A one-year bond with face value €100 and annual coupon 3% was bought for €98 and is redeemed today.
- A.Calculate the holding-period return.
A one-year bond with face value €100 and annual coupon 3% was bought for €98 and is redeemed today.
5.10%
A six-year government bond has face value €1,000, annual coupon 5% and yield 3%. Sell it one year later immediately after receiving a coupon. Consider yields of 3% and 2% at sale.
| Sale yield | Ex-coupon sale price | Holding-period return |
|---|---|---|
| 3% | 1,091.59 | 3.00% |
| 2% | 1,141.40 | 7.49% |
Returns: 3.00% with unchanged yield; 7.49% if yield falls to 2%.
Noiz has face value 100, five years to maturity and a 5% annual coupon. It is purchased at par and sold one year later, immediately after the coupon, for 98.50. Xilent has face value 100, a 4% annual coupon and six years remaining; initially it has the same yield as Noiz. Xilent is sold after one year, after the coupon, for 90.
At par, initial YTM equals the coupon rate: 5%.
The new YTM is 5.4272%.
3.50%.
94.92
The coupon rate is below the required yield, so the bond trades below par.
-0.9737%
Bond A has face 1,000, annual coupon 8%, three years to maturity and price 938. Bond B has the same face, coupon and yield but five years to maturity. A is sold one year later, after its coupon, for 910. A new five-year zero-coupon C has the same face and initial yield.
YTM = 10.515782%.
905.88
B has longer duration at the same positive coupon and yield, hence a larger percentage price decline for a small parallel yield increase.
606.57
For a bond that still has time to maturity, the yield decline raises its ex-coupon price above par. The investor receives both the coupon and a capital gain, so the one-year holding-period return exceeds the coupon rate. If the bond matures today, its redemption value is fixed and there is no such price gain.
| Bond | Face | Price | Annual coupon | Years | YTM |
|---|---|---|---|---|---|
| A | 100 | ? | 3% | 5 | 2.57% |
| B | 100 | 96 | 0% | 4 | ? |
Bond D was bought one year ago for 130, has three years remaining, face 100 and annual coupon 12%; its current YTM equals A’s. Separately, a thirty-year government bond with face 100 pays 5% annually and yields 2%.
6.8430%
167.19