Iibm Session 4 5

8/4/2019 Iibm Session 4 5

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Modern Portfolio Theory

Session IV & V

Shri Prakash Praharaj, CFPCM


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Concept of Modern portfoliotheory

General N- asset Portfolio

Efficient Frontier

Concept of market portfolio

Risk free rateBorrowing and lending rate


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Concept modern portfolio theory

1.Understand portfolio managementobjectives and calculate the return andstandard deviation of

a portfolio

2. The concepts of correlation anddiversification, and the effectiveness,methods, and benefits of internationaldiversification.


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3. It is a theory of investment which attempts tomaximize portfolio expected return for a givenamount of portfolio risk, or equivalentlyminimize risk for a given level of expected

return, by carefully choosing the proportions ofvarious assets

4. It is selecting a collection of investment assetsthat has collectively lower risk than anyindividual asset.


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3. There are four basic steps involvein portfolio construction.

a. Security valuation

b. Asset allocation

c. Portfolio optimization

d. performance measurement


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General N- asset Portfolio

It can be calculatedp2= WiWjijij

Where

p2 = Variance of portfolio returnWi = Proportion of portfolio value invested in security i

Wj = proportion of portfolio value invested insecurity j

ij = Co-efficient of correlation between the returns on

securities i and ji = standard deviation of the return on security i

j = standard deviation of the return on security j


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Efficient Frontier

1.It provides the highest return for a given level ofrisk.

2.It is given the choice between two equally riskyinvestments, an investor will chose the one withthe highest potential return.

3. It gives the choice between two investmentsoffering the same return, an investor willchoice the one that has the least risk.


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5. No other portfolio with the same expected

return has lower risks

6.No other portfolio with same risk has a higher

expected return.

7. Investors prefer efficient portfolios overinefficient ones

8. The collection of efficient portfolio is called anefficient portfolio


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Efficient Frontier GraphE(Rp)

p

M

Efficient

Frontier


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The benefit of diversification when correlation isless than 1

Minimum variance portfolio(MVP) is the

minimum standard deviation vis a vis returnThe investor can choose any mix of securities onthe frontier

The curve initially bend back words i.e the SD

decreases and return increases

No investor would invest less than the expectedreturn of MVP(minimum variance portfolio)


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Portfolio Risk can be reduced to Zero bychoosing weights of the securities

WA = SDA

SDA+SDB


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Concept Market portfolio

1. A market portfolio is a portfolio consisting of aweighted sum of every asset in the market, withweights in the proportions that they exist in the

market.2. It is consisting of all securities where theproportion invested in each security correspondsto its relative market value. The relative market

value of a security is simply equal to the aggregatemarket value of the security divided by the sum ofthe aggregate market values of all securities.


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3. A portfolio consisting of all assets available toinvestors, with each asset held -inproportion to its market value relative to thetotal market value of all assets.

4. portfolio of all assets in the economy. In

practice a broad stock market index, such as theStandard & Poor's Composite, is used torepresent the market.

5. The total of all investment opportunitiesavailable to the investor.


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E(Rp)

p

M

Efficient

Frontier

B

A

Lending

Borrowing

CML

RF


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The Efficient Frontier represents all thedominant portfolios in risk/return space.

There is one portfolio (M) which can beconsidered the market portfolio if we analyze allassets in the market. Hence, M would be aportfolio made up of assets that correspond to

the real relative weights of each asset in themarket.


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Assume you have 20 assets. With the help ofthe computer, you can calculate all possibleportfolio combinations. The Efficient Frontierwill consist of those portfolios with the highest

return given the same level of risk or minimumrisk given the same return (Dominance Rule)

Borrowing and lending investment funds at R to

expand the Efficient Frontier.a. We keep part of our funds in a saving accountLending, OR

b. We can borrow funds for a greater investment in

the market portfolio


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Portfolio A: 80% of funds in RF, 20% of fundsin M

Portfolio B: 80% of funds borrowed to buy

more of M,100% or own funds to buy MBy using RF, the Efficient Frontier is nowdominated by the capital market line (CML).Each portfolio on the capital market line

dominates all portfolios on the Efficient Frontierat every point except M.


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Risk free rateThe risk-free interest rate is the interest ratethat it is assumed can be obtained by investingin financial instruments with no default risk.

The risk-free rate represents the interest aninvestor would expect from an absolutely risk-free investment over a given period of time.

A guaranteed rate of return on an essentiallyrisk-free investment asset (e.g. T-Bills).


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Example of risk free security1. Bank Deposit

2. Treasury bill

3. RBI Bond

Borrowing rate

1. It is the price paid for the use of borrowedmoney, or, money earned by deposited funds.


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2. Interest is a fee paid on borrowed assets.3.It is most commonly the price paid for the use of

borrowed money.

4. Interest rate a lessee would have to pay if,instead of leasing, he or she finances thepurchase of same asset.

5. Investor can achieve portfolio returns greaterthan the market portfolio by constructing aborrowing portfolio.


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Lending rate

1. The lending rate is the rate of interest that youhave to pay when you are repaying a loan.

2. The interest rate charged by banks to theirlargest, most secure, and most credit worthycustomers on short-term loans.

3. This rate is used as a guide for computinginterest rates for other borrowers.

4. Any risky portfolio that is partially invested inthe risk free asset is a lending portfolio.


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p

M

Efficient

Frontier

CML

RF

Mutual Fund Portfolios

with a cash position


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Investors indifference curves are based on theirdegree of risk aversion and investmentobjectives and goals.


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Utility Function & Indifference CurvesIndifference curves represent different

combinations of risk and return, which providethe same level of utility to the investor.

An investor is indifferent between any twoportfolios that lie on the same indifference

curve.Flat indifference curves indicate that anindividual has a higher tolerance for risk. Very

steep indifference curves belong to highly risk-averse investors.

The optimal portfolio offers the greatestamount of utility to the individual investor.


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return

risk

Highly risk averse


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return

risk

Highly risk tolerant


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The markowitz model is highly information

intensive.

Var(P) = 1/n*(Var) + (n-1/n)* (COV)

It had suggested that an index, to whichsecurities are related, may be used for the

purpose of generating the covariance terms.


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It can be calculated

Ri = ai + biRM + eiWhere Ri = Return on security I

RM = Return on the market index

ai = constant returnbi = Sensitivity of the security is return on

the return on market index

ei = error term


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Thanks!

Documents

Iibm Session 4 5