Portfolio Risk

Each trade can look sensible on its own while the account is quietly one big bet. Ten positions that each risk 1% of the account don’t add up to ten separate 1% risks if they all depend on the same thing; in a sharp sell-off they can behave like one 10% position, and individual stop orders may fill far from their prices in a gap. Portfolio risk asks a different question: if the market drops 5% tomorrow and volatility jumps, what happens to everything at once? Four tools answer it: beta-weighting, correlation, combined Greeks and scenarios.

Beta-weighting and correlation

Beta measures how much a stock has tended to move with the market. A beta of 1 moves about in line with SPY, 1.5 about half again as much, and 0.5 about half as much. Beta-weighting converts each position into the number of index shares that would move the same way, usually SPY-equivalent shares: the position’s delta in shares × beta × (stock price ÷ SPY price). Once everything is in one unit, you can add it up. For options, the delta part changes as price moves, so the beta-weighted number drifts during the day; recheck it after big moves rather than treating it as fixed.

Correlation measures how closely two prices move together, from −1 to +1. Five semiconductor stocks aren’t five independent bets: they share customers, supply chains and index flows. Short options on ten different stocks are mostly one bet that volatility stays low. Correlations also tend to rise in sell-offs, so the protection from diversification often shrinks right when you need it most. Adding tickers isn’t the same as adding independent risks; positions that respond to different forces, or whose maximum loss is capped, change the picture more than another name in the same theme. Betas and correlations are measured from the past, and they can change quickly.

Combined Greeks and scenarios

The Greeks add up across positions. For options, multiply each per-share Greek by 100 and by the number of contracts, and flip the sign for short positions. Within one stock you can add them directly. Across different stocks, beta-weight delta first, as above, because a $1 move means something different in a $50 stock than in a $600 one. Gamma needs the same conversion, and adding vega assumes every implied volatility moves by the same number of points, which rarely happens. Total delta shows your exposure to a $1 move, gamma how fast that delta changes, theta what a day of time costs or earns, and vega what a 1-point change in implied volatility does. The signs tell a story. A long-gamma account tends to gain more on the moves that help it and lose less on the moves that hurt, and usually pays theta for that. A short-gamma account usually collects theta but loses faster as moves grow. A long-vega account tends to benefit when implied volatility rises, which for indexes often happens during sell-offs. A quick scenario estimate combines them: P&L ≈ delta × move + ½ × gamma × move² + vega × change in IV + theta × days. It’s an approximation. It drifts on large moves, and gaps, early assignment and thin markets can make real losses larger.

1. Beta-weight everything

   Convert each position to SPY-equivalent shares and add them up.

2. Group by theme

   Sector, style or story. Ask which positions would lose at the same time. Many traders size each group as if it were one position.

3. Total the Greeks

   Note whether the account is long or short gamma and vega overall, and what a day of theta costs or earns. A small net number can hide large offsetting positions, so glance at the gross figures too.

4. Run the bad cases

   Try a 5% drop with IV up several points, a 5% rally with IV down, and an overnight gap. Include at least one move bigger than feels likely; markets produce “rare” days more often than simple models expect. Remember the estimate is rough on big moves.

5. Compare with your limit

   If the worst case is bigger than the loss you’ve decided you can afford, the combined risk is larger than your plan allows, however reasonable each trade looked on its own.