Time Variance of Risk-Factors Effects · 2017. 4. 25. · 25.07.2014 Time Variance of Risk-Factors -MBA 2014 - Andreas Heier 18 Kalman-Filter-Approach (1) The Kalman filter was introduced

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

25.07.2014Time Variance of Risk-Factors - MBA 2014 -

Andreas Heier2

�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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25.07.2014 Time Variance of Risk-Factors - MBA 2014 - Andreas Heier 10

Capital-Asset-Pricing-Model

Uncertainty

Widely accepted

Only one factor

Easy to apply

What is the right β ?


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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• 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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• 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


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


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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-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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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 ?


� 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


0

10

20

30

40

50

60

70

80

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

β-Lanxess Market-β

Adj Close Linear (β-Lanxess)


� 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


Introduction OF COMPANY 2: Merck

0

20

40

60

80

100

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!


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

Documents

Time Variance of Risk-Factors Effects · 2017. 4. 25. · 25.07.2014 Time Variance of Risk-Factors -MBA 2014 - Andreas Heier 18 Kalman-Filter-Approach (1) The Kalman filter was introduced