SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT MODELS

PRESENTED BY; Avinash Tripathi 4111015015

CONTENT

1.Markowitz efficient market hypothesis mean variance optimization.

2.Single index market model3.Multi index market model4.Capital asset pricing model5.Arbitrage pricing model

1.Markowitz efficient market hypothesis mean variance optimization.

•The fundamental goal of portfolio theory is to optimally allocate investments between different assets. Mean variance optimization (MVO) is a quantitative tool which allow to make the allocation by considering the trade-off between risk and return

•Further classified as- Single period MVO multi-period MVO

•In single period MVO portfolio allocation is done for a single upcoming period, and the goal is to maximize expected return subject to a selected level of risk

• it was developed by Markowitz•the efficient frontier is conventionally

plotted on a graph with the standard deviation (risk) on the horizontal axis, and the expected return on the vertical axis. A useful feature of the single period MVO problem is that it is soluble by the quadratic programming algorithm

•Inputs:▫The expected return for each asset▫The standard deviation of each asset (a

measure of risk)▫The correlation matrix between these

assets

•Output:▫The efficient frontier, i.e. the set of

portfolios with expected return greater than any other with the same or lesser risk, and lesser risk than any other with the same or greater return.

•The goal of the mean variance analysis is to determine the efficient set and to reveal the portfolio structure of optimal portfolios within the framework of risk versus return.

•Therefore, the technique employed in this analysis is the quadratic programming approach.

Assumptions•all investors are risk averse so that they

prefer less risk to more for the same level of expected return;

• investors have the information regarding �the expected returns, variances and co variances of all assets;

• the investors need only to know the �expected returns, variances and the co variances of returns to determine optimal portfolios; and

• there exist no transaction costs or taxes �limitation.

2.SINGLE INDEX MARKET MODEL•Known economist William Sharpe

developed this model, this is a simple asset pricing model to measure both the risk and the return of a stock

•This model relates return to each security to the return on the common index, such as BSE, NSE and so forth

Assumption•  there is one macroeconomic factor that

causes the systematic risk affecting all stock returns and this factor can be represented by the rate of return on a market index, such as S&P 500

•Beyond this common effect all remaining uncertainty in stock return is firm specific i.e. there is no other source of correlation between securities

•Stocks covary together only because of their common relationship to the market index

Model representation• Single index model can be expressed as- • rit is return to stock i in period t

• rf is the risk free rate (i.e. the interest rate on treasury bills)

• rmt is the return to the market portfolio in period t• stock's alpha or abnormal return• stocks's beta or responsiveness to the market

return• e are the residual (random) returns, which are

assumed independent normally distributed with mean zero

• To summarize it is a relationship between a security's performance and the performance of a portfolio containing it. Model states that the security's performance is related to its portfolio's performance, according to its beta.

Return on security = alpha+ beta * return on portfolio + residual return

3.Multi Index Model• Assuming that stock returns are dependent on

market returns are inaccurate and multi index model is a more superior form of model which captures some of the non-market influences that cause securities to move together

• Non-market influences- economic factors such as inflation, interest rates and a set of industry factors.

• Two Types of multi index model-1. General Multi-Index Models2. Industry Index Models

•General Multi-Index Models- Return on stock is a function of return on the market, changes in the level of interest rates, and a set of industry indexes.

•Industry index model -This methodology assumes that the correlation between securities is caused by a market effect and industry effect

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4.Capital asset pricing model

• A model that describes the relationship between risk and expected return 

• The general idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk

• The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time.

• The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf).

Assumptions• There are no taxes or transaction costs• All investors have identical investment horizons• All investors have identical opinions

about expected returns, volatilities and correlations of available investments

• All assets have a definite value, and remains fixed in a certain period of time.

• All assets are completely divided, and pricing in a fully competitive market environment. Implied: human capital does not exist, because it is indivisible and can not be used as assets owned.

• Asset markets, there is no friction, the information at the same time for every investor, and free use. Implied: the borrowing rate equal to the loan interest rate.

Model representationCAPM model is represented as-

•Most important implication of the CAPM ▫All investors hold the same optimal

portfolio of risky assets

▫The optimal portfolio is at the highest point of tangency between RF and the efficient frontier

5.Arbitrage pricing model

• It is Based on the Law of One Price ▫Identical assets cannot sell at different prices▫Equilibrium prices adjust to eliminate all arbitrage

opportunities

•  Model holds that the expected return of a financial asset can be modelled as a linear function of various macro-economic factors, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to price the asset correctly - the asset price is equal to the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage would bring it back into line.

•The APT states that if asset returns follow a factor structure then the following relation exists between expected returns and the factor sensitivities-

= risk premium of the factor, ɼf  is the risk-free rate thus the expected return of an asset j is

a linear function of the assets sensitivities to the n factors.

• Under the APT, an asset is mispriced if its current price diverges from the price predicted by the model. The asset price today should equal the sum of all future cash flows discounted at the APT rate, where the expected return of the asset is a linear function of various factors, and sensitivity to changes in each factor is represented by a factor-specific beta coefficient.

• The arbitrageur sells the asset which is relatively too expensive and uses the proceeds to buy one which is relatively too cheap.