tailieunhanh - Portfolio theory and cone optimization

This paper will discuss portfolio optimization, Quadratic Programming (QP) and Second Order Cone Programming (SOCP). We will use simulated and empirical data to compare the two optimization routines. Daily data for SP500 stocks from 2005 to 2010 was used to show that a 20-days rebalanced portfolio strategy with an expected portfolio return of 60 percent of the maximum expected return for all stocks produced an percent return premium on an annual basis if we used QP and percent return premium on an annual basis if we used SOCP. | Journal of Applied Finance Banking 2011 173-187 ISSN 1792-6580 print version 1792-6599 online International Scientific Press 2011 Portfolio Theory and Cone Optimization Marcus Davidsson1 Abstract This paper will discuss portfolio optimization Quadratic Programming QP and Second Order Cone Programming SOCP . We will use simulated and empirical data to compare the two optimization routines. Daily data for SP500 stocks from 2005 to 2010 was used to show that a 20-days rebalanced portfolio strategy with an expected portfolio return of 60 percent of the maximum expected return for all stocks produced an percent return premium on an annual basis if we used QP and percent return premium on an annual basis if we used SOCP. JEL classification G11 Keywords QP SOCP optimization portfolio theory cone 1 Introduction and Literature Review Markowitz 7 Sharpe 9 Ross 8 Black and Litterman 1 Fama and French 5 and Carhart 3 have all made significant contributions to portfolio 1 Department of Economics Newcastle University Business School 5 Barrack Road Newcastle upon Tyne NE1 4SE UK e-mail davidsson_marcus@ Article Info Revised September 8 2011. Published online September 30 2011 174 Portfolio Theory and Cone Optimization theory. The main objective for portfolio diversification is to minimize portfolio variance. In the basic model portfolio variance is a function of the return volatility for each security in the portfolio and the cross correlation of returns. Since cross correlation can be negative return variance can be cancelled out. However the same idea can also be applied to highly positive correlated stock return portfolio by artificially creating negative cross correlation in return by short selling. Portfolio variance can also be thought as the amount of return noise around the portfolios expected return. Diversification can to a large extend eliminate such return noise. Markowitz 7 mainly looks at diversification from an asset class perspective

• Bảo hiểm
• Portfolio theory
• Cone optimization
• Discuss portfolio optimization
• Quadratic Programming
• Second Order Cone Programming