Efficient Frontier - Comparing Different Volatility Estimators

Modern Portfolio Theory (MPT) according to
Markowitz states that investors form mean-variance efficient
portfolios which maximizes their utility. Markowitz proposed the
standard deviation as a simple measure for portfolio risk and the
lower semi-variance as the only risk measure of interest to rational
investors. This paper uses a third volatility estimator based on
intraday data and compares three efficient frontiers on the Croatian
Stock Market. The results show that range-based volatility estimator
outperforms both mean-variance and lower semi-variance model.





References:
[1] Aljinović, Z., Marasović, B., Šego, B., Financijsko modeliranje, II
izmijenjeno i dopunjeno izdanje, Ekonomski fakultet Split, 2011, pp.
121-153.
[2] Aljinović, Z., Marasović, B., Vidović, J., “The alternative risk measures
in Excel”, MIPRO 2010, Proceedings of the 33rd International
Convention: Computers in Education, Opatija, Croatia, 2010, pp. 152-
157.
[3] Andersen, T.G., Bollerslev, T., Diebold, F.X., and Labys, P., “The
distribution of realized exchange rate volatility”, Journal of the
American Statistical Association 96, 2001, pp. 42-55.
[4] Arnerić, J. and Matković, M., “Ranking Open, High, Low, Closing
Volatility Estimators“, Split Faculty of Economics - Working paper,
2013.
[5] Bawa, S. and Vijay S., "Optimal Rules For Ordering Uncertain
Prospects", Journal of Financial Economics, v2(1), 1975, pp. 95-121.
[6] Cheng, P. and Woverton, M., "MPT and the Downside Risk Framework:
A Comment on Two Recent Studies", Journal of Real Estate Portfolio
Management, vol 07, no.2, 2001.
[7] Cont, R., " Empirical properties of asset returns: stylized facts and
statistical issues", Journal of Quantitative Finance, vol. 01, 2001, pp.
223-236.
[8] Dacarogna, M.M., Muller, U.A., Olsen, R.B, and Pictet, O.V.,
“Modelling short term volatility with GARCH and HARCH models”,
published in “Nonlinear Modelling of High frequency Financial Time
Series.”, edited by Christian Dunis and Bin Zhou, John Wiley,
Chichester, 1998, pp. 161-176.
[9] Duque, J., and Paxson, D., “Empirical Evidence on Volatility
Estimators”, Working Paper, Universidade Tecnica de Lisboa and
University of Manchester, 1997.
[10] Foo, T., Eng, S., “Asset Allocation in a Downside Risk Framework”,
Journal or Real Estate Portfolio Management, Vol.06, No.3, 2009.
[11] Garman, M.B., and Klass, M.J., “On the Estimation of Security Price
Volatilities from Historical Data”, Journal of Business, 53, 1980, pp. 67-
78.
[12] Harris, R.D.F., Yilmaz, F. “Estimation of the Conditional Variance-
Covariance Matrix of Returns using the Intraday Range”, University of
Exerer, XFi Centre for Finance and Investment, Working paper: 07/11,
October, 2007
[13] Konno, H., Waki, H., Yuuki, A., “Portfolio Optimization under Lower
Partial Risk Measures”, Asia-Pacific Financial Markets, vol.9,, 2002,
pp. 127-140, Kluwer.
[14] Mao, James C. T., "Models Of Capital Budgeting, E-V Vs. E-S" Journal
of Financial and Quantitative Analysis, v5(5), 1970, pp. 657-676.
[15] Markowitz, H., “Portfolio Selection: Efficient Diversification of
Investments”, Journal of Finance, Vol.7, No.1, 1952, pp. 77-91.
[16] Markowitz, H., “Portfolio Selection: Efficient Diversification of
Investments”, John Wiley and Sons, 1959.
[17] Parkinson, M., “The Extreme Value Method for Estimating the Variance
of the Rate of Return”, Journal of Business, 53, 1980, pp. 61-65.
[18] Rogers, L.C.G., and Satchell, S.E., “Estimating Variance from High,
Low, and Closing Prices”, Annals of Applied Probability 1, 1991, pp.
50-512.
[19] Sing, T. F., Ong, S. E., “Asset Allocation in a Downside Risk
Framework“, Journal of Real Estate Portfolio Management, Vol.6, no.3,
2000, pp. 213–224.
[20] Sivitanides, P. S., “A Downside-risk Approach to Real Estate Portfolio
Structuring“, Journal of Real Estate Portfolio Management, Vol.4, no.2,
1998, pp. 159–168.