An Introdiction to Asset Pricing Model

1. ST. PETER’S COLLEGE
15 dE SEPTiEmbRE ST.,bRGy. 2,
9005 baLinGaSaG, miSamiS ORiEnTaL
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an inTROduCTiOn TO aSSET
PRiCinG mOdELS

2. an inTROduCTiOn TO aSSET
PRiCinG mOdELS
Introduction
In businesses and organizations is the function that
coordinates the efforts of people to accomplish goals and
objectives by using available resources efficiently and
effectively, and by using financial asset. The presentation
concerns capital market theory and the capital asset valuation
model that was developed, almost concurrently by three
individuals. An alternative asset evaluation models that the
arbitrage pricing theory(APT) has led to led he development of
numerous other multifactor models.

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8.1 CaPiTaL maRkET ThEORy: an
OvERviEw
In particular, capital market theory extends
portfolio theory by developing a model for pricing
all risking assets. The final product, the capital
asset pricing model (CAPM), will allow you to
determined the required rate of return of any risky
asset.
The final product, the capital asset pricing model
(CAMP)>To determine the required rate of risk-free
asset.

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8.1.1 baCkGROund fOR CaPiTaL
maRkET: ThEORy
This allows one to concentrate on
developing an explanation for how
market participants will responds to
changes in the environment. In this
section, wee consider the main
assumptions that underlie development
of capital market theory.

5. aSSumPTiOn Of CaPiTaL maRkET
ThEORy
1. All investors are Markowitz-efficient in that
they seek to invest in tangent points on the
efficient frontier. The exact location of this
tangent point and, therefore, the specific
portfolio selected will depend on the
individual investor’s risk- return utility
function.

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aSSumPTiOn Of CaPiTaL maRkET
ThEORy
2. Investors can barrow or lend any amount
of money at the risk-free rate return(RFR)
clearly it is always possible to lend money at
the nominal risk- free security such as
government T- bills. It is not always possible
to barrow at the risk-free rate, but we will see
that assuming a higher borrowing rate does
not change the general results.

7. aSSumPTiOn Of CaPiTaL
maRkET ThEORy
3. All investors have homogenous expectation;
that is they estimate identical probably
distributions for future rate return.

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aSSumPTiOn Of CaPiTaL maRkET
ThEORy
4. All investors have the same one period time horizon such
as on month or one year. The model will be developed for a
single hypothetical period, and its result could be affected by
different assumption, since it requires investors to derive risk
measures and risk-free assets that are consistent with their
investment horizons.

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Assumption of CApitAl mArket
theory
5.All investment are efficiently divisible,
which means that it is possible to buy or sell
fractional shares of any asset or portfolio.

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6.There are no taxes or transaction cost
involved in buying or selling assets. This is a
reasonable assumption in many instances.
Neither pension funds nor charitable
foundation have to pay taxes, and the
transaction cost for most financial institution
are less than 1 percent on most financial
instruments.
Assumption of Capital Market Theory

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7. There is no inflation or any change in
interest rates, or inflation is fully
anticipated. This is a reasonable initial
assumption, and it can be modified.
Assumption of Capital Market
Theory

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8. Capital markers are in equilibrium.
This means that we begin with all
investments property priced in line with
their risk levels.
Assumption of Capital Market
Theory

13.  Development of CApitAl mArket theory
 The major factor that allowed portfolio theory to development into capital
market theory is the concept of a risk- free assets . This assumption of a risk-
free assets allows us to derive a generalized theory of capital asset pricing
under conditions of uncertainty from the Markowitz portfolio theory.
8.1.2 Developing the mArket line
 We have defined a risky asset as one from which future returns are uncertain ,
and we have measured this uncertainty by the variance, or standards deviation
of expected returns.
CovAriAnCe with A risk- free Asset
 Recall that the covariance between two sets of returns is the risk-free
asset. Because the returns for the risk –free asset are certain, during
all periods.
Combining A risk – free Asset with A risky portfolio
Expected Return
The expected return for a portfolio of two risky assets, the expected rate of
return for a portfolio that includes a risk- free asset with a collection of risky
assets is the weighted average of the two returns.

