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Calculating Short Log Returns After Trading Fees

Article Quant Q&A · Author: user3276418
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Summary

The document addresses how to calculate a short position’s logarithmic return when fees are included. Its accepted answer treats the short sale as the entry transaction and the later purchase as the exit transaction. On that basis, the fee adjustment is applied to the entry price, producing a log return based on net sale proceeds divided by the repurchase price.

This differs from simply negating a long return formula with the same price labels, because the economic roles of entry and exit prices are reversed for a short. The answer provides the formula choice but does not specify whether fees are charged on both transactions, how fees are quoted, or how leverage, funding, borrow costs, and other trading costs should be incorporated. The result therefore applies to the stated simplified setup and requires consistent definitions of prices and fee treatment.

Key ideas

  • For a short position, entry is the sale and exit is the later purchase.
  • The fee-adjusted short log return uses net entry proceeds divided by the exit purchase price.
  • Price labels must reflect transaction direction rather than copying a long-return formula unchanged.
  • The stated calculation does not address leverage, borrow costs, funding, or fees charged at both transactions.

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Full text
# Calculate short log return including fees


# Calculate short log return including fees












log long return is log((exitprice-fees)/entryprice) without leverage.

log short return is the negative long return.

So, from the above I would get

short return = log(entryprice/(exitprice-fees)). Which doesn't make sence.

So, should it be log(entryprice/(exitprice+fees)) or log((entryprice-fees)/exitprice) ?

## Answer by arodrisa (score 1, accepted)

https://quant.stackexchange.com/a/20739

If you are short you need to use log((entryprice-fees)/exitprice). It is the same logic as in log long return case. You just need to change your entryprice and exitprice inputs. In this case, entryprice is the selling operation and exitprice will be the buying operation (just the opposite).

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.