# shorting

a traditional short sell, or short for…short, you borrow an asset that you believe will decline in value, sell it, then buy it back before it’s due to be returned. for instance, suppose acme stock is at 2300 and you believe it will be at 2000 in one month. you borrow x shares and sell them. then you buy them back in a month and pay back the shares, pocketing the difference if you’re right, or potentially losing money if you’re wrong. note that you also pay a fee anywhere from 0.3% to 3% per year for borrowing the stock.

# #math

this can be numerically simplified so that you don’t even have to buy any shares. imagine the owner of the shares simply agrees to pay you `c — f` in one month, where c is the current price and f is the future price (plus the aforementioned fee of course). in other words, if you’re right, the owner pays you `2300 — 2000 = 300`.

what’s really interesting is that the other party need not even own any shares! any two individuals could simply gamble on the future price in this way.

one small caveat tho, before we move on. c is the actual current price, whereas f is a future price. so technically, we need to incorporate discounted cash flow. that is, c should actually be the “bull’s” predicted future price. he might expect the price to rise from 2300 to 2310 in a month, and thus he’d pay 310, not 300. if it actually does reach 2310, then he pays nothing, as we said. i’ll still use c throughout this article, but just bear this caveat in mind.

# shorting a person

but what if you want to short an individual rather than the market? suppose bob owns acme stock which is at 2000, but he believes it to be worth 2300. it turns out the same mechanism works. you pay bob a shorting fee and he pays you `c — f` at some agreed upon future date. if you’re right, then bob ends up paying you `2300 — 2000 = 300`. if bob is right, he’ll end paying you nothing.

## keeping the asset

but what if you want to short the asset and keep it? in other words, bob is going to give you the asset right now, and you’re going to pay him some amount in the future. what should that amount be? it turns out it’s just `2f — e`, where `e = bob's current expectation`. if you’re right, you’ve effectively purchased the asset for `4000 — 2300 = 1700`, pocketing the 300. whereas if bob’s right, you’ve purchased the asset for `4000 — 2000 = 2000`, which means bob’s lost nothing and you’ve gained nothing (save for the shorting fees just like in a normal short.)

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## More from Effective Economics

Devoted to studying and advocating for rational utilitarian microeconomics in the vein of Effective Altruism.

## Clay Shentrup

advocate of score voting and approval voting. software engineer. father. husband. american.