Diversification and Persistence:Implications for Personal Asset

Management

Dale Domian, Professor of Finance

School of Administrative Studies

York University

Consider 60/40 mix

• Traditional allocation for a balanced portfolio is 60% equity, 40% debt

• Some investors may consider individual stocks for the 60%, and bond mutual funds (or ETFs) for the 40%

How many stocks are enough?

• Many finance textbooks and popular publications claim that the full benefits of diversification can be obtained with just eight to 20 stocks.

• Evans and Archer, Journal of Finance, 1968

Burlington Northern Santa Fe

• Warren Buffett’s offer: $100 per share

• My cost basis: about $3.00

• Over long holding periods, some stocks deliver spectacular gains…while others go bankrupt!

Two possible approaches

• Large positions in a small number of stocks; if you’re lucky, you will have at least one big winner

• Small positions in a large number of stocks; guarantees that you will have some of the biggest winners

Table II – Studies in Economics and Finance, 2003 Cumulative Returns on the S&P 100 Stocks, 1979–1998

The figures below show cumulative rates of return, including dividends, over the 20-year period from January 1979 through December 1998. The 100 firms comprise the S&P 100 Index at the beginning of 1979. S&P 500 Index returns are used to replace missing data. Returns are expressed in decimal form rather than in percent, so -0.91 indicates a decline of 91%.

Firm Cumulative Return

1 Datapoint -0.91 2 Johns Manville -0.84 3 Storage Technology -0.54 4 Bethlehem Steel -0.36 5 Polaroid 0.17

…

50 AMP 15.44 51 Great Western Financial 15.85

…

96 General Electric 66.54 97 Burlington Northern Santa Fe 67.38 98 Coca Cola 68.74 99 Esmark 72.69 100 Squibb 87.53

Table III – Studies in Economics and Finance, 2003 Ending Wealth from Portfolios of S&P 100 Stocks, 1979–1998

The figures below show ending wealth from $100,000 invested at the beginning of 1979. All portfolios are equally weighted. Under “Dropping the Best Stocks,” the 99-firm portfolio excludes Squibb; the 98-firm portfolio excludes Squibb and Esmark; and so on. “Under Dropping the Worst Stocks,” the exclusions begin with Datapoint.

Dropping the Best Stocks

Dropping the Worst Stocks

No. of stocks

Ending Wealth

Dollar

Change

Percentage

Change

Ending Wealth

Dollar

Change

Percentage

Change

100 $2,212,141 $0 0.0% $2,212,141 $0 0.0% 99 2,145,064 -67,077 -3.0 2,234,389 22,248 1.0 98 2,091,763 -120,378 -5.4 2,257,024 44,883 2.0 97 2,041,429 -170,712 -7.7 2,279,814 67,673 3.1 96 1,991,467 -220,674 -10.0 2,302,897 90,756 4.1 95 1,941,340 -270,801 -12.2 2,325,907 113,766 5.1

Domian, Louton, and Racine,

Diversification in Portfolios of Individual Stocks:

100 Stocks Are Not Enough,

The Financial Review, November 2007

Table 1 Ending wealth per dollar invested with random and industry diversification, 1985-2004 The columns compare two stock selection techniques, “Random,” in which the stocks are randomly drawn regardless of industry group, and “Industry,” in which the firms are equally distributed across the ten industries.

10 Stocks

20 Stocks

30 Stocks

50 Stocks

100 Stocks

200 Stocks

Percentile

of Distribution

Random

Industry

Random

Industry

Random

Industry

Random

Industry

Random

Industry

Random

Industry

1%

$3.02

$3.34

$4.70

$4.92

$5.61

$5.78

$6.72

$6.83

$8.16

$8.23

$9.54

$9.57

5%

4.49

4.73

6.05

6.20

6.90

7.00

7.94

8.00

9.28

9.32

10.50

10.53

10%

5.45

5.63

6.92

7.01

7.72

7.78

8.73

8.77

9.98

10.02

11.08

11.10

25%

7.39

7.46

8.69

8.71

9.45

9.46

10.35

10.36

11.35

11.38

12.16

12.18

50%

10.40

10.34

11.63

11.60

12.21

12.20

12.76

12.75

13.25

13.26

13.60

13.60

75%

16.17

16.13

16.39

16.37

16.29

16.26

16.07

16.07

15.74

15.73

15.34

15.33

90%

25.48

25.48

23.23

23.15

21.75

21.72

20.46

20.42

18.74

18.71

17.07

17.05

95%

33.68

33.60

28.73

28.68

26.68

26.60

24.41

24.36

20.67

20.61

18.10

18.06

99%

76.58

76.96

48.00

47.66

38.68

38.39

30.93

30.67

24.13

24.03

19.94

19.87

Extensions for future research

• Leverage

• Rebalancing

• Small Stocks

Leverage

Several previous articles on this topic:• Domian and Racine, Financial Services Review, 2002• Domian and Racine, Canadian Investment Review, 2003• Domian and Racine, International Review of Economics

and Finance, 2006• Domian, Racine, and Wilson, Journal of Economics and

Finance, 2006

Extend Financial Review approach using leverage

Rebalancing and Small Stocks

• See Tables IV and V from 2006 AFS presentation

Fixed Income Mutual Funds

• How do you choose a good fund?

• Persistence – do winners repeat?

Money Market Funds

• Domian and Reichenstein, Financial Services Review, 1997

• Tables 2 and 4, next slides

Municipal Bond Funds

• Domian and Reichenstein, Journal of Investing, 2002

• Exhibits 1 and 4, next slides

Corporate Bond Funds

• Reichenstein, Journal of Investing, 1999

• Domian and Reichenstein, research in progress: persistence over longer time horizons

How do high-yield bonds (“junk bonds”) fit into the 60/40?

• Domian and Reichenstein, Journal of Fixed Income, 2008

• High-yield bonds act like a combination of 2/3 investment grade bonds, 1/6 large stocks, and 1/6 small stocks