Question

Parts d,e,f

Only bullet points needed on what I should write about

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Answer four parts of the following question. Your answer for each part should be no longer than two pages long 1. (a) Use the single index model to derive an econometric model of the capital asset pricing model. (b) With the aid of an example, show how the security market line differs from the capital market line? (c) A fully diversified portfolio will have no risk? True or false? Explain your answer. (d) The standard deviation of the return on stock A is greater than that of stock B. This does not guarantee that the Beta for stock A is greater than the Beta for stock B. True or false? Explain you answer Assume for simplicity sake that one factor has been deemed appropriate to "explain" returns on stocks and there is no idiosyncratic risk. Derive the arbitrage pricing theory (APT) model. Describe and graphically illustrate Markowitz' portfolio optimisation solution if a risk-free asset is not available. (e) ()

Answer 1

Answer d)

True ,Because of the justification given below

Standard deviation

  Standard deviation is the measure of total risk, ( systematic risk+ unsystematic risk) most common statistical indicator of an assets risk which measures dispersion around the expected value.

Beta :- It is a measure of systematic risk.

Systematic risk affects the entire stock market. It affected all stocks. On the other hand, unsystematic risk is risk that only affects a particular security.

Unsystematic risk can be eliminated with a well-diversified portfolio,by holding enough uncorrelated securities, unsystematic risk can be eliminated. However, if investors were compensated for taking risk that can be eliminated, the return of unsystematic risk would be arbitraged to zero. Therefore, investors are only compensated for systematic risk.

Beta= ( co relation coefficient of portfolio with market×standard deviation of security)/standard deviation market

Standard deviation of stock A is greater than B ,but it doesn't guarantee beta will be greater than B,The difference you see is due to correlation. between security.and also

Higher standard deviation does naturally lead directly to higher beta, but for diversified portfolios only, not necessarily for individual securities.The standard deviation of the returns of an asset has two sources: the market beta times the market's standard deviation, and the asset's own idiosyncratic (market independent) standard deviation. Hence, an asset with high idiosyncratic standard deviation can have a high standard deviation despite a low beta.

(e)

Arbitrage pricing theory

Arbitrage pricing theory(APT) is an equilibrium model of asset pricing but assumes that the returns are generated by factor Model.APT states that expected return on an investment is dependent upon how that investment reacts to a set of individual macro economic factors and the risk premium associated with each of those macroeconomics factors.

Assuming for simplicity sake that one factor has been appropriate and there is no idiosyncratic risk,APT model is derive as follows:-

E(R_i)=R_{​​​​​f+} IB_{​​​​​i}   where l is the average risk premium( E(R_​​m)- R_{​​​​​f})

R_f= Risk free securitsecurity

B= beta

R_m= market expected return

E(R_i)=expected return on security

(f)

Optimal portfolio under Markowitz Model with no risk free asset

The optimal portfolio is the portfolio on the efficient frontier that has the highest utility for a given investor. It lies at the point of tangency between the efficient frontier and the the curve with the highest possible utility.As described in  this graph, every possible combination of the risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The left boundary of this region is a hyperbola 1, and the upper edge of this region is the efficient frontier in the absence of a risk-free asset Combinations along this upper edge represent portfolios (including no holdings of the risk-free asset) for which there is lowest risk for a given level of expected return. Equivalently, a portfolio lying on the efficient frontier represents the combination offering the best possible expected return for given risk level.

Efficient Frontien LI Tangency Portfolio Individual Assets risk free rate Best possible CAL Standard Deviation

Markowitz has formalized the risk return relationship and developed the concept of efficient frontier.

As a rule ,a portfolio is efficient and optimat if there is another portfolio with

a) A higher expected value if return and a lower standard deviation

b) A higher expected value of return and the same standard deviation

c) The same expected value but a lower standard deviation