Exptected
Return for Shareholders
The Capital
Asset Princing Model [CAPM]
CAPM =
Return on stock (Rs) = Rf + ß.(Rm - Rf)
The CAPM models the
risk expected and expected return trade-off
in the capital market. CAPM Model looks at the
company in the market.
Rf : Risk free
rate : for example, Treasury- Bills, Treasury
bonds, national Bonds not affected by the markets'
ups and downs. ß = 0.
Let's suppose that the average return on US Treasury Bonds from last 30 years
is 3,7 %
Rm
: Expected market (Market = total portfolio
of shares) profitability rate. For example,
Standard & Poors Index of 500 stocks : average
annual profitability rate from Dec 1979 to Dec 2009
: 8,06 %
(Rm - Rf)
: Risk premium required from the market. Current
rate is around 4%. Over a period of 30
years, the US market risk premium rate has been
4,36 % (historic risk S&P500 from Dec 1979 to Dec 2009)
ß.(Rm
- Rf) : = total risk premium on a share
= Business Risk Premium (BRP) + Financial Risk
Premium (FRP)
ß (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 Beta is given
by the market and published by various investment
advisory services. It is the Bêta of a
levered firm (with debts). That means that the
Bêta takes in account the Business risk
and the Financial risk.
Example :
Rf : 3,70 % ; market risk premium : 4,36 %
Stocks |
ß |
Rf |
Premium |
Rs |
A |
0,49 |
3,7
% |
2,14
% |
5,84
% |
B |
1,04 |
3,7 % |
4,53
% |
8,23
% |
C |
0,78 |
3,7 % |
3,40
% |
7,10 % |
D |
0,96 |
3,7 % |
4,18
% |
7,88
% |
E |
2,20 |
3,7 % |
9,59
% |
13,29
% |
Market |
1,0 |
3,7 % |
4,36 % |
8.06 % |
Click
here to see an example showing the Security
Market Line (SML)
Final remarks
The calculations above are based on the following
hypothesis : the risk premium from the market
portfolio (e.g. S &P500) is stable in time
and for the future.
Risk free rate is not stable over
time. It is better to use the current Rf at
the time of evaluation.
The main critique concerning ß
is its instability over time. It synthesizes
a large amount of infomation in a single value,
and this strenght equally represents its main
weakness.
The CAPM is a forecasting model
which allows the calculation of expected profitability
using anticipations of risk. To use it correctly,
one should use a forecasted ß
rather than an historic ß.
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.COM, Bernard Jaquier, Professor Emeritus & Dr Honoris Causa, Lausanne, Switzerland, 2018