# Portfolio Accounting with Shorts

Hi Folks, I feel a little silly asking this, but I’m trying to set up my personal portfolio to analyze what positions are is doing what to the portfolio as a whole. I’ve done this before when I’ve only had long positions, and it’s fairly straightforward then. However, I’m having some trouble figuring out how to do it with both longs and shorts in the portfolio. The portfolio only has stocks and ETFs in it. I think I have it right, but I’m not sure, so I wanted to check. – With long-only portfolios, your exposure to each asset is fairly straightforward. Basically you take the number of shares you have, multiply by the current price to get your total dollar exposure. Then you add up all dollar exposures to get the total portfolio size, and each asset exposure is equal to % portfolio exposed to Asset X = (Total Dollars in Asset X) / (Total Dollars in Portfolio) Then, to analyze performance, if asset X is up Dx%, then: % portfolio change due to change in X = (% port in Asset X) * (Dx%) — But with shorts, it seems more complicated. What I’ve been doing is saying that Total L/S Portfolio Value = = SUM[(shares long)*(current price)] + (Short Sale Proceeds) - SUM[(shares shorted)*(current price)] Where the sums mean sums over all long and short positions, respectively. The idea here is that the net portfolio value is the sum of the long positions (as before), plus the cash you get when you sell the borrowed shares, minus the amount you would have to pay to return the shares at today’s prices. For simplicity, right now I’m assuming no dividends, short interest, or transaction costs. Then, when I compute exposures, for long positions in Xlongs, I compute them as: : Exposure in Xlong: (# shares)*(cur price) / (total L/S Portfolio) This is the same as the long only exposures, except with a different computation for the total portfolio value. For short values: : Exposure in Xshort: (-1) * (# shares shorted)*(curPrice) / (total L/S Portfolio) where the (-1) creates a negative percent exposure, signifying a short position. From there, the effect of a change in price is: % change in portfolio = (% Exposure of asset X) * (% price increase in X) ---- Question 1: Is this the right way to account for things in a L/S portfolio? Question 2: If I only took short positions, how would I compute the portfolio’s basis? At inception, the amount owed to repurchase shorted shares would exactly equal the proceeds from a short sale. Therefore the portfolio’s initial value would be 0, and a gain of even \$1 in portfolio value would signify an infinite rate of return. This just seems implausible, so am I doing something wrong? Question 3: The short position is (other than transactions cost) costless to enter (though it will tie up a margin account at a retail service). To me, this suggests that it is a) implicitly levered, and b) much riskier. Is that correct? OK, I feel dumb asking, and maybe my L3 materials cover this, but I thought maybe someone out here could point out whether I’m doing this right, and what I would need to change if I’m not.

I’ll take a stab at your questions, but some of what you touched on is discussed in level 3: #1 - there are a variety of ways to measure it depending on what you’re trying to measure. Start with cash/cash return, then measure performance of longs and shorts separately. Then measure the risk of the portfolio as a whole (expected return & standard deviation of the blend of long & shorts). #2 - basis is irrelevant… that’s why measuring risk is important. You’re using the proceeds of one asset sale to fund the purchase of another. You’re only accountable if the trades don’t work, and to that degree. #3 - short positions are risky for a lot of reasons but a simple short sale of an etf isn’t leveraged? What’s psychologically weird for me is to rack up huge gains on a short position then to see the short position decline (in nominal value) and, because of that, to have to add to the short position! It helps me to separate everything into returns and expected returns then work from there… not nominal values. It’s really a statistics game not value investing (which I’m more accustomed to).