Fin2802: Investments Spring, 2010 Dragon Tang

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Lectures 21&22 Performance Evaluation April 13 & 15, 2010 Readings: Chapter 24 Practice Problem Sets: 4,6,8,9,10-14 Fin2802: Investments Spring, 2010 Dragon Tang

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## Fin2802: Investments Spring, 2010 Dragon Tang

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Lectures 21&22

Performance Evaluation

April 13 & 15, 2010

Practice Problem Sets: 4,6,8,9,10-14

Fin2802: InvestmentsSpring, 2010Dragon Tang

Chapter 24: Performance Evaluation

You have a large jar containing 999 fair pennies and one two-headed penny. Suppose you pick one coin out of the jar and flip it 10 times and get all heads. What is the probability that the coin you chose is the two-headed one?Wall Street Interview Question

Chapter 24: Performance Evaluation

Performance Evaluation
• Objectives:
• Compute risk-adjusted rates of return.
• Decompose excess returns into components attributable to asset allocation choices versus security selection choices.
• Assess the performance of portfolio managers.
• Assess the value of Market Timing Ability

Chapter 24: Performance Evaluation

Skill

Timing ability (asset allocation)

Selection ability (security selection)

Luck

Goal of performance evaluation is to distinguish skill (and specific components) from luck!

Performance

Chapter 24: Performance Evaluation

Comparison groups:

• Blindly comparing rates of return ignores risk
• Comparison groups with similar investment styles and portfolio characteristics can be used for performance comparison

Chapter 24: Performance Evaluation

Figure 24.1 Universe Comparison

Chapter 24: Performance Evaluation

• Sharpe measure
• Treynor measure
• Jensen measure

Chapter 24: Performance Evaluation

Sharpe Method

Reward-to-volatility ratio:

_

_

Appropriate for measuring the relative performance of an entire portfolio.

Chapter 24: Performance Evaluation

Developed by Modigliani and Modigliani

Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio

If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

M2 Measure

Chapter 24: Performance Evaluation

Figure 24.2 M2 of Portfolio P

Chapter 24: Performance Evaluation

M2 Measure: Example

Managed Portfolio: return = 35% standard deviation = 42%

Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6%

Hypothetical Portfolio:

30/42 = .714 in P (1-.714) or .286 in T-bills

(.714) (.35) + (.286) (.06) = 26.7%

Since this return is less than the market, the managed portfolio underperformed

Chapter 24: Performance Evaluation

Treynor Measure

_

_

Appropriate for measuring the relative performance of parts of a portfolio.

Chapter 24: Performance Evaluation

Jensen Measure

Alpha of an investment (from CAPM):

Appropriate for measuring the absolute performance of a portfolio.

Chapter 24: Performance Evaluation

Information Ratio

Information Ratio = ap / s(ep)

Information Ratio divides the alpha of the portfolio by the nonsystematic risk

Nonsystematic risk could, in theory, be eliminated by diversification

Chapter 24: Performance Evaluation

Sharpe measure:

Useful when assets are concentrated within a single portfolio managers

Treynor and Jensen measures:

Useful when assets are spread across many portfolio managers.

Which one to use?

Chapter 24: Performance Evaluation

Figure 24.3 Treynor’s Measure

Chapter 24: Performance Evaluation

Table 24.2 Excess Returns for Portfolios P and Q and the Benchmark M over 12 Months

Chapter 24: Performance Evaluation

Table 24.3 Performance Statistics

Chapter 24: Performance Evaluation

Risk and Changing Portfolio Composition (Limitation of Performance Measures)
• Risk adjustment techniques assume that portfolio risk is constant over the relevant time period.
• However, changing the mean return and risk will add to the appearance of higher volatility.

Chapter 24: Performance Evaluation

Market Timing and Luck
• If the portfolio manager can time the market, she would shift funds from the safe asset to the market portfolio (from cash to stocks or bonds) just before the market upturn.
• This would increase the portfolio beta.
• Empirical evidence indicates that betas did not increase prior to market advances indicating no evidence of successful market timing. (EMH strikes again)!

