How Capital Allocation Affects Long-Short Strategy Returns and Sharpe Ratios

Summary

The document asks why an example of a hedged long-short strategy divides the difference between long and short returns by two when computing net returns. The stated rationale is that the strategy uses twice the capital of the long-only comparison. The author questions this adjustment because daily returns are already expressed as percentage changes in price.

The issue is the distinction between a portfolio’s dollar profit and its return on invested capital. A return series depends on the denominator used to define capital, so combining long and short legs and normalizing by total capital can change the measured return and therefore the Sharpe ratio. The document raises this accounting question but does not provide an answer or specify the legs’ capital weights, financing, or exposure conventions. Those details are necessary to determine whether the division is appropriate for the strategy being evaluated.

Key ideas

• The example forms a hedged return from the difference between long and short leg returns.
• It divides that return by two because the combined strategy is described as using twice the capital.
• Return percentages still depend on the capital base chosen for normalization.
• The document does not specify enough portfolio accounting detail to settle the adjustment.

Tags

# Relation between Sharpe ratio and amount of capital


# Relation between Sharpe ratio and amount of capital












In the book Quantitative trading by Ernest P. Chan, in one of the example we compute the Sharpe ratio of long-short strategy and one step perplexes me:

> In column L, compute the net returns for the hedged strategy as the difference between column H [Long return] and K [Short return] divided by 2. (Divided by 2 because we now have twice the capital.) [Compare to the previous example where we computed the Sharpe ratio of a long only strategy]

I fairly new to the field, but I fail to see the relation between this division by two, since the calculation of the daily return is percentage value:

$$ Daily Return = \frac{adj Close_{t}−adj Close_{t-1}}{adjClose_{t−1}} $$

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