The Capital Asset Pricing Model (CAPM)
Historical Background
CAPM was developed at a time when theoretical foundations of decision making under uncertainty were relatively new and when basic empirical facts about risk and return in the capital markets were not yet known.
Why do investors differ in their pricing of RISK?
Investors should demand high returns for high risk investments
Diversification, Correlation, and Risk
Diversification
reduces risk
MarketDetermined Expected Returns & StandAlone Risks
Portfolio Theory:
Investors choose their portfolio based on the efficient frontier
Conclusion
*Ownership of assets by diversified investors lowers their expected returns and raises their prices.
*Investors who hold undiversified portfolios are likely to be taking risks
for which they are not being rewarded.
CAPM
Theories of investor risk preferences and decisionmaking under uncertainty emerged only in the 1940s and 1950s, in the work of von Neumann and Morgenstern (1944) and Savage (1954).
Portfolio theories were not developed until the 1950s by Harry Markowitz & Roy.
The empirical measurements of risk and return were also not developed until the 1960s when the required computational power became available.
r = D/P + g
Cost of equity capital (r):
1959
D:
current dividend per share
P:
stock price of the firm
D/P:
dividend yield
g:
dividend growth rate
Unreliable & subjective:
the value of an asset does not depend on how it is financed
inferring the cost of equity capital from future dividend growth rates is highly subjective.
The Capital Asset Pricing Model
will show that there is
no need
to have
any connection between
the cost of capital
and
future growth rates of cash flows
For the purpose of determining required returns,
the risks of investments therefore must be viewed in the context of the other risks to which investors are exposed
. The CAPM is a direct outgrowth of this key idea
Diversified investors face less risk per investment than undiversified investors, and they are therefore willing to receive lower expected returns (and to pay higher prices)
Correlation
between the returns of two assets measures the degree to which they fluctuate together
1
+1
Assets are perfectly positively correlated.
They move
in the same direction and in fixed proportions
(plus a constant).
They are susbstitutes for one another
Returns are perfectly negatively correlated. They move in opposite directions and in fixed proportions
(plus a constant).
They act to insure one another
0
Knowing the return on one asset does not help predict the return on the other
If the country returns were all perfectly correlated with each other, then the standard deviation of the WEMP would be the capitalizationweighted average of the standard deviations, which is 19.9% per annum. 19.915.3=
4.6%
, which is the
Diversification Benefit

the risk reduction stemming from the fact that the world’s equity markets are imperfectly correlated
The standard deviation of the WEMP would be only 8.4 % per annum, if the country returns were uncorrelated with one another. 15.38.4=
6.9%
,
this is a measure of the extent to which the world’s equity markets share common influences
The Efficient Frontier
The "Efficient Frontier", coined by Markowitz, is a
set of optimal portfolios that offers the highest expected return for a defined level of risk
OR
the lowest risk for a given level of expected return
.
CAPM
: mainly concerned with the pricing of assets in equilibrium. In other words, it tells us how investors determine expected returns—and thereby asset prices—as a function of risk.
Is the expected return on an investment a function of its standalone risk (measured by standard deviation of return) ?
NO
Example
Consider the shares of two firms with the
same standalone risk.
If the expected return on an investment was determined solely by its standalone risk, the shares of these firms would have the same expected return, say 10 %.
Any portfolio combination of the two firms would also have an expected return of 10 % (
since the expected return of a portfolio of assets is the weighted average of the expected returns of the assets that comprise the portfolio).
However, if the shares of the firms are
not perfectly correlated
, then a portfolio invested in the shares of the two firms will be less risky than either one standalone.
Therefore, if expected return is a function solely of standalone risk, then the expected return of this portfolio must be less than 10 percent, contradicting the fact that the expected return of the portfolio is 10 percent.
Expected returns, therefore, cannot be determined solely by the measure of standalone risk.
The
incremental risk
that an asset provides when added to a portfolio should be the reliable measure
Sharpe Ratio
tells us whether a portfolio's returns are a result of
excess risk or smart investment decisions
The greater a portfolio's Sharpe Ratio, the better its riskadjustment performance.
The general idea behind CAPM is that investors need to be compensated in two ways:
1 Time value of money
2 Risk.
The time value of money is represented by the riskfree (Rf) rate in the formula and compensates the investors for placing money in any investment over a period of time.
The second part of the formula represents risk
and calculates the
amount of compensation
the investor needs for
taking on additional risk. This is calculated by multiplying BETA and the Market Premium
What is
?
BETA represents the
systematic risk/market risk.
According to CAPM, beta is the only relevant
measure of a stock's risk
.
It measures a stock's
relative volatility
 that is, it shows how much the price of a particular stock jumps up and down compared with how much the stock market as a whole jumps up and down.
If a share price moves exactly in line with the market, then the stock's beta is 1. A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15% if the market fell by 10%
Riskfree Rate (Rf) is not stable:
Rf is the yield on shortterm government securities, and they change daily.
Return on the Market (Rm)
is backward looking:
May not be representative
of future market returns.
Ability to Borrow at a Riskfree Rate is not realistic:
Individual investors are unable to borrow (or lend) at the rate the US government can borrow at.
Possible Inaccuracy in Determining the Project Proxy Beta:
Businesses that use CAPM to assess an investment need to find a beta reflective to the project or investment. Often a proxy beta is necessary. However, accurately determining one to properly assess the project is difficult and can affect the reliability of the outcome
Easeofuse:
CAPM is a simplistic calculation that can be easily stresstested to derive a range of possible outcomes to provide confidence around the required rates of return
Diversified Portfolio eliminates unsystematic risk:
The assumption that investors hold a diversified portfolio, similar to the market portfolio, eliminates unsystematic (specific) risk.
Takes into account the Systematic Risk (Beta)
: CAPM takes into account systematic risk, which is left out of other return models, such as the dividend discount model (DDM).
In the preCAPM paradigm, risk did not enter directly into the computation of the
cost of capital.
William Abi Abdallah
SUMA K4320  Sustainable Investing & Economic Growth
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The Capital Asset Pricing Model (CAPM)
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