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!
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%).
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.