14. the risk – return CombinAtion
The primary result of capital market theory. It can be interpreted as
follows investments who allocate their money between a riskless
security and the risky Portfolio M can expect a return equal tot he risk-
free rate plus compensation for the number of risk units they accept.
This outcome is consistent with the concept underlying all of
investment theory that investors perform two functions in the capital
markets for which they can expect to be rewarded. First, they allow
someone else to use their money, for which they receive the risk- free
rate of interest. Second, they bear the risk that the returns they have
been promised in exchange for their invested capital will not be repaid.
The term, is the expected compensation per unit of risk taken, which is
more commonly referred to as the investor’s expected risk premium per
unit of risk.

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The Capital Market Line
the risk – return relationship shown in equation
8.1 holds for every combination of the risk – free
asset with any collection of risky assets. However,
investors would obviously like to maximize their
expected compensation for bearing risk they would
like to maximize the bearing risk. Let us now
assume that Portfolio M is called the Market
Portfolio and, by definition, it contains all risky
assets held anywhere in the marketplace. It has the
property of receiving the higher level of expected
return per unit of risk for any available portfolio of
risky assets.

16.  risk return possibilities with leverAge
 An investor may want to attain a higher expected return than is
available at point M In exchange for accepting higher risk. One
alternative would be to invest in one of the risky asset portfolios on the
efficient frontier beyond point M such ass the portfolio at point D.A
second alternative is to add leverage to the portfolio by borrowing
money at the risk-free rate and investing proceeds in the return and risk
for your portfolio?
 If you borrow an amount equal to 50 percent of your original wealth at
the risk- free rate will not be a positive fraction but, rather, a negative
50 percent. The effect on the expected return for your portfolio.
 risk DiversifiCAtion AnD the mArket portfolio
 The investment prescription that emerges from capital market theory is clear-
cut: investors should only invest their funds in two types of assets- the risk-free
security and risky asset portfolio M with the weight of these holding determined
by the investors tolerance for risk.
 Because of the especial place that the market Portfolio M holds to all investors,
it must contain all risky assets for which there is any value in the marketplace.
This includes not just U.S common stocks, but also non-U.S. Stocks U.S and
non- U.S bonds, real estate, private equity, options and futures contrast, art,
antiques, and so on.

17. How to measure diversification
 Specifically, a completely diversified portfolio would have a correlation
with the market portfolio of all + 1.00. this is logical because complete
diversification means the unsystematic or unique risk. Once you need
eliminated all unsystematic risk, only systematic risk is left, which
cannot be diversified away. Therefore, completely diversified portfolio
would correlate perfectly with the market portfolio , which has only
systematic risk.
diversification and tHe elimination of unsystematic
risk
 This assumes in perfect correlation among securities. Ideally , as you
add securities, the average covariance for the portfolio declines. How
many securities must be included to arrive at a completely diversified
portfolio?

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tHe cml and separation tHeorem
 As we have seen, the capital market line (CML) leads all investors to invest in the
same risky asset Portfolio M. Individual investors should only differ regarding their
position on the CML, which depends on their risk references.
 In return, how they get to a point on the CML is base on their financing decisions.
If are relatively risk averse, you will lend some part of your portfolio at the RFR by
buying some risk –free securities and investing the remainder in the market portfolio
of risky assets.
0.30
Unsystematic
(Diversifiable)
Risk
Total
Risk
Standard deviation of
the Market5 Portfolio
(Systematic Risk)
0.15
Systematic
Risk
10 20 Number of Stocks in the Portfolio

19. a risk measure for tHe cml
 In discussing the Markowitz portfolio model, we noted that the relevant risk to
consider when adding a security to a portfolio is its average covariance with all
other assets in the portfolio.
8.1.4 investing an cml: an example
 After considerable research on current capital market conditions, you have
estimated the investment characteristics for six different combinations of risky
assets. List your expected return and standard deviation forecast for these
portfolios.
 You have also established that each of these portfolio completely diversified so
that its volatility estimated present systematic risk only.
8.2 tHe capital asset pricing model
 Capital market theory represented a major step forward in how investors should
think about the investment process.
 The capital asset pricing model (CAPM) extends capital asset theory in a way
that allows investor to evaluate the risk-return trade-off for both diversified
portfolios and individual securities.

