Estimating Bond Total Return from Coupon Reinvestment and Terminal Yield
Summary
The document examines how to estimate the annualized total return on a long-term coupon bond held for part of its maturity. Its calculation accumulates coupon payments at an assumed reinvestment rate, estimates the bond's sale price using a terminal yield, combines those amounts, and annualizes the result over the holding period. The example considers a bond purchased at par and compares a calculated return with a published figure.
A return matrix attributed to Jack Bogle varies reinvestment rates and terminal yields to illustrate how both assumptions affect projected returns. The author questions a discrepancy between their calculation and the book's result, but the document does not resolve it. The matrix is a forecast framework, not evidence of realized performance; the calculation also depends on coupon timing, compounding conventions, and the assumed sale yield.
Key ideas
- Total return combines reinvested coupon income with the bond's value at sale.
- The terminal yield determines the estimated sale price after the holding period.
- Reinvestment rate and terminal yield jointly affect the projected annualized return.
- The example identifies a mismatch with a published figure but does not explain its source.
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Full text
# Total Return on Bond # Total Return on Bond I'm trying to calculate the total return (in %) on a 9% coupon 20-year bond with the following assumptions: - reinvestment rate of 6% annually (3% every six months) - terminal yield of 12% (semiannual rate of 6%) - 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.