Hedge Ratios and Portfolio Returns in Cointegration Pairs Trading

Summary

The document raises two practical questions about turning cointegration relationships into a pairs trading portfolio. It compares a regression of log prices with one using raw prices, each expressed as a fitted relationship between assets and a residual spread. The central issue is how to interpret the estimated coefficient when setting the long and short positions: as share quantities or as dollar exposures.

It also asks how to calculate portfolio returns and net asset value when trading multiple cointegration vectors. The author considers tracking the market value of open long and short positions and adding these to capital, but gives no calculation, worked example, or evidence that resolves the question. The discussion is therefore a useful statement of implementation choices rather than a complete strategy guide. In practice, the meaning of the hedge coefficient depends on the regression specification, and return accounting also needs explicit assumptions about capital, rebalancing, financing, and transaction costs; those details are not covered here.

Key ideas

• The document contrasts cointegration regressions using log prices and raw prices.
• The author asks whether the fitted coefficient represents share quantities or dollar exposures.
• Portfolio return and net asset value calculations become less direct when several cointegration vectors are used.
• Tracking the market value of open positions is proposed as a possible accounting approach, but it is not developed or validated.

Tags

# Pairs trading strategy: Portfolio returns and NAV


# Pairs trading strategy: Portfolio returns and NAV












Currently trying a pairs trading approach using cointegration. Tried both formations:

$$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$

$$P_t^A=P_t^B \hat{\gamma}+\hat{\mu} +\epsilon_t\hspace{2.4cm} (2)$$

However, I am struggling in the calculation of two things: Firstly, the hedge ratio in both models, implies 1 share long (short) of A and $\hat{\gamma}$ short (long) of B or 1 dollar long (short) of A and $\hat{\gamma}$ dollar short (long) of B. Secondly, how should returns be calculated, since I have multiple cointegration vectors: $CV=[1 \hspace{0.3cm}\hat{\gamma}]$. My thought is to calculate daily, in market values the open Long and Short positions, adding the total capital at this point.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.