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Short-Sale Profit Accounting with Haircuts, Rebates, and Fees

Article Quant Q&A · Author: user2521987
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Summary

The note corrects a short-sale profit calculation that incorrectly credits interest to both the sale proceeds and the haircut collateral. The proceeds are reduced by the opening commission, while the haircut amount is restricted collateral whose interest treatment depends on the rates specified in the problem.

The answer says the only relevant interest adjustment is the lost interest from earning the lower haircut rebate rate rather than the rate available on the proceeds. It computes this difference on the haircut amount, then subtracts the cost of covering the shares including the closing commission. The resulting example profit is lower than the questioner's estimate. The calculation is specific to the stated problem assumptions; it does not describe other broker collateral arrangements, borrow fees, or taxes.

Key ideas

  • Do not assume sale proceeds and haircut collateral both earn the same interest rate.
  • The haircut's interest adjustment is the difference between the applicable rates on that collateral.
  • Include commissions on both the opening sale and the closing purchase.
  • Short-sale profit depends on the collateral and rebate terms stated in the problem.

Tags

EquitiesRisk management
Full text
# Where am I making a mistake in my calculation of profit on a short-sale?


# Where am I making a mistake in my calculation of profit on a short-sale?












I am studying financial math and here is a problem and the solution from the author:

Here are my calculations:

The short sale is $200\cdot24.82 = 4964$. Now half of this amount will be taken for a haircut and $0.3$% will be taken for a commission. Then we will have (0.5)(0.997)4964 = 2474.55 at t = 0. At t = 3 months, we will have $2474.55e^{0.06 \cdot 0.25} = 2511.95.$

Covering the short position at t = 3 requires 200(21.64) = 4328. The close commission is 200(21.64)(0.003) = 12.98.

We will receive the haircut and rebate which will be $4964(0.50)e^{0.04 \cdot 0.25} = 2506.94.$

The profit is then 2511.95 - 4328 - 12.98 + 2506.94 = 677.91.

## Answer by mkdevoogd (score 1, accepted)

https://quant.stackexchange.com/a/20782

You assume that you receive the 6% interest rate on the receivings of the short sale (2474.55) and you assume that you will receive the 4% interest rate on the haircut (2474.55). This is not stated in the question and the only thing you should calculate based on the information in the question is the loss from not being able to receive the 6% interest on the haircut, which is:

$$2474.55*e^{.06/4}-2474.55e^{.04/4} = 12.53$$

By adding the interest proceedings to both the sale proceedings and the haircut you arrive at your answer. The correct answer is indeed A, as given by the author:

\begin{align} \text{Proceedings: } & 200*24.82*.997 &= 4949.11 \\ \text{- Interest Loss: } & 2474.55*e^{.06/4}-2474.55e^{.04/4} &= 12.53 \\ \text{- Close: } & 200*21.64*1.003 &= 4340.98 \\ \text{Profit: } & 595.60 \end{align}

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