Chapter 4

Evaluating Portfolio Performance

Why Evaluating Portfolio Performance Is Not Simple

• Cash inflows and outflows mean that different, legitimate methods of computing returns will provide different performance results.

• Time-weighted vs. dollar weighted

Interim Cash Flows

• 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

Two Tools to Measure Actual Return Over a Period

• Geometric Mean Return– Time-weighted rate of return measure

• Internal Rate of Return– Dollar-weighted rate of return measure

NN

N

1tt

t0

r1

Value

r1

CFValue0

Which Rate Should Be Used?

• Depends on conditions governing cash flows– If portfolio manager controls timing of cash

flows, use IRR– If he or she does not, use GMR– Return to an investor is always IRR– Performance by portfolio manager is usually

GMR

Two Components to Benchmarking

• Selection of market index

• Selection of comparison method– Should be risk-adjusted comparison– Can adjust risk based on:

• Beta

• Variance (or standard deviation)

Choices for a Market Index

• Dow Jones Industrial Average

• Standard & Poor’s 500

• Other Domestic Indexes

• Foreign Indexes

• Bond Indexes

Dow Jones Industrial Average

• Oldest, started in 1884• Most commonly quoted• Flaws:

– Small number of stocks (30)– Industries not proportionally represented– Focuses only on large, mature companies– Ignores dividends– Price-weighted index

Price Weighted Index

• Add up all prices and divide by number of securities in index

• Unless there have been:– Stock splits– Stock dividends– Changes in composition of index

• Adjustments made via denominator• Stock with highest price has most impact

Standard & Poor’s 500

• Advantages:– Large percentage of total market capitalization– Includes stocks from multiple markets– Industry representation more typical of

economy– Value weighted (as are most indexes)

Value Weighted Index

• Capitalizations of all companies in index added together

• Capitalization = price x number of shares• Sum divided by sum of capitalizations on

start date• Neutral with regard to splits and dividends• Minor adjustment with regard to changes in

components

Other Indexes

• NASDAQ 100

• NYSE Composite

• Russell 3000, 1000, and 2000

• Dow Jones Wilshire 5000– Closest to a Total Market Index

N

1i

i

index in the stocks all oftion capitalizaMarket

icompany oftion capitalizamarket x PIndex

Other Indexes (continued)

• Value Line Index– Only equally weighted index

Foreign Indexes– FTSE 100

– MSCI EAFE

• Bond Indexes– Lehman Brothers Aggregate Bond Index

– Lehman Brothers Corporate Bond Index

– Lehman Brothers Government Bond Index

– Lehman Brothers Mortgage-Backed Securities Index

Computing Risk Adjusted Performance Using Standard Deviation

• Sharpe ratio– also called reward-to-variability ratio (RVAR)

p fp

p

R RS

σ

Also called the reward-to-volatility ratio (RVOL)

P fp

p

R RT

Treynor ratio

Other Beta-Based Measures of Performance Evaluation

•Information Ratio

– A portfolio’s alpha divided by the standard deviation of the error term from the estimation of a portfolio’s characteristic line

– The larger the value of the ratio, the more attractive the performance of the portfolio

• Jensen’s alpha

p p f M f pα R R R R β

Choosing a Performance Measure

•Use the Sharpe ratio when it is important to consider total variability and not just exposure to systematic risk

•Use the Information ratio when a portfolio is divided into two components and only one is actively managed

•Use the Treynor ratio when an overall portfolio has been allocated to multiple active managers