Chapter 24: Performance Evaluation

• Understand which decisions lead to superior or inferior performance
• Attribution studies start from the broadest asset allocation choices and progress towards every-finer details of portfolio choice.

Chapter 24: Performance Evaluation

Components of Decomposition:

1. Broad asset market allocation choices (equity, fixed income and money market funds)

2. Industries (sectors) choices within each market

3. Security choices within each sector

Chapter 24: Performance Evaluation

• The Bogey is the return an investment manager is compared to for performance evaluation.
• The bogey portfolio indicates the returns of a completely passive strategy.
• Performance at each step is to be compared to a benchmark or bogey portfolio.

Chapter 24: Performance Evaluation

Performance of the Managed Portfolio

Chapter 24: Performance Evaluation

Asset allocation

Security selection

Equity

Sector allocation

Security allocation

Fixed Income

Chapter 24: Performance Evaluation

Was superior performance due to asset allocation?

• Compare the return from the active allocation procedure to a hypothetical passive portfolio composed of indices in every category (stocks, bonds…).

Chapter 24: Performance Evaluation

Chapter 24: Performance Evaluation

Sector and Security Selection

Was superior performance due to sector and

security selection decisions?

• Compare portfolio’s equity performance to the S&P 500 Index
• Compare your fixed-income performance to the Lehman Brothers or Merrill Lynch index
• Compare sector weights in your portfolio to the S&P 500

Chapter 24: Performance Evaluation

Sector Allocation Within the Equity Market

Chapter 24: Performance Evaluation

Chapter 24: Performance Evaluation

Asset Allocation in which investment in the market is increased when the market is expected to outperform T-bills.

Perfect timing from 1927 to 1978: 34.71% p.a.!

Extremely hard to implement (forecasting)

Value of market timing is like the value of a call option on the index (in the money when index does better than T-bill)

Market Timing

Chapter 24: Performance Evaluation

Table 24.5 Performance of Bills, Equities and (Annual) Timers – Perfect and Imperfect

Chapter 24: Performance Evaluation

Rate of Return of a Perfect Market Timer

rf

rM

rf

Chapter 24: Performance Evaluation

Being “right most of the time” does not necessarily mean having forecasting abilities.

Need to examine the proportion of correct “bull market forecast” (P1) and correct “bear market forecast” (P2).

Measure of market timing ability: P1+P2-1

Value of imperfect forecasting: (P1+P2-1)xC

where C=call option value of a perfect market timer

Value of Imperfect Forecasting

Chapter 24: Performance Evaluation

Morningstar mutual fund rankings

Similar to mean Standard Deviation rankings

Companies are put into peer groups

Stars are assigned: 1-lowest; 5-highest

Highly correlated to Sharpe measures

Style analysis

Explaining percentage returns by allocation to style

Popular with the industry

Treynor-Black Model: combine actively managed stocks with a passively managed portfolio

Practical Measures

Chapter 24: Performance Evaluation

Introduced by William Sharpe

1992 study of mutual fund performance

91.5% of variation in return could be explained by the funds’ allocations to bills, bonds and stocks

Later studies show that 97% of the variation in return could be explained by the funds’ allocation to a broader range of asset classes

Style Analysis

Chapter 24: Performance Evaluation

Figure 24.8 Fidelity Magellan Fund Cumulative Return Difference: Fund versus Style Benchmark and Fund versus SML Benchmark

Chapter 24: Performance Evaluation

Summary
• Measures of portfolio performance
• Sharpe measure; Treynor measure; Jensen measure
• Shifting mean and variance of actively managed portfolios creates problems with performance measures
• Performance attribution procedures allow evaluator to judge performance based on asset allocation, industry (sector) allocation and security selection
• Market timing as a call option
• Value of imperfect forecasting
• April 22: Project Presentation
• 10 minutes per group: 8 minute presentation, 2 minutes Q&A
• Send your presentation to TA before presentation day!

Chapter 24: Performance Evaluation