Calculating Daily PnL for a Swap-Rate Momentum Strategy
Summary
The document describes a daily momentum strategy in swap rates. A positive signal leads to paying fixed and receiving floating, creating short-duration exposure; a negative signal leads to receiving fixed and paying floating, creating long-duration exposure. The signal is observed at the prior close, the position is opened at the next day’s open, and it is closed at that day’s close.
The author considers a PnL expression based on the prior signal, the daily change in the swap rate, and DV01, but is unsure about its sign convention after obtaining a negative Sharpe ratio. Using the absolute rate change is also reported to perform poorly out of sample. The document asks how to construct PnL but provides no accepted resolution or performance evidence establishing the correct formula. Transaction costs are excluded, and the proposed use is a baseline check of the indicator.
Key ideas
- The prior day’s signal determines the swap position opened at the next day’s open.
- Positive momentum corresponds to paying fixed and taking short-duration exposure in the described setup.
- Negative momentum corresponds to receiving fixed and taking long-duration exposure.
- The author questions the sign convention in a proposed PnL calculation using rate changes and DV01.
- Transaction costs are omitted, and no resolved formula is provided.
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Full text
# PnL Construction for Momentum Strategy in Swap Rate
# PnL Construction for Momentum Strategy in Swap Rate
I am currently working on a momentum strategy involving swap rates. In particular, if my momentum indicator detects +1 (i.e., positive momentum), I then want to pay fix and receive floating (short duration). Instead, if my indicator detects -1 (i.e., negative momentum), then I want to receive fixed and pay floating (long duration). The way I want to construct my strategy is:
- at closing of day t-1 I get the value of the indicator
- at opening of day t I trade based on the indicator stored at closing t-1 (trading strategy defined above)
- at closing of day t I close my position.
I am not considering transaction costs. My question then is: how can I construct a PnL for such strategy?
I didn't find much useful info online. Many agreed to use the formula below:
$PnL_t = - Indicator_{t-1} * \text{delta_r} * DV01.$
Implementing such approach, I get a negative Sharpe Ratio. Moreover, I think that delta_r is inducing error in terms of sign. Indeed, I need that "-" sign in the formula to capture the fact that when the indicator is +1 I want to short duration. However, If I get a negative daily change in the swap rate, then I get a final + sign even if the indicator detects positive momentum. I tried to consider the abs of delta_r, aiming at isolating the magnitude of the change rather than the direction, but OOS performs poorly.
Hope I was clear enough. Otherwise, do not hesitate to ask further questions. Thank you in advance!
P.S. I know this strategy may sound over-simplifying, but I only need it as a baseline strategy to see whether my indicator is working fine.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.