Calculating Duration and Yield for Long-Short Bond Portfolios

Summary

The document explains how to aggregate duration and yield when a fixed-income portfolio contains long and short positions. Its core method is a weighted sum of each position’s duration, using signed weights based on position market value and a chosen portfolio-value basis. For benchmark-relative positions, the benchmark is set to the same dollar value as the portfolio, so weights represent deviations and sum to zero. For portfolios combining bonds and derivatives, the bond value can serve as the denominator, with derivative positions weighted positively or negatively according to direction.

The same weights are proposed for yield aggregation. The note gives a general accounting convention rather than a worked calculation or evidence that the resulting portfolio yield has a unique interpretation across structures. Weight totals depend on the chosen basis and can be positive, zero, or negative, so the method requires a clearly defined portfolio value and consistent position signs.

Key ideas

• Aggregate position durations as a weighted sum, including signed weights for shorts.
• For benchmark-relative portfolios, measure each position against a benchmark with matching dollar value.
• For portfolios with derivatives, use a stated portfolio-value basis and assign negative weights to short positions.
• The note proposes applying the same weights to yield aggregation.
• Interpretation depends on the chosen denominator and the portfolio’s net exposures.

Tags

# Portfolio duration


# Portfolio duration












What is the correct way to calculate duration of a fixed income portfolio with long and short bond positions? And how to calculate portfolio YTM with long and short positions. For long only (or short only) we use weighted average duration and yield but how to calculate with long and short position?

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/40007

You do it the same way as with long only as weighted sum of the durations of each position.

You have two possibilities for calculating the weights:

long/short with respect to a benchmark: then take as basis the dollar value of your portfolio P USD, set the benchmark to the same dollar value and calculate each weight as fraction of the position $w_i = P_i/P$ and long/short can be deviations from the benchmark. The sum of these weights is zero.

long/short with derivatives: So I assume you are long derivatives and bonds and short derivatives. Then you can again use the sum of your bonds as portfolio value in P USD. Then long derivatives have weights $w_i = MV_i/P$ and short derivatives have $w_i = -MV_i/P$. The sum of these weights (bonds + derivatives) can be positive, zero or negative depending on your position.

I would use the same weights for the yield.

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