Portfolio Management and Wealth Planning
Risk and return
Mean-variance analysis builds the efficient frontier; the capital allocation line adds the risk-free asset; the optimal risky portfolio maximizes the Sharpe ratio. Multifactor models - macroeconomic, fundamental, and statistical - and APT price systematic exposures; APT requires no arbitrage, not a market portfolio.
Active management
The fundamental law: IR approximately equals TC x IC x square root of BR. Breadth (independent decisions), skill (information coefficient), and transfer coefficient (constraints) drive active returns. Risk budgeting allocates risk rather than capital, and tracking error governs deviation from the benchmark.
Risk measurement
Parametric VaR assumes normality; historical simulation uses the empirical distribution; Monte Carlo simulates paths. CVaR measures expected loss beyond the VaR threshold. Backtesting compares exceptions with the expected rate; stress tests probe tail scenarios.
IPS and institutions
Objectives (return, risk) and constraints (liquidity, time horizon, tax, legal, unique) frame every IPS. Defined benefit plans focus on the funding ratio and liability duration; defined contribution plans shift risk to participants; endowments have long horizons with spending rules; banks and insurers face capital and liquidity regulation.
Traps
- VaR says nothing about loss size beyond the threshold.
- The Sharpe ratio suits total-risk portfolios; the information ratio suits benchmark-relative ones.
- Attribution separates allocation from selection; do not double-count currency effects.
Worked example
A $10 million portfolio has a daily standard deviation of 1.5%. One-day 5% VaR = 1.65 x 0.015 x $10m = $247,500. Using a 1% confidence cutoff (2.33) gives $349,500.
Rule of thumb: always state VaR with its horizon and confidence level, and pair it with CVaR or stress tests before drawing risk conclusions.