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I'm trying to calculate the total return (in %) on a 9% coupon 20-year bond with the following assumptions:

  1. reinvestment rate of 6% annually (3% every six months)
  2. terminal yield of 12% (semiannual rate of 6%)
  3. face value of the bond is 1000

Assume I buy the bond at par and hold it for 10 years.

I keep getting 7.37% but the book I am using says it should be 6.6%.

=((1+(-((FV(0.06/2,20,45)+PV(0.12/2,20,45,1000))/(1000))^(1/(10*2))-1))^2)-1

In steps:

1. Total coupon payments plus interest on interest: -FV(0.06/2,20,45) -> 1209.167

2. Projected sale price at the end of 10 years: -PV(0.12/2,20,45,1000) -> 827.951

3. Add 1, 2: 1209.167+827.951 -> 2037.118

4. total present dollars/purchase price ^(1/h) -1 : (2037.118/1000)^(1/20)-1 -> 0.036217231

5. (semiannual rate^2) -1 : 1.036217231^2-1 -> 0.07374615

This is not homework help.

The above problem is one entry in the following matrix:

The values across the top are reinvestment rate. The Values along the left side are terminal yields. The entries are total returns. The matrix was taken from Common Sense on Mutual Funds by Jack Bogle, which is his "forecast" for bond returns in the 1990s. He calls it "Bond Market Total Return Matrix for the 1990s"

6% 7% 8% 9% 10% 11% 12%
12 6.6% 7.0% 7.3% 7.7% 8.0% 8.4% 8.2%
11 7.1 7.4 7.7 8.1 8.5 8.5 9.2
10 7.5 7.8 8.2 8.5 8.7 9.3 9.7
9 8.0 8.3 8.6 9.0 9.4 9.9 10.1
8 8.5 8.8 9.3 9.5 9.9 10.2 10.6
7 9.0 9.6 9.6 10.0 10.4 10.7 11.1
6 10.0 9.8 10.2 10.5 10.9 11.3 11.7
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    $\begingroup$ Other than the unnecessary step towards the end, your formulation and answer appear to be correct. Are you sure you understand and copy the question correctly? Which book is the question from? $\endgroup$
    – Alper
    Commented Jun 3, 2023 at 6:06
  • $\begingroup$ The book is Common Sense on Mutual Funds (updated 10th anniversary edition), by John Bogle. The question is really one entry in a matrix he builds to demonstrate the 3 factors that explain bond returns: initial coupon (yield on long-term US Treasury Bonds), reinvestment rate, and terminal yield. The matrix creates a framework of expectations for returns from bonds in the future. The terminal yields are 6-12% and terminal yields are 6-12%. The 5 steps are from Fabozzi's Handbook of Fixed Income Securities. He has a similar matrix for his discussion of Total Return, called a Scenario Analysis. $\endgroup$
    – IamGroot
    Commented Jun 3, 2023 at 20:24
  • $\begingroup$ As an exercise, I am attempting to recreate Bogle's matrix in Excel using Fabozzi's Total Return 5 step calculation. $\endgroup$
    – IamGroot
    Commented Jun 3, 2023 at 20:28
  • $\begingroup$ One thing I noticed is that Fabozzi gives you the purchase price of the bond. Bogle doesn't explicitly do that. Bogle says that given his assumptions, if the terminal yield were to rise to 12%, and the average reinvestment rate were to fall to 6%, the total return for the bond would be 6.6%. $\endgroup$
    – IamGroot
    Commented Jun 3, 2023 at 20:34
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    $\begingroup$ When the reinvestment rate and the terminal yield are also 9%, the total return, i.e. the compound annual growth rate, of the investment would be 9.2% as your new formula calculates. For that scenario, you can also get the 9.2% simply by $\left(1 + \dfrac{9\%}2\right)^2-1$ as coupons are reinvested every six months. Assuming your description of all the variables are correct, I think 7.37% is the correct answer to your original question. That means, there is a problem either with the table in Bogle’s book or your understanding / his description of the terms in it. $\endgroup$
    – Alper
    Commented Jun 3, 2023 at 22:44

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