Approximating Portfolio Yield to Maturity with Market-Value Weights
Summary
The note addresses how to combine the yields to maturity of bonds in an equally weighted portfolio. Equal weighting generally means investing equal dollar amounts, so the holdings have equal market values; face values can differ because bond prices differ. Market value is the appropriate basis for portfolio weights, rather than face value or bond count.
When each bond receives the same investment, the note proposes averaging individual YTMs with equal weights. It presents this as an approximation because yield to maturity is nonlinear. If the bonds' cash flows are available, calculating the portfolio's internal rate of return directly is preferable; the weighted average is offered for cases without those cash-flow details. The discussion gives a method but no worked example or evidence about the size of approximation error.
Key ideas
- Equal investment across bonds means equal market-value holdings, not necessarily equal face values.
- Portfolio weights should reflect market values rather than face amounts.
- For equal market-value allocations, a simple average of individual YTMs is an approximation.
- Portfolio YTM is nonlinear, so directly solving for the IRR from aggregate cash flows is more exact.
- The approximation is useful when bond cash flows are unavailable.
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Full text
# YTM computation for a bond portfolio
# YTM computation for a bond portfolio
Given a list of bond and the relative YTM, i have to compute the YTM of the equally weighted portfolio. Should i use the market value of each security or the face value is correct enough?
Thank you
## Answer by Ellinoquant (score 2)
https://quant.stackexchange.com/a/82484
"Equally weighted" typically refers to equal investment in terms of market value — not face value or the number of bonds.
This means, you invest the same amount of money in each bond, not necessarily the same face value amount since bond prices fluctuate.
Market value matters because YTM is a market-value-weighted concept. It reflects the internal rate of return (IRR) on the price for each bond, not just its face value. Therefore you need to use the market value of each bond when computing the portfolio YTM; using face value would distort the result.
So you need to 1) Determine Market Value Weights and 2) Use a Weighted Average of YTMs
If you invest the same dollar amount in each of the n bonds, then the market value of each bond in the portfolio is equal. In this case, the weight of each bond is:
$$ w_i = \frac{1}{n} = \frac{\text{MV of holdings in bond } i}{\text{Total MV of the Portfolio}}$$
Where $n$ is the number of bonds in your portfolio. Although YTM is technically non-linear, a weighted average of individual YTMs using market value weights is an acceptable approximation, but of course, since you know it is equally weighted, all you have to do is use 1/n as your weights:
$$\text{Portfolio YTM} \approx \sum_{i=1}^{n} w_i \cdot \text{YTM}_i $$
If you don’t have access to the cash flows of each bond (i.e., can't calculate the IRR of the portfolio directly) this is a good approach.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.