Probability Dstributions of Risky Asset Returns

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Recommended: challenge to the market efficiency hypothesis

We make the following assumption regarding the probability distributions of risky asset returns: Returns are jointly normally distributed random variables which is the reason that investors can focus only on mean and variance of the returns(Fama and French 2004). This implies all portfolios created from a combination of individual assets or other portfolios must have distributions that continue to be determined by their means and variances. A portfolio of assets whose returns are multivariate normally distributed also has a return that is normally distributed.

The Mean Variance Optimization model was derived from the portfolio theory by Markowitz(1952). There are several assumptions have been used when deriving this mmedel. Firstly, The mean of historical returns is used to show the expected return, the variance of these returns is used to show the risk which comprise systematic risk and unsystematic risk(Ross, Westerfield and Jordan 2008). Secondly, ‘the process that generates returns in the past is also the process that generates returns in the future’
(Frino, Hill and Chen 2009). Thirdly, all investors are rational and risk-averse, and expect higher return along with higher risk (Fame and French 2004). Fourthly, the Mean Variance Optimization model is assumed in a single period, so initially an investor creates a portfolio according to the chosen meanvariance-criterion and keeps the proportion of assets in the portfolio unchanged last to end of the period (Korn and Korn 2001). Lastly, all investors are price takers so their invesment decisions do not affect price, also there is no income tax or transaction fee.

CAPM model shares many assumptions with Mean Variance Optimization model since it is derived from Markowitz’s mean-...

... middle of paper ...

...e approach. EU Socrates Project. MaMaEuSch-Management Mathematics for European Schools, 2001. http://optimierung.mathematik.uni-kl.de/mamaeusch/
Markowitz, H.M. Portfolio Selection. Journal of Finance.1952, 7 (1): 77–91.
Ross, S. A., Westerfield, R. W. and Jordan, B. D. Corporate finance fundamentals. New York: McGraw-Hill/Irwin, 2008.
Bodie, Z., Kane, A., Marcu, A. J. Investments 9th ed. New York: McGraw-Hill/Irwin, 2008.
Fama, E. F. and French, K. R. The Capital Asset Pricing Model: Theory and Evidence. Journal of Economic Perspectives. 2004, 18 (3): 25-46.
Chamberlain, G., & Rothschild, M. (1984). Arbitrage, factor structure, and mean-variance analysis on large asset markets.
Talor, B 2006, Developing Portfolio Optimization Models, Mathworks, viewed 21 May 2014,
http://www.mathworks.com.au/company/newsletters/articles/developing-portfolio-optimization-models.html

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