Calculating Portfolio Yield with Bonds and Treasury Futures

# How is yield calculated for a portfolio?


# How is yield calculated for a portfolio?












If you have a portfolio of US government bonds and treasury futures, and you want to calculate the yield of the portfolio, how would you do this?

Would you say $\sum_{i=1}^n w_i y_i$ where $w_i$ is the value-weight of each security and $y_i$ its yield? What about the treasury futures for whom $w_i = 0$?

## Answer by nbbo2 (score 3)

https://quant.stackexchange.com/a/80440

Bond Futures in a Bond Portfolio do not contribute to yield, they are there to modify (increase or decrease) Duration (or DV01 if you prefer). In my opinion they could be left out of the calculation of weighted YTM. They certainly should be taken into account for DV01, however.

## Answer by Sane (score 2)

https://quant.stackexchange.com/a/80433

Once you have the YTM for each bond, calculate the weighted average yield based on the proportion of each bond’s market value relative to the total market value of all bonds in the portfolio.

$PortfolioYield = \sum w_i YTM_{i}$,

where $w_i =\frac{MarketValueBond_{i}}{TotalMarketValue}$.

When dealing with treasury futures, you should calculate implied yield of the contract using price of treasure contract. As you have market value of future contracts and their corresponding implied yields you can compute weighted average implied yield for future contracts, as described above for bonds. Next, you can just combine weighted implied yield with weighted YTM, with corresponding weights.

## Answer by Rylan (score 1)

https://quant.stackexchange.com/a/80448

I buy the argument from @nbbo2 that futures change DV01 but not yield (although you might need to think a bit about the margin; that's something I know nothing about but it always seems to be something you have to consider.)

As a thought, when we calculate YTM of a coupon bond, we basically decompose it into zero-coupon bonds (ZCBs) representing the coupons and the face value, and numerically find the single rate that would make the sum of all the ZCBs equal the market price. We could probably do the same for the whole portfolio (find the single rate for all payments across all holdings that makes the sum of ZCBs match the portfolio's market value).

I can't imagine that procedure would give a value hugely different from the weighted averages given above, however, so if I already had all the YTMs for each bond, I'd use the weighted average with the caveat that it might not be exactly the same.