Reconciling Theoretical and Booked Returns in a Short Sale

Summary

The document presents a short-sale backtest example and asks why an equity calculation differs from a return estimate based on the ratio of the mean price to the close. The trader sells short using a quantity determined by dividing available capital by the mean price, then computes end-of-day equity from cash proceeds less the market value of the short position at the close. The stated theoretical return applies the price ratio to starting capital.

The two calculations are close but not identical in the example. The question does not include an answer, so it does not establish the precise cause. The setup implies that share quantity, execution price, and accounting conventions must match across both calculations for exact agreement; rounding or different assumptions about short-sale proceeds and deployed capital may also matter. The example assumes fractional shares and omits fees, borrow costs, margin rules, and other trading frictions, so it does not evaluate realistic short-sale performance.

Key ideas

• The example compares end-of-day short-position equity with a return computed from mean and closing prices.
• The short position size is based on available capital divided by the assumed acquisition price.
• Matching quantities and execution assumptions is necessary for the accounting calculation and return formula to agree.
• The example omits transaction costs, borrow charges, and margin constraints.

Tags

# Theoretical returns are not matching empirical ones in my backtest


# Theoretical returns are not matching empirical ones in my backtest












I'm trying to implement a Backtest for my quant strategy but the calculated theoretical returns are not matching the returns from my implementation. Here's the example:

On a given day I have 1 million dollars available to trade and my model tells me to start a short selling operation. Also, on this day, the Mean and the Close prices of the asset I'm trading are, respectively, 38740 and 38569.1. Therefore, I start by operating (1 million)/38740 = 25,81311306 shares (I suppose that the price of acquisition is the Mean and that any fraction of the share can be bought). Since it is a short selling operation I have now 2 millions dollars (1 million I already had plus the 1 million that I got for renting 25,81311306 shares and selling them).

To calculate my equity at the end of the day I use the formula Equity = Cash available - (Number of shares operated) * (Closing Price of the asset) = 2 million - 25,81311306 * 38569.1 = 1004411,461. However, my 'theoretical' return at the end of this day is Mean/Close = 38740/38569.1 = 1,004431008. Multiplying this return by the initial 1 million I get 1004431,008, which is different from the previously calculated value of 1004411,461. Why is this happening?

Thanks in advance!

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