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Measuring Yield, part II

Horizon Return

The use of yield-to-maturity as a measurement of a bond’s expected return is based on the assumption that the investor reinvests the bond’s coupon interest in securities that offer the same rate of return. In reality, coupon income is likely to be invested in different securities yielding different returns. However, it is possible to estimate the expected return that a bond will earn if its coupon income is reinvested at an alternative rate. This measurement is known as horizon yield.

Consider the following example: Calculate the horizon yield of a semi-annual coupon bond with a $1,000 face value, a $970 market value, an 8% coupon rate, and seven years until maturity. Assume the bond’s coupon interest can be reinvested at a rate of 5%.

Deriving horizon yield requires several steps as shown below:

First, calculate the future value of all coupon payments assuming a reinvestment rate of 5% (2.5% per period for 14 periods):

N = 14 I = 2.5 PMT = 40 FV = Solve, FV = $660.76

Second, derive the future value of all cash flows by summing the future value of all coupon payments with the bond’s face value (principal to repaid at maturity):

$660.76 + $1,000 = $1,660.76

Third, use the future value of all cash flows, the bond’s market value, and the periods remaining until maturity to derive the bond’s periodic horizon return:

N = 14 PV* = $-970 FV = $1,660.76 I = Solve, I = 3.916

*Entered as a negative figure because it represents a cash outflow

Four, compute horizon yield by applying the periodic horizon return, calculated above, with the following formula:

Horizon Yield = (1 + r_PH)ⁿ – 1

Where: r_PH = periodic horizon yield; n = periods per year

Horizon Yield = (1.03916)² – 1 = .0799 or 7.99%

Determinants of Reinvestment Risk

The primary determinants of reinvestment risk are length-to-maturity, coupon rate, and market value. Reinvestment risk increases with length-to-maturity. Bonds with larger coupon rates are also more vulnerable to reinvestment risk. Finally, bonds selling at a premium have more reinvestment risk than bonds selling at a discount because a greater percentage of the former’s total return is derived from coupon interest. Bonds sold at a discount earn a lesser percentage of their total return from coupon payments and receive additional income in the form of a capital gain.

Questions:

1. Calculate the horizon yield of a semi-annual coupon bond with a $1,000 face value, a $920 market value, a 7% coupon rate, and six years until maturity. Assume the bond’s coupon interest can be reinvested at a rate of 8%.

2. Calculate the horizon yield of a semi-annual coupon bond with a $1,000 face value, a $1,075 market value, a 6% coupon rate, and three years until maturity. Assume the bond’s coupon interest can be reinvested at a rate of 5%.

3. Calculate the holding period yield of a semi-annual coupon bond purchased four years ago for $920 if it is sold today for $980. Assume a 4% coupon rate and a $1,000 face value.

Answers:

1. 9.31%       Future Value of all Cash Flows = $1,525.90
               Periodic Horizon Return = 4.301%
               Horizon Yield = 8.79%

2. 1.95%       Future Value of all Cash Flows = $1,191.63
             Periodic Horizon Return = 1.732%
               Horizon Yield = 3.49%

3. 24% HPY = [(980 – 920) + (20*8)] / 920 = 0.24