Reinvestment income can make up a large portion of the return for a bond. Before beginning with calculations, it is important to understand the difference between total future dollars, which is equal to all the dollars an investor expects to receive and the total dollar return, which is equal to the dollars the investor will realize from the three sources of income for a bond (coupon payment, capital gain/loss, and reinvestment income)

Example: Reinvestment Income

Let's look at an investor that has $96 to invest in a certificate of deposit (CD) that will mature in five years. The bank will pay 3% every six months, which equals a bond equivalent basis of 6%. The total future value of this investment today would be:

Answer:
96 x (1.03) to the tenth power = $129.02

So the investment of $96 for five years at 6% on a BEY will generate $129.02

To further break it down:
Total Future Dollars = 129.02
Return of Principal = 96.00
Total interest = 33.02

Now let's turn to a bond that has a price of $96, five-year maturity and with a coupon of 5% and YTM of 6%. As shown above an investor must generate $129.02 to provide a yield of 6% or the total dollar return must be $33.02.

So with this bond, the sources of return are a capital gain of: $4 ($100 - $96) and coupon interest of $2.50 for ten periods or $25. That equals $29 without the reinvestment of the coupon payments. As we can see, this leads to a shortfall of $4.02 when compared to the CD example above. This $4.02 can be generated if the coupon payments are invested at a 3% semi-annual rate at the time it is paid.

For the first payment the reinvestment income earned is:

$2.50 x (1.03) to 10 - 1 power - 2.50 = $2.50 x (1.03) to 9th power = $0.76.

If you were to continue this effort, which is unlikely to be required on the exam, you would find the reinvestment income would equal $4.02.

To continue this with the three sources of income would produce the following:

Capital Gain of $4
Coupon Interest of $25
Reinvestment Income or $4.02

The total would be $33.02.
Therefore, reinvestment income accounts for 12% of the total return, illustrating how important reinvestment income can be for an investor.

Factors That Affect Reinvestment Risk

There are two characteristics that affect reinvestment risk:

1. For a given yield to maturity and a given non-zero coupon rate, the longer the maturity, the more the bond's total return depends on reinvestment revenue to realize the yield to maturity at purchase time. Longer maturity = greater reinvestment risk.

2. For a given coupon-paying bond with a given maturity and yield to maturity, the higher the coupon rate, the more the total dollar return depends on the reinvestment of the coupon payments. This must occur in order to produce the yield to maturity at the time of purchase.



Spot Rates and Bond Valuation

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