When Par-Value Weighting Helps Analyze Bond Default Rates
Summary
The discussion distinguishes bond valuation from portfolio weighting. A bond’s quoted clean or dirty price is a percentage of par, so multiplying that price by the notional held gives the market value of the position. For a portfolio’s dollar value, positions are therefore weighted by the notional owned and market price; for an index, the relevant quantity is notional outstanding times market price.
Par-value weighting serves a different analytical purpose. It is described as a poor measure of short-term portfolio risk, but potentially useful for estimating long-run default rates across a broad set of corporate bonds. If bonds were issued at par, this weighting better represents the default probability associated with a dollar invested at issuance. Using current market values can instead give greater weight to bonds from higher-rate issuance periods, whose coupons and prices may be higher even when credit risk is unchanged. The discussion cites evidence of more stable default rates under par weighting, but does not provide the underlying table or establish that the measure suits every portfolio question.
Key ideas
- Bond prices are quoted as a percentage of par, and multiplying by notional gives a position’s market value.
- Market value weighting reflects the dollar value of bonds currently held or outstanding.
- Par-value weighting can help analyze long-run default rates across a broad corporate-bond universe.
- Par-value weighting is described as unsuitable for measuring short-term portfolio risk.
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# Why use par-value weighted average when valuing portfolio of bonds? # Why use par-value weighted average when valuing portfolio of bonds? I'm looking at a formula for valuing a portfolio of different bonds that sums the market value times the par value for each bond. Conceptually, why are the bond values weighted in this way by their par values, instead of simply ignoring the par value and just summing up the market values? An example would be great. Thanks! ## Answer by Lliane (score 3, accepted) https://quant.stackexchange.com/a/44043 > Sums the market value times the par value for each bond Could you clarify that formula ? From what you wrote it seems to be just a way to dollarize the bond price (market value = 97%, par value = 200 000 USD, bond value(market price) = 194 000 USD) Par value weighted average is a very poor metric of measuring (short term) portfolio risk. It is however useful for analyzing long term default probabilities in a large universe of long term bonds. Page 70 of this paper gives an interesting table that shows par-value weighted average gives more stable default rates. In a large universe of corporate bonds (assuming they were issued at par), it gives you a more accurate picture of the default probability of a dollar invested at issuance of the instruments. If you don't do that you will end up with bonds issued in periods of higher interest rate (thus high coupon and price > 100% keeping credit risk constant) weighting more than bonds issued in periods of lower interest rate (low coupon and price < 100%). ## Answer by NBF (score 2) https://quant.stackexchange.com/a/44057 The clean price (or the dirty price) of a bond is actually the percentage of par or the percentage of the notional that one has to pay to buy the bond. So if the notional or face value is \$10m and the dirty price is 102 then you will pay \$10.2m to own the bonds. (I’m a little loose here about clean vs dirty/invoice price but you should get a good intro book on fixed income to iron that out) For a portfolio you would generally weight by the notional you own of each bond multiplied by the market price. That is the dollar value of what you own. For an index you would weight by the notional outstanding multiplied by the market price.
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