Say I am a long a 10Y US govt. bond and short (i.e., pay fixed) a 10Y US IRS. The swap spread moves, for example, from -0.25 to -0.3. What do I need to calculate P&L (approximately)?

Are such swap spread trades typically made duration neutral by weighting appropriately according to the duration of the two legs?

I'm new to relative-value/swap spreads so would appreciate any relevant information and links.

Thanks, V

The fundamental underlying PnL you have is PnL on a bond and PnL on a swap, but you can choose to arbitrarily allocate this in different perspectives.

Say you have the following DV01s: Bond +102, Swap -99, and say the market movements are: Bond +2bp, Swap: +1.7bp. The corresponding PnLs are: Bond +204, Swap -168, Total: +36.

Your question thus becomes how do you allocate this PnL to a "swapspread" instrument. Let me give you a mathematical representation...

# Basic Outright Instruments

Risk: $\begin{bmatrix} Bond \\ Swap \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \begin{bmatrix} +102 \\ -99 \end{bmatrix}$, Change: $\begin{bmatrix} Bond \\ Swap \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \begin{bmatrix} +2.0 \\ +1.7 \end{bmatrix}$
Total PnL = $Risk \cdot Change = \begin{bmatrix} +102 \\ -99 \end{bmatrix} \cdot \begin{bmatrix} +2.0 \\ +1.7 \end{bmatrix} = \sum \begin{bmatrix} +204 \\ -168.3 \end{bmatrix}= +35.7$

This model attributes all bond risk to swapspread and any residual is allocated to swap delta.
Risk: $\begin{bmatrix} Swapspd \\ Swap \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 1 & 1 \\ \end{bmatrix} \begin{bmatrix} +102 \\ -99 \end{bmatrix}$, Change: $\begin{bmatrix} Swapspd \\ Swap \end{bmatrix} = \begin{bmatrix} 1 & -1 \\ 0 & 1 \\ \end{bmatrix} \begin{bmatrix} +2.0 \\ +1.7 \end{bmatrix}$
Total PnL = $Risk \cdot Change = \begin{bmatrix} +102 \\ +3 \end{bmatrix} \cdot \begin{bmatrix} +0.3 \\ +1.7 \end{bmatrix} = \sum \begin{bmatrix} +30.6 \\ +5.1 \end{bmatrix} = +35.7$

Risk: $\begin{bmatrix} Bond \\ Swapspd \end{bmatrix} = \begin{bmatrix} 1 & 1 \\ 0 & -1 \\ \end{bmatrix} \begin{bmatrix} +102 \\ -99 \end{bmatrix}$, Change: $\begin{bmatrix} Swapspd \\ Swap \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 1 & -1 \\ \end{bmatrix} \begin{bmatrix} +2.0 \\ +1.7 \end{bmatrix}$
Total PnL = $Risk \cdot Change = \begin{bmatrix} +3 \\ +99 \end{bmatrix} \cdot \begin{bmatrix} +2 \\ +0.3 \end{bmatrix} = \sum \begin{bmatrix} +6.0 \\ +29.7 \end{bmatrix} = +35.7$