26
3 Portfolio Theory and CAPM
should the market move up by 10%. If beta is negative it can be used for hedging
and offsetting other risks.
Another interpretation is that a new asset with beta equal to unity behaves just like
the market and its behavior is already covered and optimally hedged by the market
portfolio. The expected return r 1 in that case is equal to the return r M of the market
portfolio. On the other hand, a positive beta, but different from unity, implies a risk,
inherent or systematic to the new asset. This extra risk, which can not be hedged,
therefore requires a higher return r 1 . This extra cost of risk, as characterized by beta,
is thus given by the higher demand on return. The return r 1 that is consistent with
the assumption of efficient markets in equilibrium is the one given in (3.38).
We need to point out that the above results are part of the standard canon of economic theory, though not beyond reproach. The CAPM model is based on a number
of simplifying assumptions, necessary for the analytic treatment. These assumptions
can be and are questioned. See for example [7] for a comprehensive review of the
criticism.
Closely linked to the question whether to buy an asset, such as a share in a
company, is the question about the value of a company. The simple answer is “the
sum of all shares at current market value.” But that implies that the market “knows”
the real value, which in turn is determined by supply and demand. This is a bit of a
hen-and-egg problem and a way to escape the circular logic is to use other methods
to put a value onto a company. We cover two methods in the next section.
3.6 Valuation
One way to determine the value of a company, for example, before acquiring a
company or merging with it, is based on calculating the market cap, or market
capitalization of the company. It is given by the value of the (outstanding) shares,
traded at stock exchanges, multiplied by the value of the share. Note, however, that
the market cap fluctuates with the share price from one day to the next and one might
wonder how the “market” as a whole—or better, its participants—determines what
the correct price actually is.
The second method is based on evaluating the expected performance of the company keeping in mind that an investor expects to recover his investment over a finite
time, say Y = 5 years. One often used performance measure is the discounted cash
flow D, given by
D =
Y
k=1
C k
(1 + r ) k ,
(3.40)
where r is the annual discount rate, which takes the time-value of money, discussed
in Sect. 2.5, into account. C k is the expected annual cash flow k years in the future.
The cash flow C k in year k is essentially given by the difference C k = I k − P k of
the income I k the company receives for its services and the purchase price P k of the
3 Portfolio Theory and CAPM
should the market move up by 10%. If beta is negative it can be used for hedging
and offsetting other risks.
Another interpretation is that a new asset with beta equal to unity behaves just like
the market and its behavior is already covered and optimally hedged by the market
portfolio. The expected return r 1 in that case is equal to the return r M of the market
portfolio. On the other hand, a positive beta, but different from unity, implies a risk,
inherent or systematic to the new asset. This extra risk, which can not be hedged,
therefore requires a higher return r 1 . This extra cost of risk, as characterized by beta,
is thus given by the higher demand on return. The return r 1 that is consistent with
the assumption of efficient markets in equilibrium is the one given in (3.38).
We need to point out that the above results are part of the standard canon of economic theory, though not beyond reproach. The CAPM model is based on a number
of simplifying assumptions, necessary for the analytic treatment. These assumptions
can be and are questioned. See for example [7] for a comprehensive review of the
criticism.
Closely linked to the question whether to buy an asset, such as a share in a
company, is the question about the value of a company. The simple answer is “the
sum of all shares at current market value.” But that implies that the market “knows”
the real value, which in turn is determined by supply and demand. This is a bit of a
hen-and-egg problem and a way to escape the circular logic is to use other methods
to put a value onto a company. We cover two methods in the next section.
3.6 Valuation
One way to determine the value of a company, for example, before acquiring a
company or merging with it, is based on calculating the market cap, or market
capitalization of the company. It is given by the value of the (outstanding) shares,
traded at stock exchanges, multiplied by the value of the share. Note, however, that
the market cap fluctuates with the share price from one day to the next and one might
wonder how the “market” as a whole—or better, its participants—determines what
the correct price actually is.
The second method is based on evaluating the expected performance of the company keeping in mind that an investor expects to recover his investment over a finite
time, say Y = 5 years. One often used performance measure is the discounted cash
flow D, given by
D =
Y
k=1
C k
(1 + r ) k ,
(3.40)
where r is the annual discount rate, which takes the time-value of money, discussed
in Sect. 2.5, into account. C k is the expected annual cash flow k years in the future.
The cash flow C k in year k is essentially given by the difference C k = I k − P k of
the income I k the company receives for its services and the purchase price P k of the