APMA cheat sheet

Portfolio expected return is the weighted average of individual asset expected returns: E(Rp) = Σ wi·E(Ri).

Portfolio variance is σp² = ΣΣ wi·wj·σij; the covariance terms, not just individual variances, drive total risk.

Covariance σij = ρij·σi·σj; correlation ranges from -1 (perfect offset) to +1 (no diversification benefit).

With N assets and equal weights, portfolio variance approaches average covariance as N grows; only systematic risk remains.

Systematic (market) risk cannot be diversified away; unsystematic (firm-specific) risk is eliminated by diversification.

CAPM: E(Ri) = Rf + βi·[E(Rm) − Rf], where βi = Cov(Ri,Rm)/σm².

Security market line plots expected return versus beta; assets above the line are undervalued (positive alpha).

Sharpe ratio = (Rp − Rf)/σp; Treynor ratio = (Rp − Rf)/βp; Jensen's alpha = Rp − [Rf + βp(Rm − Rf)].

The Investment Policy Statement documents objectives (return and risk), constraints, and guidelines governing a portfolio.

Constraints are commonly summarized as RRTTLLU: Return, Risk, Time horizon, Taxes, Liquidity, Legal, Unique circumstances.

Risk tolerance combines ability to take risk (financial capacity) with willingness to take risk (psychological attitude).

Strategic asset allocation sets long-run target weights by asset class and drives most of a portfolio's return variability.

Tactical asset allocation makes short-term deviations from strategic weights to exploit perceived mispricing.

Rebalancing restores target weights; calendar rebalancing uses fixed dates, threshold rebalancing triggers at set drift bands.

Time horizon: short horizons favor liquidity and capital preservation; long horizons permit greater equity exposure and illiquidity.

Active strategies seek alpha through security selection and market timing; passive strategies track an index at low cost.

Value style buys low price multiples (P/E, P/B); growth style buys high expected earnings growth, often at high multiples.

Market capitalization weighting gives larger weights to larger firms; equal weighting and fundamental weighting are alternatives.

Momentum buys recent winners and sells losers; mean reversion assumes prices return toward long-run averages.

Top-down strategy starts with macro/asset-class views then selects securities; bottom-up starts with individual company analysis.

Core-satellite combines a passive core index holding with active satellite positions for alpha and risk control.

Style drift occurs when a manager's holdings migrate from the stated style; style boxes (size × value/growth) monitor this.

Contrarian investing buys out-of-favor assets; trend following buys assets in established uptrends.

Efficient frontier: set of portfolios offering the highest expected return for each level of risk; optimal risky portfolio maximizes Sharpe ratio.

Adding a risk-free asset yields the capital allocation line; the tangency portfolio is the optimal risky portfolio.

Total return decomposition: Rp − Rf = allocation effect + selection effect + interaction, as in Brinson attribution.

Time-weighted return removes the effect of cash flows and is preferred for evaluating manager skill; money-weighted return reflects investor timing.

Information ratio = (Rp − Rb)/tracking error; tracking error is the standard deviation of active returns (Rp − Rb).

M² (Modigliani) = (Rp − Rf)·(σm/σp) + Rf; expresses risk-adjusted return in benchmark-risk units.

Performance must be judged relative to a benchmark matched on style, risk, and universe; survivorship bias inflates reported results.

Return attribution separates currency, sector, and security selection contributions from the total active return.