CAPM Statistical Analysisecon.rutgers.edu/paczkows/market/CAPMStatisticalAnalysis.pdfPage 7 Coding...
Transcript of CAPM Statistical Analysisecon.rutgers.edu/paczkows/market/CAPMStatisticalAnalysis.pdfPage 7 Coding...
Page 1
CAPM Statistical Analysis
Page 2
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 ++=
Page 3
• beta is key– Each security has a beta– Each portfolio has a beta
• Portfolio beta is weighted average of individual betas
Problem 1: CAPM
Page 4
• 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
Page 5
• 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
Page 6
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
Page 7
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.
Page 8
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
Page 9
Page 10
-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
Page 11
-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
Page 12
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
Page 13
-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
Page 14
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
Page 15
-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
Page 16
-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
Page 17
-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
Page 18
Page 19
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
Page 20
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
Page 21
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
Page 22
Page 23
Page 24