Horizon Yield of a Fixed-Rate Bond

Although fixed-rate bonds have a stated maturity, they can be sold before the maturity date. Many investors choose to do just that. If a bond is sold prior to its maturity, the return will likely change. __Horizon yield__ is a calculation that applies to bonds that are sold prior to their maturity date.

Incorrect. Coupons don't change on fixed-rate bonds.

Incorrect. Stocks pay dividends, and bonds pay coupons.

What do you think caused the horizon yield to be lower than the original yield?

Incorrect. The coupon is the same in both calculations of yield.

Very good! The sale price of the bond is lower than the price assumed by the original yield.

Incorrect. The reinvestment rate is the same in both calculations of yield.

What would happen to the horizon yield in this example if the reinvestment rate were higher but the sales price remained the same?

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Incorrect. An increase in the reinvestment rate will not lower the horizon yield.

Incorrect. If the reinvestment rate is higher, the horizon yield will change.

Correct! The sales price will impact the horizon yield because it might be higher or lower than what was assumed by the original yield.

Correct! It would be slightly higher because there is only one cash flow that is compounded.

For example, suppose a bond is purchased at a price of 95.30365. The bond makes annual payments of 6.00% for five years and is based on a principal amount of 100. The original yield on the bond is 7.15%. The investor sells the bond after two years for 96. If the coupons received for the two years were reinvested at the original yield, the future value of the coupons would be: $$\displaystyle 6 \times (1.0715) + 6 = 12.429$$ So, the total cash flow on the bond at future value is equal to: $$\displaystyle 96 + 12.429 = 108.429$$ The horizon yield on the bond solves for this return: $$\displaystyle 95.30365 = \frac{108.429}{(1+r)^2}$$ If you solve for $$r$$, it is equal to the horizon yield of 0.06664, or 6.664%—a bit lower than the original yield of 7.15%.

The only time horizon yield is equal to the original yield on a bond is if the reinvestment rate is at the original yield _and_ the sales price is also at the original yield. So, in the example, a bond is purchased at a price of 95.30365, and the bond makes annual payments of 6.00% for five years. If the bond was sold after two years, there are three years left to maturity. Therefore, the price at the original yield would be: $$\displaystyle 96.990288 = \frac{6}{(1.0715)} + \frac{6}{(1.0715)^2} + \frac{106}{(1.0715)^3}$$ So, the total cash flow on the bond at future value is equal to: $$\displaystyle 96.990288 + 12.429 = 109.419288$$ The horizon yield on the bond is equal to the original yield because: $$\displaystyle 95.303650 = \frac{109.419288}{(1.0715^2)}$$

If a bond is sold before its maturity date, which of the following do you think would affect its return?

The coupon

The sale price

The reinvestment rate

It would be lower

It would be higher

It would be the same

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The sale price

Coupon changes

Dividend changes