Gross and net exposure
Two numbers describe a long/short book: how much is at work, and which way it leans. Beta tells you which way it really leans.
- Calculate gross, net and beta-adjusted net exposure
- Predict the P&L of a market move from beta-adjusted net
- Find the short book that brings net exposure to a target
- Say what gross exposure measures that net does not
The intuition
For every $100 of its investors' money, a fund owns $120 of stocks it likes and has sold short $70 of stocks it dislikes. Two questions describe that book. How much money is at work? $190: that is what can go wrong on a day when the stocks it likes fall and the ones it dislikes rise. Which way does it lean? $50 long: roughly what it gains or loses when the whole market moves.
The first number is gross exposure, the second net exposure. But a dollar of a jumpy stock moves more with the market than a dollar of a sleepy one, so net exposure in dollars can mislead. Weighting each side by its beta (how much it moves for each 1% move in the market) gives beta-adjusted net, the number the risk desk watches.
Gross = (longs + shorts) ÷ NAV. Net = (longs − shorts) ÷ NAV. Beta-adjusted net = (longs × beta of the longs − shorts × beta of the shorts) ÷ NAV. A market move m makes or costs beta-adjusted net × m × NAV.
Why it works
- The conventions here: exposures are market values as a share of NAV, the fund's own capital. Each side has one average beta. A market move is measured before any stock-specific returns.
- Gross measures leverage and stock-picking risk. 190% gross means $1.90 of positions per $1 of capital; if the longs and the shorts both go wrong, the loss is on all of it.
- Net measures direction. A fund 20% net long gains about 2% on a 10% rally, if its longs and shorts have the same beta.
- Beta removes that 'if'. When the longs carry more beta than the shorts, beta-adjusted net is above plain net; when they carry less, it is below.
- To change direction without touching the longs, resize the short book: shorts for a target net = longs − target net × NAV.
- Betas are estimates. They come from history and tend to rise in a sell-off, when everything moves together. Beta-adjusted net is the first risk number to check, not the last.
| Gross: (120 + 70) ÷ 100 | 190% |
| Net: (120 − 70) ÷ 100 | 50% |
| Beta-adjusted net: (120 × 1.2 − 70 × 0.9) ÷ 100 | 81% |
| Plain-net estimate: 50% × −10% × 100 | −$5.0M |
| Actual market P&L: 81% × −10% × 100 | −$8.1M |
| Shorts for 30% net: 120 − 30 | $90M, so add $20M |
With $90M of shorts at beta 0.9, beta-adjusted net becomes (144 − 81) ÷ 100 = 63%.
The formulas
How much is at work per dollar of capital.
Which way the book leans, in dollars.
Which way it leans, counting how much each dollar moves with the market.
What a market move does, before any stock picking.
The net formula, run backwards.
Worked example
Multiply each side by its beta first, then net them. Then compare with the plain net.
See it move
Same fund and the same capital. Change the size of each side, each side's beta, the market move and the net exposure the PM wants.
- Raise the short book. Gross rises while net and beta-adjusted net both fall.
- Raise the beta of the longs. Beta-adjusted net rises; plain net does not move.
- Raise the beta of the shorts. Beta-adjusted net falls; plain net does not move.
- Raise the net exposure the PM wants. The short book it needs gets smaller.
Run it backwards
Same fund, reversed: the PM wants a set net exposure and will only change the short book. How big should it be?
Target net × NAV is the dollar gap wanted between longs and shorts. The longs stay, so the short book is whatever leaves that gap.
Adding shorts cuts net and raises gross at the same time: more hedging, more positions, more borrow cost. Covering shorts does the opposite. Cutting longs would lower both, which is what a PM does to take less risk overall rather than less direction.
Traps
Say it in the interview
“What's the difference between gross and net exposure, and which matters more?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Gross = longs + shorts; net = longs − shorts; both over NAV.
- Beta-adjusted net is the real market exposure.
- Market P&L = beta-adjusted net × move × NAV.
- Shorts for a target net = longs − target × NAV.