BETA : A measure of RisK

Bêta is the measure of risk used for a single share. In other words, it shows the sensitivity or reaction of a share compared to the

variation of total portfolio of market shares.

the ß of debt shares (bonds) is commonly situated from 0 to 0,5
t he (ß ) of shares is most often superior to 0,5

CAPM = R_s = R_f + ß.[R_m - R_f]

How to calculate the Beta ? click here. It is also given by the market and published by various investment advisory services. The common Bêta published is the Bêta of share of levered firms (with debts).

ß.[R_m - R_f] : total risk premium of a share : Business risk premium (BRP) & Financial risk premium (FRP)

Levered firm : R_s = R_f + BRP + FRP

unlevered firm : R_s = R_f + BRP

High Business Risk Low Business Risk Highly competitive environnement Monopols Low barriers of entry in the industry High barriers of entry in the industry High potential subsitution of products Low substitution of products Debt / Equity Debt / Equity should be low Can be high Conservative financial policy More debts in financial structure

Parameters on which ß depends :

The volatility of economic assets : the higher the volatility of the value of economic assets, the higher the rate of ß. For example, if an economic sector explodes or has a high level of increase economically speaking, then the companies within that sector should have a ß superior to 1. The volatility of the results of a company is directly related to the structure of its operational costs [fixed and variable costs]. The closer the company gets to its breakeven point, the higher the rate of ß.

The financial structure : the financial structure of a firm influences the level of volatility of its net profits, and therefore influences the rate of ß through financial leverage. The higher the company's debt, the higher the rate of ß.

The quality of information : the less information given by a company, and the less the quality of that information concerning the company's evolution, the higher the rate of ß, as the market takes a risk of "non-visibility" into consideration.

Synthesis :

Parameters Ratios High/Low ß The volatility of economic assets [Tangible / Non tangible] High Low [Tangible / Non tangible] Low High [Fixed Costs / Variable Costs] High High [Fixed Costs / Variable Costs] Low Low The financial tructure [Debts / Equity] High High [Debts / Equity] Low Low The quality of information Good visibility Low No visibility High

ß of the levered and unlevered firm

ß Levered (ß^L) = ß ^Unlevered . [1 + (D / E)]

ß Unlevered (ß^U) = ß ^Levered / [1 + (D / E)]

Note : these two formulas are avalaible only if ß of debts = 0

Risk premium

BRP = ß^U. [R_m - R_f]

Note : formula available only when the beta of Debt is equal to zero

FRP = ß^U.[D/E].[R_m - R_f]

Note : formula available only when the beta of Debt is equal to zero

Starworld Group : example 1

Rf : 0,656% (Swiss Confederation Bonds - 10 years, December 2023) ; Return on market : 8,327% (SMI) ßeta of the stock: 0,90 ; beta of debts : 0,0 % ; D/E ratio : 0,47 ; Market Risk : 7,671 %

Beta of stock	D/E ratio	Rf	Rs	BRP	FRP	p
0,613	-	0,656%	5,36%	4,70%	0,00%	4,70%
0,858	0,40	0,656%	7,24%	4,70%	1,88%	6,58%
0,900	0,47	0,656%	7,56%	4,70%	2,20%	6,90%
1,226	1,00	0,656%	10,06%	4,70%	4,70%	9,41%
1,349	1,20	0,656%	11,00%	4,70%	5,64%	10,35%

CLICK HERE to see a pattern of levered and unlevered betas

Starworld Group : example 2

Let's assume that the beta of Debt of the group = 0,40 (interest rate : 2 %)

Beta of Asset = Beta of Equity. (E / V) + Beta of Debt . (D / V )

Beta of Asset = 0,90(2244/3294) + 0,40(1050/3294) = 0,741

We deduce that

Beta of Equity = [ (Beta of Asset) + D/E.( Beta of Asset - Beta of Debt)]

Beta of Equity = 0,741 + (1050/2244)(0,741 - 0,40) = 0,900

Note : Click here to learn how to find this formula

ßeta of stock	Beta of Debt	Beta of Asset	D/E	Rf	Rs	BRP	FRP	P
0.900	0.40	0.741	0.47	0,656 %	7,56 %	5,68%	1.22%	6,90 %

Sources :

Financial Leverage, the CAPM and the Equity cost of capital, 1999, Marc Bertonèche, Ph. D. in Finance from the Northwestern University, Professor at the Bordeaux University and at Sciences-PO Paris, Visiting Professor at Harvard Business School and Oxford University.

Principles of Corporate Finance, 8th edition, Richard A. Brealey & Stewart C. Myers, McGraw-Hill

 

 

© ECOFINE - Bernard Jaquier, Professor Emeritus & Dr Honoris Causa, Lausanne, Switzerland, 2024