# Calculating relative performance of a short trade

This may seem incredibly simple, but I just can't get my head around it.

Example:

I make a short trade and the stock falls by 20%. During that period, the index falls by 10%.

Have I made a +10% positive return on that trade relative to the index or a +30% positive return relative to the index and why?

Thanks!

Who cares what the index (or anything else) returned. If your trade earns 20% you earned 20%. What you could have earned with a different trade is a separate issue.

There isn’t much point to comparing a long trade, buying the index, to a short trade, shorting the stock.

If you’re comparing shorting the index which would have earned 10%, based on your question, to shorting the stock which earned 20% I would say you outperformed by 100%. Because 20 is double 10.

You gain 30% compared to the index - here's why:

Let's say the stock is trading for \$10 and its benchmark index is at \$100. You put a \$1,000 short trade on the stock (short 100 shares).

The stock goes down to \$8 and the index to \$90. Your short position is now worth \$1,200 (you gain 100*\$2 = \$200) for a 20% gain and the index has a 10% loss, so relative to the index you've gained 30%.

I will say that a "long" index is not a great benchmark to use for a short trade. The returns will be in opposite directions.

• I'm confuzzled. If the index dropped 10%, it moved in the same direction as the short position on the stock but 1/2 as much. Mar 13, 2020 at 14:43
• If that's the case then how did one gain 30%? Mar 13, 2020 at 15:31
• If my benchmark index loses 10% and my trade is up 20%, I am 30% better off than the index. That makes sense to me. +1. Consider, if the index is up 10% but I am down 20. I lagged by 30%. Dec 8, 2020 at 23:19
• @JTP - Apologise to Monica - I still disagree with these comments. Per the OP's set up, if you're short the index and it drops 10%, you gain 10%. If you're short the stock and it drops 20%, you gain 20%. That isn't a lag of 30%. Jan 8, 2021 at 2:35
• The OP wrote: I make a short trade and the stock falls by 20%. During that period, the index falls by 10%. He didn't write that he went long the index. He then asked, Have I made a +10% positive return on that trade relative to the index or a +30% positive return relative to the index and why? I take the question to mean that he's comparing the drop in the index to drop in stock. If you believe that to be a comparison is long the index versus short the stock then we have different interpretations and our respective answers are correct for our interpretations. Jan 8, 2021 at 15:31

Suppose instead you reversed everything to the long side.

Example:

• I make a long trade and the stock rises by 20%. During that period, the index rises by 10%.

• Have I made a +10% positive return on that trade relative to the index or a +30% positive return relative to the index and why?

Assuming an equal dollar investment in the stock and an index ETF, you made 10% on the index and 20% on the stock. That's also twice the return if you're comparing ROI.

The answer is the same for the short positions, assuming that the respective margin requirements are the same.

It's not so easy. Here are the numbers I get:

Asset Sell at Buy back at Profit from short
Stock 100 80 20
Index 100 90 10

So, by shorting the stock instead of the index, you made twice the money (100% more), or 10 percentage points more (10% of the original amount).

Edit: it is not clear whether you bought the index or shorted it. If you had bought the index instead of shorting, you would have lost 10. Compared to gaining 20, that is a 30 percentage points.

This is because the double subtraction means addition: 20 - (-10) = 20 + 10 = 30.

But to be cheeky you can also say you got negative twice the return :)