# Stern School of Business

## Presentation on theme: "Stern School of Business"— Presentation transcript:

Stern School of Business
New York University Stern School of Business Portfolio Management Prof. Ian Giddy New York University

Agenda How to evaluate portfolio performance What portfolio theory tells us How to put stocks or funds that outperform the market into your “active” portfolio

Why Measure Performance?
Performance evaluation: “the science of attribution” Example: Why did this taxi take so long? The traffic; the driver; my lousy instructions? How much should I tip this taxi driver? Would I use this taxi company again?

Portfolio Performance Evaluation
How well did the portfolio do? How do we adjust for risk, to compare different managers? Why? Risk Timing Asset allocation Security selection

Abnormal Performance What is abnormal?
Performance can be measured against: Benchmark portfolio Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe measure: E (rp-rf) / p

Performance Evaluation Issues
Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active management leads to measurement problems

Measuring Portfolio Returns
Dollar-weighted return (IRR) vs Time-weighted return Arithmetic average Geometric average

Performance Evaluation Measures
Sharpe’s measure The portfolio’s average excess return per unit of total risk Treynor’s measure The portfolio’s average excess return per unit of systematic risk Jensen’s measure The excess of the portfolio’s return over that predicted by the CAPM Appraisal ratio Portfolio’s abnormal return per unit of risk that could be diversified by holding a market index portfolio

Performance Evaluation Measures
Sharpe’s measure Treynor’s measure Jensen’s measure  Appraisal ratio

Risk Adjusted Performance: Sharpe
1) Sharpe Index rp = Average return on the portfolio rf = Average risk free rate p = Standard deviation of portfolio return

Risk Adjusted Performance: Treynor
2) Treynor Measure rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average for portfolio

Risk Adjusted Performance: Jensen
3) Jensen’s Measure = Alpha for the portfolio p rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port.

Which Measure is Appropriate?
It depends on investment assumptions 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market. 2) If many alternatives are possible, use the Jensen or the Treynor measure The Treynor measure is more complete because it adjusts for risk

Limitations Assumptions underlying measures limit their usefulness When the portfolio is being actively managed, basic stability requirements are not met Practitioners often use benchmark portfolio comparisons to measure performance

Factors That Lead to Abnormal Performance
Market timing Superior selection Sectors or industries Individual companies

Decomposing overall performance into components Components are related to specific elements of performance Example components Broad Allocation Industry Security Choice Up and Down Markets

Asset allocation choices Broad market allocations: equity, bonds, etc. Industry choices Security selection Evaluation: compare the portfolio returns at each level with returns on the appropriate index (benchmark portfolio or passive strategy)

Process of Attributing Performance to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure

Process of Attributing Performance to Components
Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories

Performance Attribution: 1. Excess Return

Performance Attribution: 2. Asset Allocation

Performance Attribution: 3. Security Selection

Performance Attribution: 4. Summary
Source:

Active Portfolio Management
Stock-picking and active portfolio management must pay, else the market would not be efficient! The optimal risky portfolio maximizes the reward-to-variability ratio; the slope of the CAL: ACTIVE CAPITAL ALLOCATON LINE E(rp) PASSIVE CAPITAL ALLOCATON LINE

Lure of Active Management
Are markets totally efficient? Some managers outperform the market for extended periods While the abnormal performance may not be too large, it is too large to be attributed solely to noise Evidence of anomalies such as the turn of the year exist The evidence suggests that there is some role for active management 2

Market Timing Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta

Adjust the portfolio for movements in the market
Market Timing Adjust the portfolio for movements in the market Shift between stocks and money market instruments or bonds Results: higher returns, lower risk (downside is eliminated) With perfect ability to forecast behaves like an option 3

Example of Market Timing
rp - rf * * * * * * * * * * * * * * * * * * * * * rm - rf * * Steadily Increasing the Beta

Market Timing: An Option on the S&P
Value of perfect timing is a call option worth C Timing ability measured by PBull+ PBear-1 Value of timing ability is (PBull+ PBear -1)C P = the proportion of correct forecasts rf rM rf

Rate of Return of a Perfect Market Timer
rM rf 4

Returns on Stocks and Bills
Year 71 72 73 74 75 76 77 78 79 80 Stock Ret. .1431 .1898 -.1466 -.2647 .3720 .2384 -.0718 .0656 .1844 .3242 T-Bill Ret .0439 .0384 .0693 .0800 .0580 .0508 .0512 .0718 .1038 .1124 Avg. Ret. S.D. Ret. .1034 .2068 .0680 .0248 5

With Perfect Forecasting Ability
Switch to T-Bills in ‘73, ‘74, ‘77, ‘78 No negative returns or losses Average Ret. = .1724 S.D. Ret. = .1118 Results with perfect timing 70% increase in mean return 46% lower S.D. 6

With Imperfect Ability to Forecast
Long horizon to judge the ability Judge proportions of correct calls Bull markets and bear market calls 7

Conclusion: Hold Three Things
Risk-free asset Passive portfolio Active portfolio

Superior Selection Ability
Concentrate funds in undervalued stocks or undervalued sectors or industries Balance funds in an active portfolio and in a passive portfolio Active selection will mean some unsystematic risk 8

Used to guage performance of professional portfolios
Sharpe’s Ratio Used to guage performance of professional portfolios ACTIVE CAL E(rp) PASSIVE CAL

Treynor-Black Model Model used to combine actively managed stocks with a passively managed portfolio Using a reward-to-risk measure that is similar to the the Sharpe Measure, the optimal combination of active and passive portfolios can be determined 9

Security Selection Alpha is the expected return on a security above that explained by its beta and the security market line: Treynor-Black model says weight of each security should be based on ratio of its mispricing to its nonsystematic risk:

Treynor-Black Model: Assumptions
Analysts will have a limited ability to find a select number of undervalued securities Portfolio managers can estimate the expected return and risk, and the abnormal performance for the actively-managed portfolio Portfolio managers can estimate the expected risk and return parameters for a broad market (passively managed) portfolio 10

Reward to Variability Measures
Passive Portfolio : [ E ( r m ) - f m ] 2 S 2 m = 11

Reward to Variability Measures
Appraisal Ratio A (ep) = Alpha for the active portfolio A = Unsystematic standard deviation for active (Ap) 12

Reward to Variability Measures
Combined Portfolio : [ A [ E ( r m ) - f m 2 2 S 2 = ] + ] p eA 13

Treynor-Black Allocation
CAL Optimal Portfolio E(r) CML Active Portfolio Market Portfolio Rf 14

Implementing the Treynor-Black Approach
Use passive portfolio (index fund) as baseline; find its E(rM) and E(VarM) Analyze a few securities; find mispriced ones For each security, use estimates of Alpha, Beta and residual risk to determine optimum weights Determine optimal weights for active and passive portfolios

Summary Points: Treynor-Black Model
Sharpe Measure will increase with added ability to pick stocks Slope of CAL>CML (rp-rf)/p > (rm-rf)/p P is the portfolio that combines the passively managed portfolio with the actively managed portfolio The combined efficient frontier has a higher return for the same level of risk 15

Summary How to evaluate portfolio performance How to put stocks or funds that outperform the market into your “active” portfolio Portfolio theory helps construct the right active/passive/riskfree mix.

Ian Giddy Ian H. Giddy NYU Stern School of Business
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