Beta. Prof. Dr. Martin Užík

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1 Beta Prof. Dr. Martin Užík

2 Beta equity CAPM r r rf rm rf tan

3 Beta - A quantitative measure of the volatility of a given stock, mutual fund, or portfolio, relative to the overall market - Calculation of expected return of risky investment - To make an rational investment decision

4 Beta equity PV ( CF ) n t1 CF 1 r equity t CAPM equity, t t equity NPV ( CF ) I o n equity t CAPM 1 1 requity, t t CF r r r r CAPM equity f M f j M, j j M Cov(r j,r M ) M

5 Beta Risk Free 2,991% Market Return 9,64% Beta 1,00 Equity Risk CAPM 9,64% Equity 296,82 Mio. EBQ 64,48% Debt 163,50 Mio. EMQ 64,50% Total 460,32 Mio. Diff -0,02% Interest of Debt 10,00% Tax Shield 19,00% WACC 9,09% Real Period Period 0,08 1 1,082 2,083 3,084 TV Cash Flow in Mio. 243,00-100,00-50,00 20,00 40,00 Present Value in Mio. 241,38-91,05-41,73 15,30 336,53 Sum of PV(CF) = Enterprise Value 460,43 Mio. Market Value of Equity 296,93 Mio.

6 Beta Risk Free 2,991% Market Return 9,64% Beta 0,00 Equity Risk CAPM 2,99% Equity 899,12 Mio. EBQ 84,61% Debt 163,50 Mio. EMQ 84,61% Total 1.062,62 Mio. Diff 0,00% Interest of Debt 10,00% Tax Shield 19,00% WACC 3,78% Real Period Period 0,08 1 1,082 2,083 3,084 TV Cash Flow in Mio. 243,00-100,00-50,00 20,00 40,00 Present Value in Mio. 242,31-96,09-46,29 17,84 944,85 Sum of PV(CF) = Enterprise Value 1.062,62 Mio. Market Value of Equity 899,12 Mio.

7 Portfolio Theory Portfolio Selection Theory Harry Max Markowitz published in 1952 and 1956 Paper and 1959 Book about Portfolio Selection. : underlying factor, the general properity of the market expressed by some index (Markowitz, 1959, S. 100) Focus on mean and standard deviation. Goal: a) Maximum Return b) Minimum Risk Sharpe (1963): Diagonal Modell Sharpe (1964), Lintner (1965), Mossin (1966): Capital Asset Pricing Model (CAPM)

8 Portfolio Theory

9 Beta Alternative Modells Multi Beta CAPM R i b i1 F 1... b im F m U i m j1 b ij F j U i Arbitrage Pricing Theorie m R i R f b ij {E[R M ( j)] R f } j1 Intertemporal CAPM E t r i,t 1 r f,t 1 V ii 2 im (E t r m,t 1 r f,t 1 V mm 2 ) ih (E t r h,t 1 r f,t 1 V hh 2 )

10 Investment Risk Need to consider two kinds of risk: Business risk Standard measure is beta (controlling for financial risk) Factors: Demand variability Sales price variability Input cost variability Ability to develop new products Foreign exchange exposure Operating leverage (fixed vs variable costs

11 Investment Risk Financial risk The additional risk placed on the common stockholders as a result of the decision to finance with debt Leverage increases shareholder risk Leverage also increases the return on equity (to compensate for the higher risk) Financial leverage concentrates the firm s business risk on the shareholders because debt-holders, who receive fixed interest payments, bear none of the business risk.

12 Optimal Capital Structure

13 Optimal Capital Structure

14 Praxis Working-Capital Gewinnrücklagen EBIT Eigenkapital Z Score *6,56 *3,26 *6,72 *1,05 3,25 Bilanzsumme Bilanzsumme Bilanzsumme Fremdkapital Z-Score Scoringstufe Level Ausfallwahrscheinlichkeit probability of default from 6,925 1 Until 0,02% 6,525 6, ,03% - 0,05% 6,325 6, ,06% - 0,11% 5,450 6, ,12% - 0,40% 4,625 5, ,41% - 1,33% 4,325 4, ,34% - 7,70% 3,475 4, ,71% - 16,99% Until 3,474 8 From 17,00%

15 Praxis Z-Score vs. financial leverage (GEX Companies) financial leverage

16 wacc vs. financial leverage (debt to equity ratio) Praxis financial leverage

17 debt to equity ratio Praxis

18 Beta estimation Equity Beta Stock price sensitivity i Cov i im, i, M 2 M M Indepted company: EK Unternhmen Equity Debt EV FK EV 100% Equity financing : Unternhmen Equity

19 Debt Beta/Asset Beta Debt Beta Risk if the company goes bankrupt: r FK r f Assumtion: debt capital is riskless Debt 0 Assetbeta Only business risk Adjustement of Equity Beta (Aktienbeta) by capital structure effect Asset Equity EK EV

20 (Un-)Levered Beta (Un-)Levered Beta Unlevering: unlevered levered FK debt 1s EK FK 11s EK Relevering: FK levered unlevered 1 1 debt 1 EK s s FK EK

21 Fundamental Beta Fundamental Betas Beta is determined by the decisions the firm made, concerning the type of business to be in, the degree of operating leverage and financial leverage Can also be used to calculate beta for the APT and multifactor models.

22 Company Valuation Examples for company valuation causes Dominated situations Order of the court to institute bankruptcy proceedings Close of agreement to transfer profits and contracts of domination ( 305 II 2 und 3 AktG) Change through conveyance of assets ( 174 UmwG) Squeeze-out-method ( 327a-f AktG) Compensation for the increase in value at divorcement Non dominated situations Aquisition/selling a business unit or company shares IPO Impairment tests Purchase Price Allocation Settlement of an estate Financial restructuring Value based management

23 Non listed company Non publicly traded company 1. Detecting a peer group Regarding only liquid assets 2. Detecting an industry beta Regarding a clear assignment to the industry sector 3. Selection of an adequate market portfolio 4. Define the estimation period 5. Define the return interval

24 Non listed company Stability of beta Theory:Beta is stable over time and a naive estimation is possible. Truth: Beta is instable. A bias in estimation is caused by illiquidity and regression outliners. Fundamental structural breaks were caused by: Changes in a capital weighted proxy Macro economic factors e.g. Political events, changes in the risk free rate, rate of inflation and GDP Industry specific factors e.g. Capital structure/debt ratio Aquisition/selling a business unit or company shares Test for structural breaks: Chow-Test (F-statistic) Heavy calculation An usual adjustment of regression outliners could lead to neglecting fundamental structural breaks.

26 Code of practice Bloomberg supplies raw and adjusted beta. There is an empirical tendency, that beta moves to 1, because of diversification of the array of products and expansion of the customer base. Estimation Period S&P s: 5 Years Bloomberg: 2 Years Return Interval Proxy Weekly Monthly At least 60 Observations Index of the reviewed equity: German Stocks: DAX, british Stocks: FTSE, japanese Stocks: Nikkei and US Stocks: NYSE Composite oder S&P 500. Consider the R 2 (coefficient of determination). ADJB RAWB(0,67) 1(0,33)

27 Industry Sector Beta

28 Industry Sector Beta

29 Market Portfolio

30 Market portfolio

31 Marketportfolio

32 Return period

33 Return period

Beta. Prof. Dr. Martin Užík

Beta. Prof. Dr. Martin Užík Beta Prof. Dr. Martin Užík Beta equity CAPM r r rf rm rf tan Beta - A quantitative measure of the volatility of a given stock, mutual fund, or portfolio, relative to the overall market - Calculation of