Normalizing Long and Short Portfolio Returns for Index Comparison

Summary

The document asks how to combine separately calculated long and short portfolio returns to compare their performance visually with an index. It defines each side’s return as a weighted average of constituent returns, normalized by the sum of weights within that side. It then asks whether subtracting the short-side return from the long-side return is sufficient, or whether the difference should be divided by two before compounding the series.

No answer or evidence is included, so the appropriate scaling cannot be determined from the prompt alone. It depends on how the weights represent capital, gross exposure, and leverage, and on whether the intended comparison is a return on invested capital or a return on total long-plus-short exposure. The proposed cumulative product illustrates compounding periodic returns, but it does not resolve that denominator choice. A meaningful comparison therefore requires matching the long–short return’s exposure basis to the index return convention.

Key ideas

• Each side’s return is defined as a weighted average of its constituent returns.
• The document asks whether the long return minus the short return needs scaling by two.
• The correct scaling depends on the portfolio’s capital and exposure convention.
• Compounding periodic returns does not by itself make the long–short series comparable to an index.

Tags

# Comparing Long Short Portfolio to Index Return


# Comparing Long Short Portfolio to Index Return












I understand this is a stupid question, but I couldn't find this precise variant already asked on here.

Suppose I have two portfolios, a long portfolio and a short portfolio. I calculate the return of each: $$r_L = \frac{\sum w_l r_l}{\sum w_l}, r_S = \frac{\sum w_s r_s}{\sum w_s}$$

I want to get a return that's comparable to a generic index return. Would it suffice to do $(r_L - r_S)$, or do I have to divide by 2? I want to compare visually the performance of each via

```
(1 + series_return).cumprod()
```

Where index returns are calculated as:

```
index_return = index_level.pct_change()
```

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.