Empirical testing of the CAPM on
the JSE
Mike Ward, Chris Muller
Gordon Institute of Business Science
University of Pretoria
NERSA Conference
August 2012
An economic return on the RAB?
Shareholder Capital
The cost of equity
“The CAPM”
Re = Rf + β.MRP
Debt Capital
The cost of debt
Regulatory Asset
Base
The Capital Asset Pricing Model
Return
High beta
shares are
more risky, so
give better
returns
Rf = 11%
MarketRiskPremium = 5%
Rf = 7%
0.8
Beta = 1.0
Risk (beta)
Prior Research
Data: All US Shares
1928 - 2009
Betting Against Beta, Andrea Frazzini and Lasse H. Pedersen, Oct 2011
Data: 18 International Markets
1984 - 2009
Betting Against Beta, Andrea Frazzini and Lasse H. Pedersen, Oct 2011
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
256.000
128.000
64.000
32.000
16.000
8.000
BetaOLS60m1
BetaOLS60m2
BetaOLS60m3
BetaOLS60m4
BetaOLS60m5
Relative
J203T
Relative to J203T
21.6%
20.4%
18.1%
15.8%
12.1%
7.7%
4.000
2.000
1.000
0.500
0.250
0.125
0.063
-6.9%
-10.5%
0.031
0.016
Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12
OLS Betas - weekly
256.000
128.000
64.000
32.000
16.000
8.000
BetaOLS104w1
BetaOLS104w2
BetaOLS104w3
BetaOLS104w4
BetaOLS104w5
Relative
J203T
Relative to J203T
20.4%
19.9%
19.3%
15.8%
15.4%
4.000
4.6%
2.000
1.000
0.500
0.250
0.125
0.063
0.031
-9.6%
-12.3%
0.016
Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12
Dimson Betas - monthly
256.000
128.000
64.000
32.000
16.000
8.000
BetaDimson60m1
BetaDimson60m2
BetaDimson60m3
BetaDimson60m4
BetaDimson60m5
Relative
J203T
Relative to J203T
19.3%
19.0%
17.4%
16.3%
15.8%
7.9%
4.000
2.000
1.000
0.500
0.250
0.125
-6.8%
-8.1%
0.063
0.031
0.016
Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12
Dimson Betas - weekly
256.000
128.000
64.000
32.000
16.000
8.000
BetaDimson104w1
BetaDimson104w2
BetaDimson104w3
BetaDimson104w4
BetaDimson104w5
Relative
J203T
Relative to J203T
20.8%
19.5%
19.0%
15.8%
15.3%
4.000
5.7%
2.000
1.000
0.500
0.250
0.125
-8.7%
0.063
0.031
-12.5%
0.016
Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec- Dec84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12
Volatility - Daily
Summary of Results
Annualised returns for equal weighted portfolio quintiles over the period 31Dec1986 31Dec2011
Number
Risk Measure
of Obs
OLS Monthly Beta
60
OLS Weekly Beta
104
Dimson Monthly Beta
60
Dimson Weekly Beta
104
Volatility Daily
Average annualised
Return
60
ALSI Highest
Lowest
Index
Beta Quintile Quintile Quintile Beta
R203 Quintile
2
3
4
Quintile
15.7%
7.7% 12.1% 18.1% 21.6% 20.4%
15.7%
4.6% 15.4% 20.4% 19.9% 19.3%
15.7%
7.9% 16.3% 19.3% 19.0% 17.4%
15.7%
5.7% 15.3% 19.0% 19.5% 20.8%
15.7%
9.7%
13.5%
17.7%
20.8%
18.2%
15.7%
7.1%
14.5%
18.9%
20.2%
19.2%
Style: BetaOLS60m
Characteristic: BetaOLS60m
1.80
Portfolio 1 (Beta VH)
Portfolio 2 (Beta H)
1.60
Portfolio 3 (Beta M)
Portfolio 4 (Beta L)
1.40
Portfolio 5 (Beta VL)
1.20
1.00
0.80
0.60
0.40
0.20
Dec 11
Dec 10
Dec 09
Dec 08
Dec 07
Dec 06
Dec 05
Dec 04
Dec 03
Dec 02
Dec 01
Dec 00
Dec 99
Dec 98
Dec 97
Dec 96
Dec 95
Dec 94
Dec 93
Dec 92
Dec 91
Dec 90
Dec 89
Dec 88
Dec 87
Dec 86
Dec 85
Dec 84
0.00
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/