Weight:50% Format:3,000-word written report (plus or minus 10%) Assessment brief Using the data provided in Appendix 1 (i.e. Tables 2-4) for numerical questions, write a report addressing the...

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Capital market models give the relationship between the risk and return of an individual security and portfolio. There are many models in which CAPM, CML, CAL are few of the important ones.
The Capital Asset Pricing Model (CAPM) is a linear relationship between the expected rate of return on a security and its systematic risk. Mathematically it is represented as
                E(r) = Rf + β (Rm – Rf)
Where,
    E(r) = Expected rate of return on security
    Rf = Risk free rate of return
    Rm = Market return
    β = Beta of security.
There are certain assumptions that CAPM holds. They are as follows:
· Investors hold a diversified portfolio – It means that investors required return only for the systematic risk of portfolio. Unsystematic risk is removed as it can be ignored.
· Single period transaction horizon – In CAPM, the single transaction period is taken and it is usually one year. It means the return on a security over six months can’t be compared with the return on other security over twelve months.
· Investors can borrow and lend at risk free rate of return – It means the risk free rate is the minimum level of return required by investors.
· Perfect capital market – It means all the securities are correctly valued and can be drawn on security market line (SML). Perfect capital market shows that there is no transaction cost, no taxes, security related all the information are equally available to all the investors, all the investors are rational, risk averse and want to maximize their utility and there are large number of buyers and sellers in the market.
Single Index model is another kind of asset pricing model that shows the relationship between securities return with any one of the economic variable that is relevant to that security.
Mathematically it is represented by the equation –
Where,
    Ri = Expected return on the security i
    αi = Abnormal return on the stock
    β = Beta of the security i.e. measurement of systematic risk
    RM = Market return
    ei = Unsystematic risk of the security
Single Index Model (SIM) divides the firm’s total risk into two parts – Systematic risk and Unsystematic Risk.
Following are the assumptions of SIM –
· There is a single macroeconomic factor that causes the systematic risk and thus affects the return on the security
· The security’s abnormal return is due to the firm’s specific risk called unsystematic risk and a part of other risk is due to the single factor market risk.
Barton Waring & Duane Whitney (2009) has suggested an update to earlier model of CAPM in his research paper where he proposed An Asset Liability version of CAPM with a multi period two-fund theorem. In his paper, he incorporates investors’ deferred spending plan or economic liabilities which are the underlying purpose of all investment plans. Thus, he created a new risk free asset – the investors’ liability matching asset portfolio. In combination of world market portfolio of risky assets, he forms a new two fund theorem that is more practical and usable than SAPM. Thus, the authors’ new version of CAPM is a try to bridge the gap between the original simple CAPM and other complex theorem of later time.
Arbitrage pricing theory (APT) was given by Stephen Ross in 1976. This theory established the relationship between the expected rate of return and the different macro economical factors that affect risks. Through this model, sensitivity of the asset’s return is captured due to change in macro economical variables. This theory assumes that market doesn’t hold to be efficient all the time. At most of the occasion market gets temporarily inefficient and the securities turn to be mispriced. Assets may become either undervalued or overvalued. However, the market corrects itself eventually and the assets come back at its fair price. Arbitrageurs reap the benefit of volatility in market and thus, make the riskless profit through temporarily mispriced securities.
Unlike CAPM model where there is a single factor, APT is multi factor model. However, like CAPM, APT can effectively describe the correlation between risk and return of any security. Thus, APT provides a more comprehensive approach for determining the return on a security against risk inherited due to several macro economical variables. It provides the flexibility to investors as well as researchers to form the well suited factor model to determine the risk return trade off of a security. But, it is difficult to determine the suitable risk factors with limited information and data. It’s also a tedious job to work upon this model.
Following underlying assumptions lie for APT –
Various risk factors are for systematic risk used in this model.
· Specific or unsystematic risks can be reduced or eliminated through diversification by forming an efficient portfolio.
· A well diversified portfolio doesn’t possess any arbitrage opportunities. If such opportunity arises, it will be exploited away immediately by investors.
The APT can be expressed through a mathematical formula –
Where,
    E(rj) = Security’s expected return
    rf = Risk-free rate of return
    ßn = Systematic risk of security with respect to macro economical factor n.
    RPn = Risk premium of factor n
The macro economical factor may be GDP per capita income, Unemployment rate, inflation, interest rate etc. The choice of selecting the factors is completely upon the willingness of investors and fund managers.
Fama French three-factor model is extension of CAPM model by adding size risk and value risk factor to the market risk factor. It is given by Eugene Fama in 1962. This model considers the facts that small cap stocks outperform the market regularly and thus, inclusion of two more factors adjust the tendency of outperformance.
To estimate the Fama-French 3-factor model, Ordinary Least Squares regression is performed. The regression...