CAPM Statistical Analysisecon.rutgers.edu/paczkows/market/CAPMStatisticalAnalysis.pdfPage 7 Coding...

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Page 1 CAPM Statistical Analysis

Transcript of CAPM Statistical Analysisecon.rutgers.edu/paczkows/market/CAPMStatisticalAnalysis.pdfPage 7 Coding...

Page 1: CAPM Statistical Analysisecon.rutgers.edu/paczkows/market/CAPMStatisticalAnalysis.pdfPage 7 Coding Sheet for CAPM Data Variable Possible Values Source Mnemonic Excess returns for an

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CAPM Statistical Analysis

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Problem 1: CAPM

• Problem– Estimate , the systematic risk, for CAPM

• CAPM is

• An empirical version is

β

[ ]ftmifti r )|E(rβ r )|E(r −Ω+=Ω

0 = α r - r = r~

r - r = r~ )σN(0,~ε

εr~βαr~

fmm

fii

2imii ++=

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• beta is key– Each security has a beta– Each portfolio has a beta

• Portfolio beta is weighted average of individual betas

Problem 1: CAPM

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• beta is proportionality factor

– Excess returns for security over riskless return is proportional to excess returns in market overriskless returns

– Excess is extra return to compensate for risk for not holding the market portfolio

• Premium on security is proportional to premium on the market portfolio

ftm

ftii r )|E(r

r )|E(rβ−Ω−Ω

=

Problem 1: CAPM

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• If

1 r )Ω|E(rr )Ω|E(rβ

ftm

ftii >

−−

= mi Premium Premium >⇒

then asset i is viewed as riskier than the market

Problem 1: CAPM

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beta Interpretation Example1 Moves With Market Conglomerates (AT&T)>1 More Volatile Companies Sensitive

To Macro Events(Autos)

0<beta<1 Less Volatile Mildly Sensitive ToMacro Events (ElectricUtilities)

<0 Move Counter To Goldmining StocksMarket

Problem 1: CAPM

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Coding Sheet for CAPM Data

Variable Possible Values Source Mnemonic

Excess returns for an overall stock market index of the total market in the UK.

Monthly, 1/80-12/99. Percentages* DataStream

(2000) rendmark

Excess returns on an index of 104 stocks in the cyclical consumer goods sector in

the UK. Monthly, 1/80-12/99. Percentages* IBID. rendcyco

Excess returns on an index of 104 stocks in the noncyclical consumer goods sector

in the UK. Monthly, 1/80-12/99. Percentages* IBID. rendncco

Excess returns on an index of 104 stocks in the information tech sector in the UK.

Monthly, 1/80-12/99. Percentages* IBID. rendit

Excess returns on an index of 104 stocks in the telcom sector in the UK. Monthly,

1/80-12/99. Percentages* IBID. rendtel

*Note: See calculations note.

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Problem 1: CAPM

• Excess returns are calculated as follows– Let pi be the closing price of the index at the

last trading day in month i and let ri be the one-month interest rate at the start of month i. Then the return vi of the index is and the excess return is vi – ri. The reported numbers are 100(vi – ri).

( ) 11 / −−−= iiii pppv

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-40

-20

0

20

40

60

RENDTEL RENDNCCO RENDMARK RENDIT RENDCYCO

Exc

ess

Ret

urns

(%)

Excess Returns DistributionsStock Market Sectors (UK)

1980 - 1999

Note: Monthly data

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-30

-20

-10

0

10

20

80 82 84 86 88 90 92 94 96 98

Exc

ess

Ret

urns

(%)

Excess ReturnsOverall Stock Market Index (UK)

1980 - 1999

Note: Monthly data

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0

10

20

30

40

50

60

70

-30 -20 -10 0 10

Series: RENDMARKSample 1980M01 1999M12Observations 240

Mean 0.808884Median 1.204026Maximum 13.46098Minimum -27.86969Std. Dev. 4.755913Skewness -1.157801Kurtosis 8.374932

Jarque-Bera 342.5191Probability 0.000000

Excess ReturnsOverall Stock Market Index (UK)

1980 - 1999

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-40

-30

-20

-10

0

10

20

30

80 82 84 86 88 90 92 94 96 98

Exc

ess

Ret

urns

(%)

Excess ReturnsCyclical Consumers Goods Sector (UK)

1980 - 1999

Note: Monthly data

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0

10

20

30

40

-30 -20 -10 0 10 20

Series: RENDCYCOSample 1980M01 1999M12Observations 240

Mean 0.499826Median 0.309320Maximum 22.20496Minimum -35.56618Std. Dev. 7.849594Skewness -0.230900Kurtosis 4.531597

Jarque-Bera 25.59050Probability 0.000003

Excess ReturnsCyclical Consumer Goods Sector (UK)

1980 - 1999

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-40

-30

-20

-10

0

10

20

80 82 84 86 88 90 92 94 96 98

Exc

ess

Ret

urns

(%)

Excess ReturnsNoncyclical Consumer Goods Sector (UK)

1980 - 1999

Note: Monthly data

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-40

-20

0

20

40

60

80 82 84 86 88 90 92 94 96 98

Exc

ess

Ret

urns

(%)

Excess ReturnsInformation Technology Sector (UK)

1980 - 1999

Note: Monthly data

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-30

-20

-10

0

10

20

30

40

80 82 84 86 88 90 92 94 96 98

Exc

ess

Ret

urns

(%)

Excess ReturnsTelecommunications Sector (UK)

1980 - 1999

Note: Monthly data

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Problem 1: CAPM

• Interpretation– The intercept is highly insignificant suggesting that the line goes

through the origin– The slope is highly significant and positive at the 0.0 level

indicating that the market rate of return (excess returns) have a positive effect on the returns for the cyclical consumer goods sector in the UK

– The R2 is 0.50 suggesting that 50% of the variation in returns in the cyclical consumer goods sector is accounted for by the market excess returns

– The model is significantly different from the naïve model as indicated by the p-value for F

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Problem 1: CAPM

• Interpretation– Since this is a CAPM, the slope has the

interpretation of systematic risk• Since it is greater than 1.0, this indicates that the

cyclical consumer goods sector is riskier that the market as a whole

• When the market rises, the excess returns in this sector will rise more than the market

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Problem 1: CAPM

241.3363(0.0000)

FC

Notes: p-value in parenthese; *=significant

0.5035R2

1.17*(0.0000)

RendMark

-0.477(0.2188)

Intercept

ModelModel Portfolio

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