Including Coupon Income in Fixed-Income Portfolio Optimization
Summary
The document asks how to apply mean-variance optimization to a portfolio of municipal, high-yield, and investment-grade bond indexes when coupon information and option-adjusted duration are also available. It distinguishes monthly index returns from coupon rates and duration observations, and focuses on how coupon income should enter the optimization rather than treating the assets like stocks.
No proposed calculation, portfolio weights, or empirical comparison is supplied; the material is a homework question with a short time series of example data. It therefore identifies a modeling issue rather than demonstrating a solution. The key distinction is whether the return series already includes coupon income: if total returns are used, adding coupons separately could count that income twice, while price returns may require income to be incorporated. The document does not clarify the return definition or provide enough context to resolve that choice, and duration is presented as data without a specified role in the objective or constraints.
Key ideas
- The optimization compares municipal, high-yield, and investment-grade bond indexes.
- The data include monthly returns, coupon rates, and option-adjusted durations.
- Whether coupons should be added depends on whether the return series already includes income.
- The document poses the modeling question but does not specify a solution or the role of duration.
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Full text
# Opimization on a Bond Portfolio
# Opimization on a Bond Portfolio
```
+++++++ returns+++++++ === Coupon Return======/////// OAD /////////
Muni_return HY_return IG_return Muni_coup HY_coup IG_coup Muni_oad HY_oad IG_oad
11/30/07 1.11 -2.17 0.60 0.39 0.67 0.49 6.37 4.60 6.21
12/31/07 0.28 0.29 0.16 0.38 0.70 0.49 6.39 4.55 6.23
01/31/08 2.03 -1.33 1.02 0.38 0.69 0.49 6.56 4.62 6.24
02/29/08 -4.15 -1.36 0.11 0.38 0.72 0.49 6.78 4.61 6.25
03/31/08 2.57 -0.34 -1.27 0.39 0.73 0.49 6.76 4.54 6.23
04/30/08 0.59 4.31 0.91 0.38 0.74 0.50 6.62 4.43 6.28
05/30/08 0.50 0.36 -0.95 0.38 0.71 0.50 6.52 4.39 6.20
06/30/08 -1.04 -2.80 -0.64 0.38 0.72 0.51 6.53 4.45 6.21
07/31/08 0.77 -1.33 -0.75 0.39 0.74 0.51 6.62 4.41 6.14
08/29/08 1.40 0.35 0.72 0.39 0.79 0.52 6.61 4.39 6.13
```
Hey guy I am stuck on a homework for one of my financial engineering classes. I apologize for the data formatting but I am trying to optimize by using Mean-Variance optimization of a portfolio of 3 assets of fixed income bond index securities (Muni, HighYield, InvestmentGrade). First Column is the date, the next 3 columns are the monthly percentage returns, the next three are the coupon rates at the point in time of Muni,HY,IG, respectively. The last three are the option adjusted duration at the point in time of the bond, all he same order.
I know how to do MVO optimization on any number of securities with returns. my problem are the coupons, how do I include the coupons into the MVO optimization?? These aren't stocks and I need to include the coupons in the optimization somehow. Anyone have any idea? Thank you!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.