CHAPTER 22MEASURING RISKS AND RETURNS OF PORTFOLIO

MANAGERSFIN 330

Principles of Investing

STUDENT LEARNING OBJECTIVESA. Learning from Historical Trends

1. Measuring Holding Period Returns: Geometric vs. Arithmetic

2. Fund Objectives and Risk AttributesB. Three measures of investment performance

based on modern portfolio theoryC. Past performance as a predictor of future

performanceD. Applying modern portfolio theory to investment

decisions

Learning from Historical TrendsA. Measuring Holding Period Returns

1. Arithmetic: simple averages of daily weekly, monthly, quarterly, or annual stock or index returns. (dollar weighted)

E(r) = / N

2. Geometric: the n-root of the product of n-period returns

(time weighted)E(1/T - 1

3. Arithmetic mean returns are upwardly biased v-v Geometric mean returns.

Learning from Historical TrendsA. Example of upward bias in arithmetic returns

1. Three daily closing prices:a. P1 = 1.00b. P2 = 1.10c. P3 = 1.00

2. 2 daily returnsa. R1,2 = (.10 / 1.00) = 0.10 or 10% gainb. R2,3 = (-.10 / 1.10) = -0.0909 or 9.09% lossc. Mean r = (0.10 + -0.09090) / 2 = 0.0046 or 0.46% gaind. Geometric r = [(1.10) * (0.9091)]1/2 – 1 = 0.0000 or 0% gain

Note that 1 + -.0909 = .9091

Three performance measures1. Treynor measure is reward per unit of beta risk

(Actual Rp – Rf) / Beta

2. Sharpe measure is reward per unit of total risk (total risk = std. dev.)

(Actual Rp – Rf) / sp

3. Jensens’s Alpha measures the actual mean excess return minus the CAPM return

a = (Actual Rp – Rf) – b (Rm – Rf)

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Performance Measures• Sharpe Performance Index (1966)• Reward to Variability (risk) (CML construct)

• S = (Rp – Rf) / sp

• S is the slope of a line whose intercept is the risk free rate (Rf)

• the STEEPER the line, the better the performance.

• Best used to [performance] rank portfolios

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Performance Measures• Treynor Performance Index• Reward per unit of Beta Risk (SML construct)• T = (Rp – Rf) / bp

• Beta computed using historical rates of return• How well did the investment portfolio do in terms of percentage return on a

risk-adjusted basis.

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Performance Measures• Jensen’s Alpha: • Mean Excess Return minus the CAPM return

• Excess return = Rp – Rf

• CAPM Return = b (Rm – Rf)

• a = (Rp – Rf) – b (Rm – Rf)• 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.

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Supplemental Material• Gauging impact of MPT on Investor Behavior• How do investors implement efficient market theory?

• True Believers• Doubtful• Percentage players

Applying MPT to 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

Applying MPT to 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

Copyright © 1998 by Harcourt Brace & Company

Applying MPT to 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

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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

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