CHAPTER 22 MEASURING RISKS AND RETURNS OF PORTFOLIO MANAGERS FIN 330 Principles of Investing

STUDENT LEARNING OBJECTIVES A.Learning from Historical Trends 1.Measuring Holding Period Returns: Geometric vs. Arithmetic 2.Fund Objectives and Risk Attributes B.Three measures of investment performance based on modern portfolio theory C.Past performance as a predictor of future performance D.Applying modern portfolio theory to investment decisions

Learning from Historical Trends

A.Example of upward bias in arithmetic returns 1.Three daily closing prices: a.P1 = 1.00 b.P2 = 1.10 c.P3 = daily returns a.R 1,2 = (.10 / 1.00) = 0.10 or 10% gain b.R 2,3 = (-.10 / 1.10) = or 9.09% loss c.Mean r = ( ) / 2 = or 0.46% gain d.Geometric r = [(1.10) * (0.9091)] 1/2 – 1 = or 0% gain Note that =.9091

Three performance measures reward per unit of beta risk 1.Treynor measure is reward per unit of beta risk  (Actual Rp – Rf) / Beta reward per unit of total risktotal risk = std. dev.) 2.Sharpe measure is reward per unit of total risk (total risk = std. dev.)  (Actual Rp – Rf) / s p actual mean excess return minus the CAPM return 3.Jensens’s Alpha measures the actual mean excess return minus the CAPM return   = (Actual Rp – Rf) –  (Rm – Rf)

Chapter #4All Rights Reserved6 Performance Measures A.Sharpe Performance Index (1966) 1.Reward to Variability (risk) (CML construct) 2.S = (R p – R f ) /  p 3.S is the slope of a line whose intercept is the risk free rate (R f ) 4.the STEEPER the line, the better the performance. 5.Best used to [performance] rank portfolios

Chapter #4All Rights Reserved7 Performance Measures A.Treynor Performance Index 1.Reward per unit of Beta Risk (SML construct) 2.T = (R p – R f ) /  p 3.Beta computed using historical rates of return 4.How well did the investment portfolio do in terms of percentage return on a risk-adjusted basis.

Chapter #4All Rights Reserved8 Performance Measures A.Jensen’s Alpha: 1.Mean Excess Return minus the CAPM return 2.Excess return = R p – R f 3.CAPM Return =  (R m – R f )  = (R p – R f ) –  (R m – R f ) 5.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 Reserved9 Supplemental Material A.Gauging impact of MPT on Investor Behavior 1.How do investors implement efficient market theory? a.True Believers b.Doubtful c.Percentage players

Applying MPT to investor decisions A.Different groups of investors apply MPT differently depending on how strongly they believe in market efficiency strong-form efficient 1.Group 1 MPT investors believe the market is strong-form efficient and will invest in any naïve diversified portfolio naïve strategy invests in a well-diversified portfolio 2.Passive or naïve strategy invests in a well-diversified portfolio because one cannot “beat the market” – index portfolio

Applying MPT to investor decisions Semistrong market efficiency A.Group 2 MPT investors believe in Semistrong market efficiency and invest in a well-diversified portfolio of growth stocks to gain both benefits 1.Group 2 investors will analyze securities to determine which stock to include in a well-diversified portfolio 2.Group 2 investors will also analyze optimal allocation of the portfolio

Copyright © 1998 by Harcourt Brace & Company Applying MPT to investor decisions A.Third group is somewhere between group 1 and group 2 B.They believe the market offers undervalued and overvalued stocks, but that finding them is nearly impossible, so they may act as group 1 investors C.Other investors scorn MPT D.Technicians may fall in this group

Chapter #4All Rights Reserved13 Implications for investors A.Diversify by investing in several securities or in mutual funds B.Measure performance using reward per risk to determine fund performance C.Measure performance over a long period of time, perhaps five years or more D.Understand the tradeoffs between picking high growth stocks over a well-diversified portfolio

Homework A.Discussion Questions: 1, 3, 4, 5, 6, 7 B.Problems: 1, 2 (parts a & c)