Capital Market Line and the Efficient Frontier

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  • 7/27/2019 Capital Market Line and the Efficient Frontier


    Capital market theory


    The CAP-model is a ceteris paribus model. It is only valid within a special set

    of assumptions. They are:

    Investors are risk averse individuals who maximize the expected utility of

    their end of period wealth. Implication: The model is a one period model.

    Investors have homogenous expectations (beliefs) about asset returns.

    Implication: all investors perceive identical opportunity sets. This is,

    everyone have the same information at the same time. Asset returns are distributed by the normal distribution.

    There exists a risk free asset and investors may borrow or lend unlimited

    amounts of this asset at a constant rate: the risk free rate (kf).

    There is a definite number of assets and their quantities are fixed within the

    one period world.

    All assets are perfectly divisible and priced in a perfectly competitive

    marked. Implication: e.g. human capital is non-existing (it is not divisible

    and it cant be owned as an asset).

    Asset markets are frictionless and information is costless and simultaneously

    available to all investors. Implication: the borrowing rate equals the lending


    There are no market imperfections such as taxes, regulations, or restrictions

    on short selling.

    Capital Market Line and the Efficient Frontierthe efficient frontier is trying to do is determine the best possible combination of assets in a

    portfolio that maximises the expected level of returns for a given level of risk (as defined by

    volatility / standard deviation). In effect the efficient frontier gives a very formal relationship

    between risk and returns. Any portfolio that is below the efficient frontier line is deemed to be sub-

    optimal this is quite intuitive as any point below will offer the same return for greater risk or

    same risk and less return. This leads to 2 formal definitions:

    1) Maximise expected return for a given level of volatility

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    2) Minimise volatility for a given level of returns

    The set of optimal portfolios that we get from all the possible combinations of portfolios in the risk-

    return is known as the efficient frontier. You can see a very clear illustration below where the

    lighter pinkish area is the set of all possible portfolios and the dark red line is the actual efficient


    Efficient Frontier

    Investors can make a choice of how they allocate funds between the risk free asset and the risky

    portfolio. This can range from all assets in the risk free asset to all (or more than all with leverage)

    in the risky portfolio. When we plot this in a graphical fashion we get a linear line with mean on

    the Y axis and the volatility on the x axis. Note that the line is linear as the risk free asset has no

    volatility. The important point to take away here is that each risky portfolio will have its own capital

    allocation line. The capital allocation line that lies at a tangent to the efficient frontier and is the

    highest possible line is known as the Capital Market line (because it is the market portfolio).

    Given the mean-variance criterion all investors will hold their portfolio in the same weights as the

    market portfolio (and hence lie on the capital market line).

    The CML is derived by drawing a tangent line from the intercept point on the efficient

    frontier to the point where the expected return equals the risk-free rate of return.

    The CML is considered to be superior to the efficient frontier since it takes intoaccount the inclusion of a risk-free asset in the portfolio. The capital asset pricing

    model (CAPM) demonstrates that the market portfolio is essentially the efficientfrontier. This is achieved visually through the security market line (SML).

    Limitations of Capital Asset Pricing Model in Capital Markets
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    The Capital Asset Pricing Model (CAPM) states that it uses various assumptions aboutmarkets and investment behavior to predict the rate of return of an asset for a systematicrisk. However, there are many flaws with the valuation model. Different investors requiredifferent required rate of return,there are no transaction costs or no taxes, holding periodvaries from one investor to another and borrowing rate is not equal as lending rate andmany others. CAPM fails to act as an efficient valuation model in reality because the

    model works on a generalized principle rather than breaking it apart for different kind ofinvestments.

    The beta coefficient used in CAPM is basically a variance of an assets price to the

    market. Investors usually use beta for stocks to generate the required rate ofreturn.

    The time value does matter when evaluating the required rate of return. The

    short-term and long-term rate would be affected so does the borrowing andlending cost. CAPM should consider the short-term rates as a risk-free ratesrather than using long-term rates because the outlook for the country is negative

    and perhaps they may get downgraded again. Capital Asset Pricing Model- CAPM valuation model is not a suitable model to use in

    stock exchange or for any other investments for many reasons.

    It is based on a number ofunrealistic assumptions.

    It is difficult to test the validity.

    Betas do not remain stable over time. (Beta is a measure of a

    securitys risk).

    Implifications of cml for investors

    . Capital asset pricing model (CAPM) based on a number of assumptions.Given those assumptions, it provides a logical basis for measuring risk andlinking risk and returnCapital asset pricing model (CAPM) has the following implications,

    Investors will always combine a risk free asset with a marketportfolio of risky assets. They will invest in risky assets in proportionto their market value.

    Investors will be compensated only for that risk which they cannotdiversify. This is the market related systematic risk. Beta which is a

    ratio of the covariance between the asset returns and the marketreturns divided by the market variance is the most appropriatemeasure of an assets risk.

    Investors can expect returns from their investment according to therisk. This implies a liner relationship between the assets expectedreturn and its beta.
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    The concepts of risk and return as developed under capital asset pricingmodel (CAPM) have intuitive appeal and they are quite simple tounderstand. Financial managers use these concepts in a number offinancial decisions making such as valuation of securities, cost of capitalmeasurement, investment risk analysis excreta. However in spite of its

    intuitive appeal and simplicity capital asset pricing model (CAPM) suffersfrom a number of practical problems.

    Assumptions of CAPM

    There are many investors. They behave competitively (price


    All investors are looking ahead over the same (one period)planning horizon.

    All investors have equal access to all securities.

    No taxes. No commissions.

    Each investor cares only about ErC and C.

    All investors have the same beliefs about the investmentopportunities: rf , Er1,. . .,Ern, all i, and all correlations

    (homogeneous beliefs) for the n risky assets.

    Investors can borrow and lend at the one riskfree rate.

    Investors can short any asset, and hold any fraction of an asset

    Aim to maximize economic utilities.

    Are rational and risk-averse.

    Are broadly diversified across a range of investments.

    Trade without transaction or taxation costs.

    Deal with securities that are all highly divisible into small parcels.

    Assume all information is available at the same time to all investors.

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    What is Portfolio Revision ?

    The art of changing the mix of securities in a portfolio is called as portfolio revision.

    The process of addition of more assets in an existing portfolio or changing the ratio of fuinvested is called as portfolio revision.

    The sale and purchase of assets in an existing portfolio over a certain periodof time to maximize returns and minimize risk is called as Portfolio revision.

    Need for Portfolio Revision

    An individual at certain point of time might feel the need toinvest more. The need for portfolio revision arises when anindividual has some additional money to invest.

    Change in investment goal also gives rise to revision in portfolio.Depending on the cash flow, an individual can modify his financialgoal, eventually giving rise to changes in the portfolio i.e. portfoliorevision.

    Financial market is subject to risks and uncertainty. An individualmight sell off some of his assets owing to fluctuations in thefinancial market.

    Portfolio Revision Strategies

    There are two types of Portfolio Revision Strategies.

    1. Active Revision Strategy

    Active Revision Strategy involves frequent changes in an existingportfolio over a certain period of time for maximum returns andminimum risks.

    Active Revision Strategy helps a portfolio manager to sell and purchasesecurities on a regular basis for portfolio revisio