Two books, one equity denominator
Let E be positive net asset value, L the current market value of long shares and S the absolute market value of short shares. Account equity includes cash, long assets, short liabilities and accrued costs. Short-sale proceeds are accompanied by a liability to return shares; receiving those proceeds does not create equity. The following definitions apply to cash equity positions in one reporting currency.
- For E = $100,000, L = $80,000 and S = $80,000, gross exposure is 160% and net exposure is 0%. If betaL = 1.3 and betaS = 0.7, estimated portfolio beta is 0.8 × 1.3 - 0.8 × 0.7 = 0.48 despite dollar neutrality.
- Sector, size, currency and liquidity exposures can remain after a beta adjustment. Estimated betas can also change during stress. Market neutrality is an objective that needs measurement, not a property of every long-short portfolio.
- Recalculate exposure as prices and equity change. If equity is zero or negative, these ratios are not a usable sizing rule; stop new allocation and apply the account liquidation policy.
| Measure | Formula | What it tells you |
|---|---|---|
| Long exposure | L / E | Size of the long book relative to equity. |
| Short exposure | S / E | Absolute size of the short book relative to equity. |
| Gross exposure | (L + S) / E | Combined stock exposure before offsetting directions. |
| Net exposure | (L - S) / E | Signed dollar imbalance; not a complete market-risk estimate. |
| Approximate market beta | (L / E) × betaL - (S / E) × betaS | A model estimate using consistent beta measurements, not a guaranteed hedge. |