12. Portfolio Performance Evaluation

Question 1

Benchmarking

Answer 1

Measuring portfolio performance against relevant benchmark/standard

Question 2

Popular benchmarks

Answer 2

S&P 500, Russell 2000 (small cap stocks), Russell 3000 (large cap or entire stock universe), S&P 400 (mid cap)

Question 3

Performance measures

Answer 3

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

Question 4

Performance measures

Treynor

Answer 4

Looks like SR, but with beta = (Rp - Rf)/ 𝛽p, dividing by beta

• Appealing, because it weighs excess returns against systematic risk -> non- systematic risk diversified away with other portfolios

Question 5

Performance measures

Sharpe Ratio

Answer 5

Sharpe Ratio = (Rp - Rf) / 𝜎p gives slope of line from risk-free asset to portfolio. For M move

Question 6

Performance measures

M^2 measure

Answer 6

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

Question 7

Performance measures

Information Ratio

Answer 7

Information ratio = αp / 𝝈(ep)

Question 8

Problems SR

Answer 8

• SR assumes constant mean and variance of return distribution, which isn’t 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

Question 9

Forecast ability

Answer 9

• 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

Question 10

Test for market timing ability

Answer 10

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 𝑟𝑀 and 𝑟𝑓, the stronger the outperformance

Question 11

Evaluating performance

Answer 11

Two key problems:

1. Many observations needed for significant results
2. Shifting parameters when portfolios are actively managed makes accurate performance evaluation more elusive

Question 12

Performance attribution

Answer 12

Decomposes performance into three components:

1. Allocation choices across broad asset classes
   a. Bogey portfolio: select benchmark index portfolio for each asset class
2. Industry/sector choice within each market
   a. Choose weights based on market expectations
3. Security choice within each sector
   a. Choose portfolio of securities within each class by security analysis (benchmark within asset class)

Question 13

Performance measures

Jensen alpha

Answer 13

𝛼𝑃 = 𝑅𝑃 − 𝑅𝐹 − 𝛽𝑃(𝑅𝑀 − 𝑅𝐹), subtracting beta, especially different if beta is big