1

Performance Evaluation and Active

Portfolio Management

CHAPTER 18

2

Introduction• Complicated subject• 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 managements leads to

measurement problems

3

Abnormal Performance

What is abnormal? Abnormal performance is measured:• Comparison groups• Market adjusted• Market model / index model adjusted• Reward to risk measures such as the Sharpe

Measure:E (rp-rf) / sp

4

Factors That Lead to Abnormal Performance• Market timing• Superior selection

– Sectors or industries– Individual companies

5

Comparison Groups• Simplest method• Most popular• Compare returns to other funds with similar

investment objectives

6

Risk Adjusted Performance: Sharpe 1) Sharpe Index

rp - rf

rp = Average return on the portfolio

rf = Average risk free rate

p= Standard deviation of portfolio

return

ps

s

7

Risk Adjusted Performance: Treynor

2) Treynor Measure rp - rf

ßp

rp = Average return on the portfolio

rf = Average risk free rate

ßp = Weighted average b for portfolio

8

= rp - [ rf + ßp ( rm - rf) ]

3) Jensen’s Measure

p

p

rp = Average return on the portfolio

ßp = Weighted average Beta

rf = Average risk free rate

rm = Avg. return on market index port.

Risk Adjusted Performance: Jensen

= Alpha for the portfolioaa

9

M2 Measure

• 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

10

M2 Measure: ExampleManaged Portfolio Market T-bill

Return 35% 28% 6%

Stan. Dev 42% 30% 0%

Hypothetical Portfolio: Same Risk as Market

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

11

Figure 17-2 The M2 of Portfolio P

12

T2 (Treynor Square) Measure• Used to convert the Treynor Measure into

percentage return basis• Makes it easier to interpret and compare• Equates the beta of the managed portfolio with the

market’s beta of 1 by creating a hypothetical portfolio made up of T-bills and the managed portfolio

• If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market

13

T2 ExamplePort. P. Market

Risk Prem. (r-rf) 13% 10%

Beta 0.80 1.0

Alpha 5% 0%

Treynor Measure 16.25 10

Weight to match Market w = bM/bP = 1.0 / 0.8

Adjusted Return RP* = w (RP) = 16.25%

T2P = RP

* - RM = 16.25% - 10% = 6.25%

14

Figure 17-3 Treynor Square Measure

15

Which Measure is Appropriate?

It depends on investment assumptions1) 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 a or the Treynor measureThe Treynor measure is more complete because it adjusts for risk

16

Exercise2• 1. A managed portfolio has a standard deviation equal to 22% and a beta

of 0.9 when the market portfolio's standard deviation is 26%. The adjusted portfolio P* needed to calculate the M2 measure will have _____ invested in the managed portfolio and the rest in T-bills. a. 84.6%b. 118%c. 18%d. 15.4%

17

Exercise 2• Use the following to answer questions 2-4:

The average returns, standard deviations and betas for three funds are given in previous slide along with data for the S&P 500 index. The risk free return during the sample period is 6%.

• 2. You wish to evaluate the three mutual funds using the Sharpe measure for performance evaluation. The fund with the

highest Sharpe measure of performance is __________. a. Fund Ab. Fund Bc. Fund Cd. Indeterminable

•  • 3. You wish to evaluate the three mutual funds using the Treynor measure for performance evaluation. The fund with the

highest Treynor measure of performance is __________. a. Fund Ab. Fund Bc. Fund Cd. Indeterminable

•  • 4. You wish to evaluate the three mutual funds using the Jensen measure for performance evaluation. The fund with the

highest Jensen measure of performance is __________. a. Fund Ab. Fund Bc. Fund Cd. S&P500

18

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

19

Performance Attribution• Decomposing overall performance into

components• Components are related to specific elements of

performance• Example components

– Broad Allocation– Industry– Security Choice– Up and Down Markets

20

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

21

rf

rf

rM

Rate of Return of a Perfect Market TimerWhat if the forecast is not precise?

22

Market Timing & Performance Measurement

Adjusting portfolio for up and down movements in the market

• Low Market Return - low ßeta• High Market Return - high ßeta

23

Figure 17-6 Characteristic Lines

24

Style Analysis• Introduced by Bill Sharpe• Explaining percentage returns by allocation to

style• Style Analysis has become popular with the

industry

25

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