Calculating a Bond’s One-Year Total Return from Spot Curves

Summary

The document poses a one-year holding-period return problem for a coupon bond using annual spot rates today and a projected spot curve one year later. The calculation must combine the coupon received during the year with the bond’s sale value after that coupon date, then compare the total proceeds with the purchase price. This distinguishes holding-period return from simply discounting a single future cash flow or comparing the bond’s initial price with an incomplete sale-price estimate.

The question gives a current bond value and reports an answer of 0.77 percent, while the response points to a present-value table for the bond at purchase and after twelve months. The table itself is not included in the supplied text, so its intermediate calculations and assumptions cannot be checked here. The result depends on the specified future spot curve, coupon timing, and valuation immediately after the first coupon is paid; it should not be generalized as a forecast or a guaranteed return.

Key ideas

• A bond’s one-year holding-period return includes both the coupon received and the change in its market value.
• The sale price should be valued using the spot curve expected to prevail at the sale date.
• Cash-flow timing matters: the future bond value here is considered after payment of the first coupon.
• The stated return relies on the assumed future spot curve and the problem’s coupon and timing conventions.

Tags

# Total return of a bond using spot rates


# Total return of a bond using spot rates












Suppose that the current spot rate curve (annually compounded) is s1=0.2%, s2=0.8%, s3=1.2%.

Assume that one year from now, the spot rate curve will be s'1=0.8%, s'2=1.4%, s'3=1.8%.

Consider a 3-year bond with annual coupon 5%. If you purchase that bond today and hold it for one year, what will be your total return (i.e. consider both price change and coupon)? (nearest 0.01%, and e.g. write 5.02 for 5.02%).

Answer should be: 0.77

What I have tried: step 1: find the current price of a three year bond: 111.2199

Find the sell price: 105/1.008= 104.16

But why the sell price is less than a buy price? and I m ending up with negative return. How to get to 0.77?

Thank you!!!

## Answer by demully (score 2, accepted)

https://quant.stackexchange.com/a/60475

Hopefully clear from the table below. On the left, the NPV of the bond today is 111.2199, exactly as you say. On the right is the same for 12 months time, after the payment of the first coupon.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.