + (95.79-94.81))/94.81 = 2.75%

Given that the bond 1 year return is equal to the yeild prevailing at the time of investment, it should be considered satisfactory