A Quantitative Risk Optimization Of Markowitz Model

A Quantitative Risk Optimization of Markowitz Model An Empirical Investigation on Swedish Large Cap List MASTER THESIS IN MATHEMATICS /APPLIED MATHEMATICS By Amir Kheirollah Oliver Bjärnbo Supervisor Lars Pettersson

Agenda ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Short Description of Markowitz Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Assumptions of Modern Portfolio Theory ,[object Object],[object Object],[object Object],[object Object],[object Object]

Harry Markowitz & Portfolio Selection/Risk & Reward ,[object Object],[object Object]

Mathematics of Markowitz Model ,[object Object],[object Object],[object Object]

Diversification in Markowitz Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Capitial Allocation Line (CAL) and Efficient Frontier ,[object Object],[object Object]

The Sharpe Ratio ,[object Object],[object Object],[object Object],[object Object]

Skewness & Kurtosis ,[object Object],[object Object]

Normality of the Asset Returns; ”Is it a myth?” ,[object Object],[object Object],The result of JB-Test The study on 5 different data time series resulted in strong rejection of normality hypothesis for daily, weekly and monthly asset returns, as well as good level of confidence for rejection of normality for quarterly data time series.

Normality of the Asset Returns; ”Is it a myth?” ,[object Object],[object Object],[object Object]

Normality of the Asset Returns; ”Is it a myth?” Frequency Distribution of Assets’ Return This plotting system let us observe closely any deviation from a normally distributed sample. The peakedness and deviation from the expected mean is traceable. The tails are clearly supporting the argument of non-Gaussian distribution, as the top of the distributions confirm it.

Normality of the Asset Returns; ”Is it a myth?” ,[object Object],[object Object]

Is Sharpe Ratio Still Reliable? If not so, Why? ,[object Object],[object Object]

Is Sharpe Ratio Still Reliable? If not so, Why? ,[object Object]

Is Sharpe Ratio Still Reliable? If not so, Why? ,[object Object],[object Object],MVaR, accounts for the effect of Skewness and Kurtosis.

Is Sharpe Ratio Still Reliable? If not so, Why? Traditional Sharpe VS. Modified Sharpe ratio

Is Sharpe Ratio Still Reliable? If not so, Why? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Historical VS. Future Portfolios & Which Time Series to Use? ,[object Object]

Historical VS. Future Portfolios & Which Time Series to Use? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Historical VS. Future Portfolios & Which Time Series to Use? ,[object Object],[object Object],[object Object]

The Higher Statistical Moments in Construction of the Model, Are They Positive Factors in Decision Making? ,[object Object],[object Object],[object Object],[object Object]

The End Thank You for Your Attendance!

A Quantitative Risk Optimization Of Markowitz Model

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