Ramuada_vhahangwele

Capital Asset Pricing Model
What is Beta?
Brief description of the Australian economy
Plots
Regression output from CAPM
Residual plots
Durbin Watson test for Autocorrelation
Conclusion
The Sytematic Risk of Australian Economic
Sector: Capital Asset Pricing Model
Ramuada Vhahangwele Cedrick
African Institute for Mathematical Sciences
April 27, 2016
Ramuada Vhahangwele Cedrick The Sytematic Risk of Australian Economic Sector: Capital Asset

What is Beta?
Plots
Residual plots
Conclusion
1 Capital Asset Pricing Model
2 What is Beta?
3 Brief description of the Australian economy
4 Plots
5 Regression output from CAPM
6 Residual plots
7 Durbin Watson test for Autocorrelation
8 Conclusion

What is Beta?
Plots
Residual plots
Conclusion
What is Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model describes the relationship
between risk and expected return
It helps us to calculate the investment risk and and what we
should expect from our investment. It was ﬁrst introduced by
William Sharpe in his book ”Portfolio Theory and Capital
markets”,published in 1970

What is Beta?
Plots
Residual plots
Conclusion
Formula for CAPM
describe by the linear regression
ri,t = αi + βi rM,t + i,t (1)
Where ri,t is the return of asset i, rM,t is the return of market
portfolio and i,t is the error term. The goal is to estimate β
(Beta) for each individual asset i

What is Beta?
Plots
Residual plots
Conclusion
What is Beta?
It measures the co-movement between return of sharei and
the return of the market portfolio

What is Beta?
Plots
Residual plots
Conclusion
Interpretation of Beta(β)
If β = 1 , the stock has same level of risk as the entire stock
market
If β > 1, the stock has higher level of volatility and risk
compared to the stock market
If β is between 0 and 1, the stock price is less volatile than
the market

What is Beta?
Plots
Residual plots
Conclusion
GDP by sector :services 58%, , mining 8.5%, construction 9%,
manufacturing 7% , (2016)
Banks are part of the service sector
The resources and energy sectors represent around a tenth of
GDP, and is responsible for more than half of the country
exports
Make up of Australian economy is similar to that of the South
African economy,they both heavily depend on the mining
sector

What is Beta?
Plots
Residual plots
Conclusion
Description of data
Share prices index of Banking sector, Industrials sector,
Resources sector and entire market index SP200
5 year monthly data from 2010 − 2015

What is Beta?
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Residual plots
Conclusion
Transformed data
to capture the percentage change
Figure : banks Figure : industrial

What is Beta?
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Residual plots
Conclusion
Figure : resources Figure : SP200

What is Beta?
Plots
Residual plots
Conclusion
The estimated regression line for Banks is
ri,t = 0.002995
(0.003308)
+ 1.235420
(0.090740)
rM,t
The estimated regression line for Industrials is
ri,t = 0.004134
(0.001397)
+ 0.932253
(0.038312)
rM,t
The estimated regression line for resources is
ri,t = −0.014295
(0.004805)
+ 1.169781
(0.131800)
rM,t

What is Beta?
Plots
Residual plots
Conclusion
Interpreting beta (β)
beta for banking sector
β = 1.2354 =⇒ more systematic risk. The stock price move
strongly with the market
beta for industrial sector
β = 0.93225 =⇒ least systematic risk. The stock price
doest not move strongly with the market
beta for resources sector
β = 1.169781 =⇒ more systematic risk. The stock price for
resources sector moves strongly with the market

What is Beta?
Plots
Residual plots
Conclusion
Residual plot
Figure : banks Figure : resources

What is Beta?
Plots
Residual plots
Conclusion
Figure : industrials

What is Beta?
Plots
Residual plots
Conclusion
Durbin Watson test
Hypothesis for the Durbin Watson test
H0 : Φ = 0 ( no signiﬁcant Autocorrelation)
Ha : Φ = 0 (signiﬁcant Autocorrelation)
DW value lies between 0 and 4
If DW value is equal to 2 (no Autocorrelation)
If DW value substantially above 2 means there is evidence of
negative serial correlation
If DW value substantially below 2 (and especially a value less
than 1) means that the data is positively autocorrelated

What is Beta?
Plots
Residual plots
Conclusion
Test statistic is given by DW =
2
i (ei −ei−1)2
n
i=1 e2
i
where, ei = yi –ˆyi are the residuals, n = the number elements in
the sample and k = the number of independent variables

What is Beta?
Plots
Residual plots
Conclusion
Figure : Durbin watson graphical illustration(source:www.slideshare.net)

What is Beta?
Plots
Residual plots
Conclusion
Results of the Durbin Watson test
DW=2.526976 for model where we regress banks with market
DW=2.268896 for model where we regress industrials with
market
DW=2.392952 for model where we regress resources with
market
From the table we ﬁnd critical value dl = 1.55 and du = 1.62,for
n = 60,k = 1 , with α = 0.05 signiﬁcance level .Therefore
4 − du = 4 − 1.62 = 2.38, 4 − dl = 4 − 1.55 = 2.45
DW = 2.526976 for model for banks,
DW = 2.526976 > 4 − dL, =⇒ DW = 2.526976 > 2.45,
there exists evidence of negative autocorrelation =⇒
2 < DW = 2.268896 < 2.33, there is no evidence of
autocorrelation

What is Beta?
Plots
Residual plots
Conclusion
DW = 2.268896 for model for industrials,
2 < DW = 2.268896 < 4 − du, =⇒
2 < DW = 2.268896 < 2.33, there is no evidence of
autocorrelation DW = 2.392952 for model for resources
,4 − du < DW = 2.392952 < 4 − dl =⇒
2.38 < DW = 2.392952 < 2.45 test is inconclusive
Consequences of Autocorrelation
Standard errors are incorrect
estimates are still correct

What is Beta?
Plots
Residual plots
Conclusion
Conclusion
Australia is the world’s largest exporter of both iron ore and
coal.The beta for resources sector was 1.169781, which implies
that the stock price moves strongly with the market. The resources
sector is aﬀected by many external factors. The systematic risk for
for banking sector was 1.2354 , the stock price strongly moves with
the market i.e we have more systematic risk.The systematic risk for
industrial sector was found to be the least of all the sectors
considered on this study, with beta 0.93225. Australia’s major
banks and mining giants make up nearly half the value on the
Sydney stock exchange.There are concerns Australian banks are
not revealing the extent of the loans they have made to oil, gas
and mining companies

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