Investment Risk in Portfolio Management Settings: Sizing, Stops, and Tail Risk
What Level III tests
This domain tests risk as a portfolio-level constraint, not a footnote to a trade. You must translate volatility, drawdown, correlation, and tail risk into position sizes, stop policy, and allocation limits, and recognize when statistical risk measures fail.
Core rules and concepts
- Volatility targeting. Position size can be scaled by target portfolio volatility divided by asset volatility; higher-volatility assets get smaller weights for the same risk budget.
- Risk-based sizing. Risk per trade in dollars = portfolio equity x risk percentage. Shares = risk dollars / (entry price - stop price). Position value is an output, not an input.
- Stop policy. Place stops beyond noise using ATR multiples or structural levels; arbitrary percentage stops get hit in normal volatility.
- VaR limits. VaR estimates a loss threshold at a confidence level but says nothing about the size of losses beyond it and assumes a distribution. Use expected shortfall, stress tests, and scenario analysis for tails.
- Correlation instability. Correlations rise in crises; diversification must be tested under stress, not only in calm periods.
- Drawdown and risk of ruin. Maximum drawdown and recovery time matter more than average return for leveraged or concentrated books.
- Behavioral risk. Loss aversion and the disposition effect cause traders to hold losers and cut winners; precommitment rules reduce that bias.
Worked example
A $1,000,000 portfolio allows 0.75% risk per position, or $7,500. A stock trades at $100; ATR is $4, and the structural stop is $92, an $8 risk per share. Shares = $7,500 / $8 = 937; position value = $93,700, or 9.37% of the portfolio. The name is 0.85 correlated with an existing holding, so you halve the size to 468 shares. Reasoning: risk dollars, not position value, drive size; the ATR/structural stop keeps the stop outside normal noise; correlation adjustment prevents hidden concentration.
Traps that cost marks
- Sizing from a fixed position value instead of risk dollars.
- Placing stops inside one ATR of entry, guaranteeing noise stop-outs.
- Treating VaR as the maximum possible loss.
- Assuming historical correlation holds in a drawdown.
- Ignoring gap risk and liquidity when setting stops or sizing.
- Overweighting a high-conviction idea without a portfolio-level risk budget.