Skip to content
All library documents

Combining Long and Short Asset Returns in a Weighted Portfolio

Article Quant Q&A · Author: Pogger
Read the original

Summary

The document asks how to combine two return series when holding a long position in one asset and a short position in another, with capital weights of 0.7 and 0.3. The response describes converting each period’s return into a gross return factor, applying a negative sign to the short asset’s return before adding one, and taking the weighted sum of the resulting factors for each period.

To obtain a cumulative portfolio value, multiply the period portfolio factors across time. The example provides no computed result or worked numerical validation, and it assumes the input series are aligned in time. The treatment also leaves leverage, financing, transaction costs, rebalancing, and the interpretation of portfolio weights unspecified; those assumptions can affect realized long-short returns.

Key ideas

  • Align the two return series by time before combining them.
  • Represent the short leg by negating its return before converting it to a gross return factor.
  • Combine the two gross return factors using the chosen portfolio weights for each period.
  • Compound portfolio factors over time to calculate cumulative performance.
  • The method does not specify leverage, financing, costs, or rebalancing assumptions.

Tags

EquitiesPortfolio constructionBacktesting
Full text
# How to calculate weighted return of two stock prices?


# How to calculate weighted return of two stock prices?












I have 2 list of returns A = [0.00538467, 0.04701923, 0.00170811,...] B = [0.00299271, -0.0060228 , -0.07761099,...]

I take long position in A and short in B.

How to calculate the total return and the return if I want to invest in ratio of 0.7 in A and 0.3 in B.

## Answer by KaiSqDist (score 1)

https://quant.stackexchange.com/a/76783

Welcome to the forum. I assume your returns in the list are ordered by time?

You can simply add 1 to both lists (while multiplying the short position by a minus '-' sign BEFORE adding the 1) such that the returns become 'A Return' and 'B Return' columns:

The 'Portfolio Return' is just the weighted sum 0.7 * 'A Return' + 0.3 * 'B Return'. The final cell in that column is the cumulative product and is your final answer.

PS. I am not sure why the table formatting is not working, so I used a picture instead.

Hopefully this helps!

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.