Modern Portfolio Theory.ppt

Separation Theorem
 According to this theorem, choice of portfolio
involves 2 separate steps:
 Determination of optimum risky portfolio
 Investor’s decision to form portfolio of risk-free asset
and optimum risky portfolio

 A risk averse investor would choose a portfolio
that has more investments in risk free asset
 A risk seeker would invest higher proportions in
optimum risky portfolio.

 In a market situation, a large number of investors
holding portfolios consisting of a risk-free security
and multiple risky securities participate.
 Rational investors will choose the portfolios along
CML since those portfolios offer highest return for
the same level of risk.

Risk
Return
Capital Allocation Line
Capital Market Line
Rf

 Capital Allocation Line is a line which shows the
manner in which capital is allocated
 Capital Market Line is tangent to Efficient
Frontier
 CML is an efficient set of risk-free and risky
securities and it shows risk-return trade-off in the
market equilibrium

Slope of CML
 Slope of CML is also known as reward to
variability ratio
 Slope of CML describes the best price at a given
level of risk
Slope,  = E(Rm ) – Rf
m

A portfolio on CML gives 11 % return
m=3.6, Rf =5%,
Calculate Reward to variability ratio or the slope of
CML.

 Slope of CML = 1.67
 Slope of CML shows the equilibrium price of risk
in market.
 This means that in the given example market
demands 1.67% return for 1% increase in portfolio
risk

 CML, thus is important in describing the
equilibrium relationship between expected return
and risk for efficient portfolios that contain no
unsystematic risk.
 This give rise to the most important question:
 What is appropriate relationship b/w risk and return
for all securities – efficient and inefficient portfolios

Expected Return on portfolio along
CML
E(Rp)= Rf + λ* p

Relationship between CML & SML

Risk
Return Security Market Line
Rf
SML

 All fairly priced securities plot exactly on SML
 Over valued assets plot below SML and
 Under valued assets plot above SML
 The difference between actual expected return and
Fair Return is called as Alpha (α)
Alpha (α) = Actual Expected return – Fair Return

Difference between CML and SML
 CML represents the risk premiums of efficient
portfolios as a function of portfolio standard
deviation
 SML represents individual security risk premium
as a function of Security Beta.

Arbitrage Pricing Theory (APT)
E(Rj)= Rf + 1*[E(Rm)-Rf] + 2*[E(Rm)-Rf]

Modern Portfolio Theory.ppt

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