12. Portfolio Performance Evaluation Flashcards
Benchmarking
Measuring portfolio performance against relevant benchmark/standard
Popular benchmarks
S&P 500, Russell 2000 (small cap stocks), Russell 3000 (large cap or entire stock universe), S&P 400 (mid cap)
Performance measures
Capture risk-return trade off
- Portfolio is added to existing portfolios, one of many combined into investment fund, measure systematic risk
- Evaluating portfolio in isolation, interested in total risk
- If adding small number stocks to passively managed portfolio, idiosyncratic risk
Performance measures
Treynor
Looks like SR, but with beta = (Rp - Rf)/ π½p, dividing by beta
- Appealing, because it weighs excess returns against systematic risk -> non- systematic risk diversified away with other portfolios
Performance measures
Sharpe Ratio
Sharpe Ratio = (Rp - Rf) / πp gives slope of line from risk-free asset to portfolio. For M move
Performance measures
M^2 measure
Alternative for SR, combine portfolio (P*) with riskless investment such that it has same standard deviation as market and then compare returns, M^2 = rP - rM
Performance measures
Information Ratio
Information ratio = Ξ±p / π(ep)
Problems SR
- SR assumes constant mean and variance of return distribution, which isnβt realistic
- Even if mean and variance are constant, very long period to measure performance precisely is needed
- Many unobservable things: liquidity risk, extreme tail risk
Forecast ability
- Manager cannot perfectly forecast market return, but is able to forecast if market outperforms risk-free asset = market timer
- Beta risk varies: into market before market outperforms, out market otherwise
Test for market timing ability
Regress return on market: two regressions:
- C: two values for bets (high and low market)
o Henriksson and Merton: create dummy variable to run two betas - B: in reality beta may take more than two values, quadratic relation between portfolio and market returns
o Treynor and Mazuy: risk-return in convex: the bigger the difference between ππ and ππ, the stronger the outperformance
Evaluating performance
Two key problems:
- Many observations needed for significant results
- Shifting parameters when portfolios are actively managed makes accurate performance evaluation more elusive
Performance attribution
Decomposes performance into three components:
- Allocation choices across broad asset classes
a. Bogey portfolio: select benchmark index portfolio for each asset class - Industry/sector choice within each market
a. Choose weights based on market expectations - Security choice within each sector
a. Choose portfolio of securities within each class by security analysis (benchmark within asset class)
Performance measures
Jensen alpha
πΌπ = π π β π πΉ β π½π(π π β π πΉ), subtracting beta, especially different if beta is big