Inventory Valuation and Exposure

Inventory is your net position: everything bought minus everything sold. Positive is long, negative is short.

Inventory value=position×fair value\text{Inventory value} = \text{position} \times \text{fair value}

That is the easy part. The useful question is not how much you hold, but how much you stand to lose.

Exposure is risk, not size

A position of 10,000 shares means nothing on its own. What matters is what happens when the market moves:

Exposure=position×fair value×σ\text{Exposure} = \text{position} \times \text{fair value} \times \sigma

10,000 shares of a stable utility at $50 with 1% daily volatility carries about $5,000 of daily risk. The same dollar position in a volatile biotech at 5% daily volatility carries $25,000. Same capital, five times the risk.

This is why risk limits are usually expressed in risk units rather than share counts, and why a trader flat in shares can still be far from flat in risk.

Key takeaway

Position size and exposure are different quantities. Two positions of equal value can carry very different risk, and it is the risk that limits should be set against.

Net versus gross

Net exposure nets longs against shorts. Gross adds their absolute values.

Long 1,000 of stock A and short 1,000 of stock B gives net zero and gross 2,000. If A and B are near-identical (two share classes of the same company), the net figure is the honest one and you are close to flat. If they are unrelated, you hold two independent risks and the gross figure is what matters.

Reporting only net exposure is a classic way for real risk to hide. The netting is only valid to the extent the positions genuinely offset, which depends on a correlation that is estimated, unstable, and prone to failing exactly when it is needed. See covariance and correlation.

Aggregating across instruments

A desk holds many positions, and total exposure is not their simple sum. Correlated positions compound; offsetting ones cancel:

σportfolio2=iwi2σi2+ijwiwjρijσiσj\sigma_{\text{portfolio}}^2 = \sum_i w_i^2\sigma_i^2 + \sum_{i \neq j} w_i w_j \rho_{ij}\sigma_i\sigma_j

The practical consequence is that a trader can be within limits on every individual instrument and far over on aggregate risk, if all the positions lean the same way. This is why desks monitor factor exposures, such as total market beta or total exposure to a sector, rather than only per-instrument limits.

Beyond linear positions

For derivatives, position count is not exposure at all. An option's sensitivity to the underlying is its delta, and 100 options with a delta of 0.5 carry the exposure of 50 units of underlying.

Worse, delta changes as the underlying moves (that rate of change is gamma), so a derivatives position's exposure is not stable even when the position is. Hedging such a book requires continuous rebalancing, which is a large part of what an options market maker does all day.

Monitoring in practice

Desks watch exposure continuously through position dashboards showing net and gross by instrument and factor, aggregated risk in dollars per standard-deviation move, stress scenarios (what if the market drops 5%), and automated skewing that pushes quotes to reduce inventory before a human needs to intervene.

Tip

The question that reveals whether someone understands their book is not "what do you hold" but "what do you lose if the market drops 3%". If those two answers are not connected in your head, the position is not being managed.

Test your knowledge

A desk holds 10,000 shares of a biotech trading at \( \$50 \) with a daily volatility of \( 5\% \). What is the approximate one-standard-deviation daily exposure, in dollars?
A desk is long 1,000 of stock A and short 1,000 of stock B, reporting net exposure of zero. When is that the honest number?