Calculating Returns for a Long–Short Stock Position

Summary

The document asks how to calculate a daily percentage return for a position that is long one stock and short a scaled amount of another. It presents two candidate expressions: one subtracts the scaled log return of the short asset from the long asset’s log return; the other compares the change in the portfolio’s net market value with a denominator based on the prior prices of both holdings.

The key issue is that these formulas encode different return conventions and capital bases, so they need not yield the same number. The prompt does not provide an answer, trading-account assumptions, or a definition of the capital invested in the short leg. As a result, it serves as a useful framing of the calculation problem but does not establish which expression is appropriate. A return calculation requires a clearly specified portfolio value or capital base and consistent treatment of short-sale proceeds and financing.

Key ideas

• A long–short position combines a long holding with a scaled short holding.
• Subtracting scaled log returns and calculating net-value change over a capital base can produce different measures.
• The appropriate percentage return depends on the chosen definition of portfolio capital.
• The document poses the question but supplies no resolution or assumptions about short-sale proceeds and financing.

Tags

# Correct return calculation if short position involved


# Correct return calculation if short position involved












I wanted to calculate the daily return for a long-short position. Say one has 1 unit of stock A (long) and alpha units of stock B short. How can one now calculate correctly the daily percentage return? The literature puts different formulas forward, but they reach different values. Two of them are

- $\log(P^{A}_t / P^{A}_{t-1}) - alpha * \log(P^{B}_t / P^{B}_{t-1})$, or

- $(P^{A}_t - alpha * P^{B}_{t}) / (P^{A}_{t-1} + alpha * P^{B}_{t-1}) -1 $

Are they both correct?

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