Volatility & Beta — Sizing for the Instrument

Realized volatility

Volatility = the standard deviation of returns: how violently the instrument moves. A 2%-daily-move stock is ~3× as volatile as a 0.7%-daily one. For position sizing this means equal dollar positions are NOT equal risk: $10,000 of the wild stock carries ~3× the daily swing of $10,000 of the calm one.

Beta — vs the market

Beta measures co-movement with an index: beta 1.0 moves with the market, 1.8 amplifies it 80%, 0.5 dampens it. High-beta portfolios are implicit leveraged-market bets — a "diverse" 8-stock tech portfolio at beta ~1.5 behaves like 1.5× the index in every storm. Check the PORTFOLIO beta, not each stock's.

Volatility-adjusted sizing

The fix: size positions inversely to volatility so each contributes similar risk — a 3×-volatility stock gets ~1/3 the dollar position. ATR-based stops (size the stop at 2× average true range) automate this: the formula from day 29 then naturally shrinks volatile positions.

Sources

• BetaInvestopedia
• Average True Range (ATR)Investopedia