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25.07.2014
Time Variance of Risk-Factors Effects
1
MBA 2014 - Andreas Heier
Presentation: July 25th 2014 1:15 PM
Structure
�Motivation
�Econometric Approach�Method
�Estimation
�Results of Estimation �Market Results
�Case 1: Lanxess
�Case 2: Merck
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�Motivation
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U.S. Survey: Cost of Capital
�How do U.S. Companies estimate their Cost of
Capital ?
�Forecast-Horizon
�What´s the Cost of Debt ?
�What´s your Debt-to-Equity Ratio ?
�What Risk-Free rate to use ?
�What´s your Beta-Period ?
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U.S. Survey: Cost of Capital
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U.S. Survey: Cost of Capital
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U.S. Survey: Cost of Capital
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U.S. Survey: Cost of Capital
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U.S. Survey: Cost of Capital
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Capital-Asset-Pricing-Model
Uncertainty
Widely accepted
Only one factor
Easy to apply
What is the right β ?
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1.0430.931 0.868 0.879
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1 year 2
years
3
years
5
years
Beta-Coefficient (April 2014):
Beta-Coefficient:
What is the right β ?
July 2014
�Econometric Approach
�Method
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State space model for time-varying parameter CAPM-Model
• Consider the following time series model for asset �return in period �:
• ��� = �� �� + ����,� + ����
• �� ���� = �� �� + ��η�,��
• ���� = �� + ��η�,��
• for � = 1,… , �, where ���~�(0,1), η�,��~�(0,1), η�,��~�(0,1) are independent; ���is the daily stock return minus the risk free rate; � ,� is the daily stock index return minus the risk free rate representing the common market factor
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State space model for time-varying parameter CAPM-Model
• In the Capital Asset Pricing Model (CAPM), the
!� coefficient is zero. However, in practice, we may estimate non-zero �� coefficients. !� is interpreted as mispricing on the financial
market and it is called the active return on the
financial asset.
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State space model for time-varying parameter CAPM-Model
• In the Capital Asset Pricing Model (CAPM), the
coefficient measures the sensitivity of the asset return to the common market factor.
• As this factor influences all firms on the
market, it represents the impact of general
economic conditions in the economy and their
impact on investors´ views about how these
influence firm value.
�Econometric Approach
�Estimation
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Estimation by the maximum likelihood method
Log likelihood function:
• ln $ = ∑ ln & �� '�(�)�*� =
• −),
�ln 2. −
�
�∑ ln /� + 0�′ /�
(�0�)�*�
� The parameter estimates maximize the log likelihood
function. The optimization procedure is done numerically
� ln L is computed by the Kalman filter procedure
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Kalman-Filter-Approach (1)
� The Kalman filter was introduced by Kalman (1960)
� Kalman filter is a method of computation for the evaluation of the likelihood of data
� It is used because the econometric model of this thesis is a special case of the Linear Gaussian State Space ModelThese models are estimated by maximum likelihood method employing the Kalman filter Technique
�Results of Estimation
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1.043
0.9310.868 0.879
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1 year 2 years 3 years 5 years
Beta-Coefficient (April 2014):
Beta-Coefficient:
What is the right β ? – Part 2
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What is the right β ? – Part 2
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
β-Google
β-Nasdaq
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German DAX-30
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Kalman-Filter-Application on DAX30
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4/1/2008 2/1/2009 12/1/2009 10/1/2010 8/1/2011 6/1/2012 4/1/2013 2/1/2014
β-Bmw β-Continental β-Daimler β-Heid.Cement
β-Infineon β-Siemens β-Thyssen β-Linde
DAX 30 - INDUSTRY / MANUFACTURING
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Kalman-Filter-Application on DAX30
-1.5
-1
-0.5
0
0.5
1
1.5
4/1/2008 2/1/2009 12/1/2009 10/1/2010 8/1/2011 6/1/2012 4/1/2013 2/1/2014
β-Bayer β-Fres. Med. Care β-Fresenius β-Merck
DAX 30 - MEDICAL / PHARMACEUTICAL
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Kalman-Filter-Application on DAX30
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
4/1/2008 2/1/2009 12/1/2009 10/1/2010 8/1/2011 6/1/2012 4/1/2013 2/1/2014
β-Basf β-Eon β-KS β-Rwe β-Lanxess
DAX 30 - CHEMICALS / ENERGY
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Linear Regresion vs. Time Series
�Estimation of 1 year return with CAPM
�β-4 years static vs. β-Time Series
�Will considering the β of the time series lead
to a more precise future return estimation ?
�Results of Estimation
� Case 1: Lanxess
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�Special Chemicals
�Bayer AG Spin-Off
�Foundation 2004 – Since 2013 Dax-Company
�Headquarter in Cologne, Central Germany
�17,000 Employees
�€ 8,300 Million Sales
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0
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60
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80
0
0.2
0.4
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0.8
1
1.2
1.4
1.6
1.8
2
β-Lanxess Market-β
Adj Close Linear (β-Lanxess)
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�Results of Estimation
� Case 2: Merck AG
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�Pharmaceuticals and Chemicals
�Headquarter in Darmstadt, South of Germany
�Founded in 1668, IPO 1995 and since 2007 in DAX
�40,000 Employees
�€ 12,000 Million Sales
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Introduction OF COMPANY 2: Merck
0
20
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120
140
160
0
0.2
0.4
0.6
0.8
1
1.2
β-Merck Market-βAdj Close Linear (β-Merck)
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Conclusion:
�β-average does not always need to be used in
CAPM
�Before CAPM Time-Series should be observed
�Market risk can have specific tendency and
behavior
�Great Tool for market risk observation
�With time-varying beta coefficient, the estimation
of cost of capital can be more precise!
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References:
1. HBR Cost of Capital Survey:
� http://hbr.org/2012/07/do-you-know-your-cost-of-capital/ar/pr
2. Stock & Market returns / Financial Data:
� www.finance.yahoo.com
3. State Space Method / Kalman Filter:
� Lecture UFM, 2014, Szabolcs Blazsek
� Harvey, Andrew C., 1989. "Forecasting, Structural Time Series Models and the
Kalman Filter," Cambridge Books, Cambridge University Press.
� Kalman, R. E. (1960) A new approach to linear filtering and prediction
problems, Journal of Basic Engineering, Transactions ASMA, Series D, 82, 35-45
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