Chapter #4All Rights Reserved1 Chapter 4 Evaluating Portfolio Performance

Chapter #4All Rights Reserved2 Student Learning Objectives  Issues in Measuring Performance  Three measures of investment performance based on MPT  Past performance as a predictor of future performance  Applying MPT to investment decisions  Applying the Treynor-Black model

Chapter #4All Rights Reserved3 Issues in Measuring Performance  Cash inflows and outflows mean that different, legitimate methods of computing returns will provide different performance results.  Time-weighted (Geometric Average)  dollar weighted (Arithmetic average)  Internal Rate of Return (IRR; makes NPV = 0)

Chapter #4All Rights Reserved4 Issues in Measuring Performance   Additions of cash to or removals of cash from a portfolio   Dividends or interest payments left in portfolio are not interim cash flows   Charges in a margin account added to the debit balance, or offset against a cash position are not interim cash flows

Chapter #4All Rights Reserved5 Benchmarking  Selection of market index  DJIA: Price-weighted  SP500: Value-weighted (price * shares)  NASDAQ: Value-weighted  Bond Indexes  Foreign Market indexes

Chapter #4All Rights Reserved6 Benchmarking  Selection of comparison method  Should be risk-adjusted comparison  Can adjust risk based on:  Beta  Variance (or standard deviation)

Chapter #4All Rights Reserved7 Performance Measures  Sharpe Performance Index (1966)  Reward to Variability (risk) (CML construct)  S = (R p – R f ) /  p  S is the slope of a line whose intercept is the risk free rate (R f )  the STEEPER the line, the better the performance.  Best used to [performance] rank portfolios

Chapter #4All Rights Reserved8 Source: Investments, Haim Levy & Thierry Post Prentice-Hall (2005). Chapter 22, page 771.

Chapter #4All Rights Reserved9 Performance Measures  Treynor Performance Index  Reward per Beta Risk (SML construct)  T = (R p – R f ) /  p  Beta computed using historical rates of return  How well did the investment portfolio do in terms of percentage return on a risk-adjusted basis.

Chapter #4All Rights Reserved10 Source: Investments, Haim Levy & Thierry Post Prentice-Hall (2005). Chapter 22, page 774.

Chapter #4All Rights Reserved11 Performance Measures  Jensen’s Alpha:  Mean Excess Return minus the CAPM return  Excess return = R p – R f  CAPM Return =  (R m – R f )   = (R – R) –  (R m – R f )   = (R p – R f ) –  (R m – R f )  One problem with Jensen’s measure is that we do not know the magnitude of non- systematic risk incurred in order to achieve the excess.

Chapter #4All Rights Reserved12 Performance Measures   Information Ratio   A portfolio’s alpha divided by the standard deviation of the error term from the estimation of a portfolio’s characteristic line   IR =  /     The larger the value of the ratio, the more attractive the performance of the portfolio

Chapter #4All Rights Reserved13 Supplemental Material  Gauging impact of MPT on Investor Behavior  How do investors implement efficient market theory?  True Believers  Doubtful  Percentage players

Chapter #4All Rights Reserved14 MPT and Investor Decisions  Different groups of investors apply MPT differently depending on how strongly they believe in market efficiency  Group 1 MPT investors believe the market is strong-form efficient and will invest in any naïve diversified portfolio  Passive or naïve strategy invests in a well- diversified portfolio because one cannot “beat the market” – index portfolio

Chapter #4All Rights Reserved15 MPT and Investor Decisions  Group 2 MPT investors believe in Semistrong market efficiency and invest in a well-diversified portfolio of growth stocks to gain both benefits  Group 2 investors will analyze securities to determine which stock to include in a well- diversified portfolio  Group 2 investors will also analyze optimal allocation of the portfolio

Chapter #4All Rights Reserved16 MPT and Investor Decisions  Third group is somewhere between group 1 and group 2  They believe the market offers undervalued and overvalued stocks, but that finding them is nearly impossible, so they may act as group 1 investors  Other investors scorn MPT  Technicians may fall in this group

Chapter #4All Rights Reserved17 Treynor-Black Portfolio Combination Model  Mathematical Model to determine optimal combinations between undervalued stocks and the well-diversified naïve portfolio  Shows the tradeoff between buying growth stocks and the naïve portfolio  Finds the optimal allocation of the stocks  Appeals to group 2 MPT investors

Chapter #4All Rights Reserved18 Applying the Treynor-Black Portfolio Combination Model  Determine a well-diversified portfolio on the efficient frontier - a market portfolio  Identify a group of undervalued stocks using security analysis  Optimize the market portfolio using the undervalued portfolio  Select the proportion of allocations using the Sharpe measure

Chapter #4All Rights Reserved19 Implications for investors  Diversify by investing in several securities or in mutual funds  Measure performance using reward per risk to determine fund performance  Measure performance over a long period of time, perhaps five years or more  Understand the tradeoffs between picking high growth stocks over a well-diversified portfolio