Sains Malaysiana 42(6)(2013): 875–880

Risk Measures and Portfolio Construction in Different Economic Scenarios

(Pengukuran Risiko dan Penjanaan Portfolio dalam Senario Ekonomi Berbeza)

Saiful Hafizah Jaaman*, Weng Hoe Lam & Zaidi Isa

Centre for Modelling and Data Analysis (DELTA), School of Mathematical Sciences

Faculty of Science and Technology, Universiti Kebangsaan Malaysia

43600 UKM Bangi, Selangor, Malaysia

Received: 18 May 2012/Accepted: 13 September 2012

ABSTRACT

This paper compared the composition and performance of portfolios constructed by employing different risk measures utilizing the Malaysian share market data in three diverse economic scenarios. The risk measures considered were the mean-variance (MV) and their alternatives; the semi-variance (SV), mean absolute deviation (MAD) and conditional value at risk (CVAR). The data were divided into three sub-periods representing the growth period in the economy, financial crisis and the recovery period. The results of this study showed different optimal portfolios’ performances and compositions for the three economic periods. Nevertheless, among the risk models tested, CVAR(0.99) model gave the highest portfolio skewness. High skewness means that the probability of getting large negative returns is decreased. As a conclusion, for the Malaysian stock market, the CVAR(0.99) model is the most appropriate portfolio optimization model for downside risk aversion investors in all three economic scenarios.

Keywords: Optimization; return; share market; skewness; variance

ABSTRAK

Kertas ini membandingkan komposisi dan prestasi portfolio yang dibina menggunakan pengukuran risiko berlainan ke atas data pasaran saham Malaysia dalam tiga senario ekonomi berbeza. Ukuran risiko yang dipertimbangkan ialah min-varians (MV) dan alternatifnya; semi-varians (SV), min sisihan mutlak (MAD) dan nilai bersyarat pada risiko (CVAR). Data dibahagi kepada tiga sub-tempoh yang mewakili tempoh pertumbuhan ekonomi, krisis kewangan dan tempoh pemulihan. Keputusan kajian menunjukkan prestasi dan komposisi portfolio yang optimum adalah berbeza bagi tiga tempoh ekonomi tersebut. Namun begitu, daripada model risiko yang diuji, model CVAR(0.99) memberikan kepencongan portfolio tertinggi. Kepencongan tinggi bermakna kebarangkalian mendapat pulangan negatif yang besar berkurangan. Kesimpulannya, untuk pasaran saham Malaysia, model CVAR(0.99) merupakan model pengoptimuman portfolio yang paling sesuai untuk pelaburan penghindaran risiko ke bawah dalam ketiga-tiga senario ekonomi.

Kata kunci: Kepencongan; pasaran saham; pengoptimuman; pulangan; varians

REERENCES

Arditti, F.D. 1967. Risk and the required return on equity. Journal of Finance 22: 19-36.

Bodie, Z., Kane, A. & Marcus, A. 2011. Investments and Portfolio Management. 9th ed. New York: McGraw-Hill.

Byrne, P. & Lee, S. 2004. Different risk measures: Different portfolio compositions? Journal of Property Investment & Finance 22(6): 501-511.

Chow, K. & Denning, K.C. 1994. On variance and lower partial moment betas: The equivalence of systematic risk measures. Journal of Business Finance and Accounting 21: 231-241.

Chunhachinda, P., Dandapani, K., Hamid, S. & Prakash A.J. 1997. Portfolio selection and skewness: Evidence from international stock markets. Journal of Banking & Finance 21: 143-167.

Elton, E.J., Gruber, M.J., Brown, S.J. & Goetzmann, W.N. 2007. Modern Portfolio Theory and Investment Analysis. 7th ed. New York: Wiley.

Fama, E.F. 1965. Portfolio analysis in a stable Paretian market. Management Science 11: 404-419.

Feinstein, C.D. & Thapa, M.N. 1993. Notes: Areformulation of a mean-absolute deviation portfolio optimization model. Management Science 39(12): 1552-1553.

Grootveld, H. & Hallerbach, W. 1999. Variance vs downside risk: Is there really that much difference? European Journal of Operational Research 114: 304-319.

Jaaman, S.H., Lam, W.H. & Isa, Z. 2011. Higher moment portfolio management with downside risk. American Journal of Social and Management Sciences 2(2): 220-224.

Kon, S.J. 1984. Models of stock returns- a comparison. The Journal of Finance 39(1): 147-165.

Konno, H. & Yamazaki, H. 1991. Mean-absolute deviation portfolio optimization model and its applications to Tokyo Stock Market. Management Science 37(5): 519-531.

Konno, H. & Yamazaki, H. 2001. Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Mathematical Programming 89: 233-250.

Konno, H., Waki, H. & Yuuki, A. 2002. Portfolio optimization under lower partial risk measures. Asia-Pacific Financial Markets 9: 127-140.

Kraus, A. & Litzenberger, R. 1976. Skewness preference and the valuation of risky assets. Journal of Finance 21: 1085-1094.

Krokhmal, P., Palmquist, J. & Uryasev, S. 2002. Portfolio optimization with conditional value-at-risk objectives and constraints. Journal of Risk 42(2): 124-129.

Lai, T.Y. 1991. Portfolio selection with skewness: Amultiple-objective approach. Review of Quantitative Finance and Accounting 293-305.

Li, X., Qin, Z. & Kar, S. 2010. Mean-variance-skewness model for portfolio selection with fuzzy returns. European Journal of Operational Research 202: 239-247.

Lima, A.E.B., Shanthikumarb, J.G. & Vahn, G-Y. 2011. Conditional value-at-risk in portfolio optimization: Coherent but fragile. Operations Research Letter 39: 163-171.

Liu, M. & Gao, Y. 2006. An algorithm for portfolio selection in a frictional market. Applied Mathematics and Computation 182: 1629-1638.

Markowitz, H. 1952. Portfolio selection. Journal of Finance 7(1): 77-91.

Markowitz, H. 1959. Portfolio Selection: Efficient Diversification of Investments. New York: John Wiley & Sons.

Markowitz, H. 1993. Computation of mean-semivariance efficient sets by the critical line algorithm. Annals of Operational Research 45: 307-317.

Prakash, A.J., Chang, C. & Pactwa, T.E. 2003. Selecting a portfolio with skewness: Recent evidence from US, European, and Latin American equity markets. Journal of Banking and Finance 27: 1375-1390.

Rockafellar, R.T. & Uryasev, S. 2000. Optimization of conditional value-at-risk. Journal of Risk 2: 21-41.

Saiful Hafizah Jaaman, Weng Hoe Lam & Zaidi Isa. 2011. Different downside risk approaches in portfolio optimization. Journal of Quality Measurement and Analysis 7(1): 77-84.

Samuelson, P. 1970. The fundamental approximation theorem of portfolio analysis in terms of means, variances, and higher moments. Review of Economic Studies 37: 537-542.

Simaan, Y. 1997. Estimation risk in portfolio selection: The mean variance model versus the mean absolute deviation model. Management Science 43(10): 1437-1446.

Szegö, G. 2002. Measures of risk. Journal of Banking & Finance 26: 1253-1272.

Tanaka, H. & Guo, P. 1999. Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 114: 115-126.

*Corresponding author; email: shj@ukm.my