Stochastic and Normally Distributed Probability Distributions Allow for Statistical Analysis and Modelling of Returns

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Question 1

The probability distribution assumption on risky asset returns is that returns are stochastic and normally distributed around the mean return. This assumption allows for statistical analysis and modelling of returns.

The assumptions of the models are listed below.

i) No Transaction Cost for buying or selling an asset. Since transaction costs are normally a minimal percentage of the investment it becomes a minor importance to investors and reduces the complexity of the Capital Asset Pricing Model (CAPM).

ii) Assets are infinitely divisible. An investor can take any position in an investment, whether it is a managed fund or Australian equity. For example, buying one dollar worth of BHP Billiton Shares.

iii) Absence of personal tax.

iv) Regardless of the size of an investment, an individual cannot affect stock prices by his/herself. Similar to ‘perfect competition,’ assumptions investors as an aggregate determine prices.

v) Investors are expected to make financial decisions solely based on the expected return and variance of the returns in their desired portfolio.

vi) Unlimited short selling is legal. This is selling a security that you do not own, with the expectation of buying it back. Hence an investor may wish to short sell $50,000 worth of BHP shares.

vii) Unlimited borrowing and lending at the risk free rate.

viii) Homogeneity of expectations. Thus investors are concerned with mean and variance of returns and all investors have identical expectations with respect to these inputs to the portfolio decision.

ix) All assets are marketable, and hence can be sold and bought on a form of market.

Certain hypotheses will hold for CAPM regardless if it is a simple or two-factor general equilibrium mode...

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...t managers to be able to identify the limitations and risks associated with MVO to ensure that the estimation error is minimised and to factor in the total cost of the portfolio.

References

1) Fama, E.F.; French, K.R (2004) The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives: Volume 18.3 pp 25-46.

2) E.J. Elton, M.J. Gruber, S.J. Brown and W.N. Goetzmann, Modern Portfolio Theory and Investment Analysis, J. Wiley & Sons (8th Edition) 2009.

3) Lummer, S. L., Reipe, M. W. & Siegel, L. B., 1994. Taming Your Optimizer A Guide Through the Pitfalls of Mean - Variance Optimization. In: J. Lederman & R. A. Klein, eds. Global Asset Allocation: Techniques for Optimizing Portfolio Management. s.l.:John Wiley & Sons.

4) Rajkumar, S. and Dorfman, M. 2011.Governance and investment of public pension assets. Washington, D.C.: World Bank.

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