Empirical testing of the CAPM on the JSE

Mike Ward, Chris MullerGordon Institute of Business Science

University of PretoriaNERSA Conference

August 2012

An economic return on the RAB?

Regulatory Asset Base

Shareholder Capital

Debt Capital

The cost of equity“The CAPM”

Re = Rf + β.MRP

The cost of debt

The Capital Asset Pricing Model

Beta = 1.0

Retu

rn

Rf = 7%

MarketRiskPremium = 5%

High beta shares are

more risky, so give better

returns

0.8

Rf = 11%

Risk (beta)

Betting Against Beta, Andrea Frazzini and Lasse H. Pedersen, Oct 2011

Prior ResearchData: All US Shares 1928 - 2009

Betting Against Beta, Andrea Frazzini and Lasse H. Pedersen, Oct 2011

Data: 18 International Markets 1984 - 2009

Fama and French (2004) estimated betas for every share on the NYSE, AMEX and NASDAQ from 1923 – 2003 using 2-5 years prior

data and compared with their return over the next 12 months:

Prior research on the JSE• Strugnell, Gilbert & Kruger (2011) IAJ

– “Beta has no predictive power for returns on the JSE”

– Data from 1994 – 2007– Included too many small shares

• van Rensburg & Robertson (2003) IAJ– “If anything, beta is inversely related to

returns!”– Data from 1990 – 2000– Included too many small shares

Rational for research• The CAPM is a pillar of financial

theory:– taught on all finance courses– found in all finance text books– used regularly in the financial services

industry– Markowitz, Miller & Sharpe shared a

Nobel prize• We have 25 years of JSE data

– 1985 to 2011• We can improve on the methodology

Methodology• Select the largest 160 companies in Dec 1984• Estimate betas using prior years return data

– OLS beta• 60 monthly data points

– Dimson• Multiple regression (+1,0,-1,-2,-3,-4)

• Rank betas• Construct 5 equal weighted portfolios of 32

shares• Measure portfolio return over the next 3

months• Repeat for next quarter

99% of JSE’s market capitalisation

Presentation of findings• We track the daily value of each

portfolio (quintile)• We re-balance each portfolio quarterly

– We retain the value of the portfolio– Equally weight– We ignore transaction costs

• We graph the results• We benchmark against the ALSI total

return index• We plot a price relative versus the

J203

Results

OLS Betas - monthly

Dec-84

Dec-85

Dec-86

Dec-87

Dec-88

Dec-89

Dec-90

Dec-91

Dec-92

Dec-93

Dec-94

Dec-95

Dec-96

Dec-97

Dec-98

Dec-99

Dec-00

Dec-01

Dec-02

Dec-03

Dec-04

Dec-05

Dec-06

Dec-07

Dec-08

Dec-09

Dec-10

Dec-11

Dec-12

0.016

0.156

1.563

15.625

156.250

7.7%

12.1%

18.1%

21.6%20.4%

-10.5%

15.8%

-6.9%

BetaOLS60m1BetaOLS60m2BetaOLS60m3BetaOLS60m4BetaOLS60m5RelativeJ203TRelative to J203T

OLS Betas - weekly

Dec-84

Dec-85

Dec-86

Dec-87

Dec-88

Dec-89

Dec-90

Dec-91

Dec-92

Dec-93

Dec-94

Dec-95

Dec-96

Dec-97

Dec-98

Dec-99

Dec-00

Dec-01

Dec-02

Dec-03

Dec-04

Dec-05

Dec-06

Dec-07

Dec-08

Dec-09

Dec-10

Dec-11

Dec-12

0.016

0.156

1.563

15.625

156.250

4.6%

15.4%

20.4%19.9%19.3%

-12.3%

15.8%

-9.6%

BetaOLS104w1BetaOLS104w2BetaOLS104w3BetaOLS104w4BetaOLS104w5RelativeJ203TRelative to J203T

Dimson Betas - monthly

Dec-84

Dec-85

Dec-86

Dec-87

Dec-88

Dec-89

Dec-90

Dec-91

Dec-92

Dec-93

Dec-94

Dec-95

Dec-96

Dec-97

Dec-98

Dec-99

Dec-00

Dec-01

Dec-02

Dec-03

Dec-04

Dec-05

Dec-06

Dec-07

Dec-08

Dec-09

Dec-10

Dec-11

Dec-12

0.016

0.156

1.563

15.625

156.250

7.9%

16.3%

19.3%19.0%17.4%

-8.1%

15.8%

-6.8%

BetaDimson60m1BetaDimson60m2BetaDimson60m3BetaDimson60m4BetaDimson60m5RelativeJ203TRelative to J203T

Dimson Betas - weekly

Dec-84

Dec-85

Dec-86

Dec-87

Dec-88

Dec-89

Dec-90

Dec-91

Dec-92

Dec-93

Dec-94

Dec-95

Dec-96

Dec-97

Dec-98

Dec-99

Dec-00

Dec-01

Dec-02

Dec-03

Dec-04

Dec-05

Dec-06

Dec-07

Dec-08

Dec-09

Dec-10

Dec-11

Dec-12

0.016

0.156

1.563

15.625

156.250

5.7%

15.3%

19.0%19.5%20.8%

-12.5%

15.8%

-8.7%

BetaDimson104w1BetaDimson104w2BetaDimson104w3BetaDimson104w4BetaDimson104w5RelativeJ203TRelative to J203T

Volatility - Daily

Summary of Results

Annualised returns for equal weighted portfolio quintiles over the period 31Dec1986 - 31Dec2011

Risk MeasureNumber of Obs

ALSI Index R203

Highest Beta

QuintileQuintile

2Quintile

3Quintile

4

Lowest Beta

QuintileOLS Monthly Beta 60 15.7% 7.7% 12.1% 18.1% 21.6% 20.4%OLS Weekly Beta 104 15.7% 4.6% 15.4% 20.4% 19.9% 19.3%Dimson Monthly Beta 60 15.7% 7.9% 16.3% 19.3% 19.0% 17.4%Dimson Weekly Beta 104 15.7% 5.7% 15.3% 19.0% 19.5% 20.8%Volatility Daily 60 15.7% 9.7% 13.5% 17.7% 20.8% 18.2%Average annualised Return 15.7% 7.1% 14.5% 18.9% 20.2% 19.2%

Dec 8

4

Dec 8

5

Dec 8

6

Dec 8

7

Dec 8

8

Dec 8

9

Dec 9

0

Dec 9

1

Dec 9

2

Dec 9

3

Dec 9

4

Dec 9

5

Dec 9

6

Dec 9

7

Dec 9

8

Dec 9

9

Dec 0

0

Dec 0

1

Dec 0

2

Dec 0

3

Dec 0

4

Dec 0

5

Dec 0

6

Dec 0

7

Dec 0

8

Dec 0

9

Dec 1

0

Dec 1

1

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

Portfolio 1 (Beta VH)

Portfolio 2 (Beta H)

Portfolio 3 (Beta M)

Portfolio 4 (Beta L)

Portfolio 5 (Beta VL)

Style: BetaOLS60m

Characteristic: BetaOLS60m

Conclusion:

High risk (beta) = Low return

Ben Graham once argued that: "Beta is a more or less useful measure of past price fluctuations of common stocks. What bothers me is that authorities now equate the beta idea with the concept of risk.

Questions…

• For those interested:• The full paper will be published in the forthcoming:

– Investment Analyst Journal– http://www.iassa.co.za/journals/