20. 8.2.1 a conceptual development of tHe capm
 As note earlier, sharp( 1964), along with Lintner (1965) and Mossin (1966), develop the
CAPM in a formal way. In addition to the assumptions listed before, the CAPM requires
others, such as that asset return come from normal probability distribution.
tHe security market line
 The CAPM can be also illustrated in graphical form as the security market line.
E(R)
E(RM)
NEGATIVE
BETA
RFR
0 1.0 Bi

21. • determining tHe expected rate of return for
risky asset
 To demonstrate how would you compute expected or required rates of return,
consider the fallowing example stocks assuming you have already computed
betas.
Stock Beta
A 0.7
B 1.00
C 1.15
D 1.40
E -0.30
 Assuming that we accept the economy’s RFR to be 5 percent (0.05) and the
expected return on the market portfolio (E(RM) to be 9 percent (0.9). This implies
a market risk premium of 4 percent (0.04). With the inputs, the SML would yield
the following required rates of return for these five stocks
 That is, all asset s should be priced so that their estimated rates of return,
which are the actual holding period rates of return that you anticipate, are
consistent with their levels of systematic risk.

22. • identifying undervalued and overvalued assets
 Now that we understand how to compute the rates of return one should expect
or require for a specific risky asset using the SML, we can compare this
required rate of return of the asset’s estimated rate of return over a specific
investment.
calculating systematic risk
 There are two ways that a stock’s beta can be calculated in practice. First, given
our conceptual discussion of the CAMP, a beta coefficient for security i can be
calculated directly.
tHe impact of tHe time interval
 In practice, the number of observations and the time interval used in the
regression vary widely . Example , Morningstar derives characteristic lines for
common stocks using monthly return for the most recent five year period( 60
observations). Returns Analytics calculates stock betas using daily returns over
the prior two years(504 observations). Bloomberg uses two years of weekly
returns (104 observations) in its basic calculations, although its system allows
the user to select daily, weekly, monthly, quarterly , or annual return over other
time horizons.

23. tHe effect of tHe market tHeory
 Another significant decision when computing an asset’s
characteristics line is which indicator series to use as a proxy for the
market portfolio of all risky assets.
computing a cHaracteristic line: an example
 Twelve monthly rates are not typical considered sufficient for
statistical purposes, but they are adequate for demonstration
purposes. We calculated betas for PG using two different proxies for
the market portfolio:
 1. the S&P 500(SPX), an index of stocks mostly domiciled in the
United State, and
 2. the MSCI World Equity (MXWO) index, which represent a global
portfolio of stocks.
 Farther, ever more extreme difference are possible when stock betas
are calculated relative to market proxies that contain other asset
classes, such as fixed-income securities or real state.

24. 8.3 relaxing tHe assumptions
 In this section, we discuss the impact on the capital market line(CML) and the
security market line(SML) when we relax several of these assumptions.
8.3.1 differential barrowing and lending rates
 One of the assumption of the CAMP was that investors could borrow and lend
any amount of money at the risk-free rate.
For example , when T-Bills are yielding the 4 percent, most individuals would
have to pay about 6 to 7 percent to barrow at the bank.
 Because of this differential, there will be two different lines going to the
Markowitz efficient frontier.
 The segment RFR-F indicates the business opportunities available when an
investors combines risk-free assets.
8.3.2 zero beta model
 If the market portfolio (M) is mean variance efficient, an alternative model,
derives by Black (1972), does not require a risk- free asset.
 Within the set of feasible alternative portfolio, several exist where the returns
are completely uncorrelated with the market portfolio; the beta of these
portfolios with the market portfolio is zero.

