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Using the ICAPM to estimate the cost of capital of stock portfolios: empirical evidence on the Warsaw Stock Exchange

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Urbański S., Leśkow J.
Statistics in Transition new series
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2020
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vol. 21
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issue 1
73-94
EN
The aim of this paper is to present the method for estimating the cost of capital of typical portfolios available on the Warsaw Stock Exchange. The authors introduce the three factor Fama-French model and its two modifications. They also apply the bootstrap method to evaluate the variability of their estimation method. The cost of capital they refer to is related to portfolios of real options linked to projects. The market returns are generated both by stock companies running such projects and by real options modifying selected projects. The estimated cost of capital can serve as a valuable indicator for investors and for managers overseeing portfolios of stocks. Also, such an indicator can serve as a general reference while making business decisions related to new. The study demonstrated that the estimated cost of capital assumes highest values for value portfolios and stock companies with high financial indicators and, at the same time, low market prices compared to their book value. By the same token, the estimated cost of capital assumes low values for growth portfolios and for stock companies characterised by low financial indicators and, at the same time, high market prices compared to their book values.
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Functional data analysis and its application to local damage detection

100%
Leśkow J., Skupień M.
Statistics in Transition new series
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2019
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vol. 20
|
issue 1
131-151
EN
Vibration signals sampled with a high frequency constitute a basic source of information about machine behaviour. Few minutes of signal observations easily translate into several millions of data points to be processed with the purpose of the damage detection. Big dimensionality of data sets creates serious difficulties with detection of frequencies specific for a particular local damage. In view of that, traditional spectral analysis tools like spectrograms should be improved to efficiently identify the frequency bands where the impulsivity is most marked (the so-called informative frequency bands or IFB). We propose the functional approach known in modern time series analysis to overcome these difficulties. We will process data sets as collections of random functions to apply techniques of the functional data analysis. As a result, we will be able to represent massive data sets through few real-valued functions and corresponding parameters, which are the eigenfunctions and eigenvalues of the covariance operator describing the signal. We will also propose a new technique based on the bootstrap resampling to choose the optimal dimension in representing big data sets that we process. Using real data generated by a gearbox and a wheel bearings we will show how these techniques work in practice.
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