Scaling Long-Short Returns for a Zero-Investment Equity Portfolio

Summary

The document asks how to calculate daily returns for a changing, equally weighted long-short stock portfolio. It gives an example with three long positions and one short on the first day, followed by one long and two shorts on the next day. The proposed calculation averages the long holdings’ returns, assigns negative signs to short holdings, and adds the two sides to form the long-short return.

The underlying issue is how to define the return denominator and portfolio scale. If each side is normalized to one dollar of gross exposure, the long and short component returns can be combined to describe profit relative to one side’s capital, while gross exposure is two dollars and net investment is zero. The day-two short expression in the prompt appears to apply inconsistent signs or weights, so it should not be assumed correct as written. The exchange contains the question but no answer, leaving financing, rebalancing, and the precise return convention unresolved.

Key ideas

• Equal-weighted long returns are calculated as the weighted average of the constituent stock returns.
• A short position contributes the negative of the underlying asset’s return, subject to the chosen exposure convention.
• A zero-net-investment portfolio can still have positive gross exposure on both the long and short sides.
• The document raises questions about return scaling but supplies no resolution, so denominator and weighting assumptions must be specified.

Tags

# Calculating Daily Returns for a Zero Net Investment Portfolio


# Calculating Daily Returns for a Zero Net Investment Portfolio












I'm trying to create a zero net investment portfolio in an equally weighted manner using daily holding period returns for stocks. Here is my setup:

- Day 1: Long: Stocks A, B, C Short: Stock D

- Day 2: Long: Stock D Short: Stocks B, C

I want to calculate the daily returns for the long, short, and long-short (LS) positions.

- Day 1 Calculations:

$R_{long}=R_{A}*1/3+R_{B}*1/3+R_{C}*1/3$

$R_{short}=-R_{D}$

$R_{LS} = R_{long}+R_{short}$

- Day 2 Calculations:

$R_{long} = R_{D}$

$R_{short} = -R_{B}*1/2 + R_{C}*1/2$

$R_{LS} = R_{long}+R_{short}$

Is this calculation correct I think we're investing one dollar on each side (long and short). What is the total investment amount now? Are there any adjustments I need to apply for this calculation? Do these newly calculated returns align (in scale) with the holding period returns?

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