25. TransacTion cosT
 The CAMP assume transaction cost, that there are no transaction cost, so
investors will buy or sell mispriced securities until they plot on the SML. If there
are transaction cost, investor will not correct all mispricing because in some
instances the cost of buying and selling the mispriced security will exceed any
potential excess return.
8.3.4 heTerogeneous expecTaTions and planning
periods
 If the investors had expectations about risk and return, each would have a
unique CML or SML, and the composite graph would be a set( band) of lines
with a breadth determined by the divergence of expectations.
 If all investors had similar information and background, the band would be
reasonably narrow.
 The impact of planning periods is similar. Recall that the CAPM is a one- period
model, corresponding to the planning period for the individual investor. Thus, if
you are using a one- year planning period, your CML and SML could differ from
someone with a one- month planning period.

26. 8.3.5 Taxes
E(Ri ( AT) = (Pe−Pb) x(1-Tcg)+(Div)x (1- Ti)
Pb
Where: Ri (AT) = after tax rate of return
Pe = ending price
Pb = beginning price
Tcg = tax on capital or loss
Div = dividing paid during period
Ti = tax on ordinary income
8.4 addiTional empirical TesT of The camp
 When testing the CAPM , there are two major questions. First, how
stable is the measure of systematic risk( beta)?
 Because beta is our principal risk measure, it is important to know
whether past betas can be used as of return betas.
 Second, is there a positive linear relationship as hypothesized
between beta and the rate of return on risky assets?

27. 8.4.1 sTabiliTy of beTa
 Numerous studies have examined the stability of beta and generally
concluded that the risk measure was not stable for individual stocks,
but the stability of the portfolio of stocks increased dramatically.
8.4.2 relaTionship beTween risk and reTurn
 Specifically, is there a positive linear relationship between the
systematic risk and the rates of return on these risky assets?
1. Most of the measure SML,s had a positive slope
2. The slopes change between period.
3. The intercepts are not zero, and
4. The intercepts change between periods.
effecT of skewness on The relaTionship
 Beyond the analysis of return and beta, several authors also have
considered the impact of expected returns.
 Skewness reflects the presence of too many large positive or negative
onbservations in a distribution.

28. effecT of size, p/e and leverage
 These result imply that size and P/E are additional risk factors that
need to be considered along with beta. Specifically, expected returns
are a positive function of beta, but investors also require higher return
from relatively small firms and for stocks with relatively low P/E ratios.
effecT of book- To markeT value
 In the multivariate test, the results that the negative relationship
between size and average returns is robust to the inclusion of other
variables.
 Further, the positive relation between BE/ME and average returns also
persist when the other variables are included.
8.4.3 summary of capm risk-reTurn empirical
resulTs
 Most of the early evidence regarding the relationship between rates of
return and systematic risk of portfolio supported the CAPM; there was
evidence that the intercepts were generally higher than implied by the
RFR prevailed, which is either consistent with a zero-beta model or
the existence of higher borrowing rates.

29. 8.5 The markeT porTfolio: Theory versus pracTice
 The market portfolio included all the risky assets in the economy.
Further the equilibrium, the various assets would be include in the
portfolio in proportion to their market value.
 Market portfolio should contain not only U.S stocks and bonds but also
real state, options, arts, foreign stocks and bonds, and so on, with
weights equal to their relative market value.
 A market portfolio is reasonable in theory, it is difficult to implement
when testing or using the CAPM. The easy part is getting an index
series for U.S and foreign stocks and bonds. Because of the difficulty
in deriving series that are available monthly and timely fashion for
numerous other assets, most studies have been limited to using a
stock or bond series alone.

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