Timing Prediction Error Volatility and Dynamic Asset Allocation

Abstract

We solve a portfolio selection problem in which return predictability, risk predictability and transaction cost are incorporated. In the problem, both expected return, prediction error volatility, and transaction cost are time-varying. Our optimal strategy suggests trading partially toward a dynamic aim portfolio, which is a weighted average of expected future tangency portfolio and is highly influenced by the common fluctuation of prediction error volatility (CPE). When CPE is high, the investor would invest less and trade less frequently to avoid risk and transaction cost. Moreover, the investor trades more closely to the aim portfolio with a more persistent CPE signal. We also conduct an empirical analysis based on the commodities futures in Chinese market. The results reveal that by timing prediction error volatility, our strategy outperforms alternative strategies.

Keywords

Dynamic asset allocation / prediction error volatility / transaction cost / return predictability / volatility timing

References

[1] Ang A, Chen J. Asymmetric correlations of equity portfolios. Journal of Financial Economics, 2002, 63(3): 443-494.

[2] Ang A, Hodrick R J, Xing Y, Zhang X. The cross-section of volatility and expected returns. The Journal of Finance, 2006, 61(1): 259-299.

[3] Balduzzi P, Lynch A W. Transaction costs and predictability: Some utility cost calculations. Journal of Financial Economics, 1999, 52(1): 47-78.

[4] Ball R, Kothari S. Nonstationary expected returns: Implications for tests of market efficiency and serial correlation in returns. Journal of Financial Economics, 1989, 25(1): 51-74.

[5] Bekaert G, Wu G. Asymmetric volatility and risk in equity markets. The Review of Financial Studies, 2000, 13(1): 1-42.

[6] Busse J A. Volatility timing in mutual funds: Evidence from daily returns. Review of Financial Studies, 1999, 12(5): 1009-1041.

[7] Collin-Dufresne P, Daniel K, Sağlam M. Liquidity regimes and optimal dynamic asset allocation. Journal of Financial Economics, 2020, 136(2): 379-406.

[8] Constantinides G M. Capital market equilibrium with transaction costs. Journal of Political Economy, 1986, 94(4): 842-862.

[9] Cui X, Gao J, Li X, Li D. Optimal multi-period mean-variance policy under no-shorting constraint. European Journal of Operational Research, 2014, 234(2): 459-468.

[10] Ding Y, Engle R, Li Y, Zheng X (2020). Factor modeling for volatility. Working paper.

[11] Fleming J, Kirby C, Ostdiek B. The economic value of volatility timing. The Journal of Finance, 2001, 56(1): 329-352.

[12] Fleming J, Kirby C, Ostdiek B. The economic value of volatility timing using “realized” volatility. Journal of Financial Economics, 2003, 67: 473-509.

[13] Gao J, Li D. Optimal cardinality constrained portfolio selection. Operations Research, 2013, 61(3): 745-761.

[14] Gârleanu N, Pedersen L H. Dynamic trading with predictable returns and transaction costs. The Journal of Finance, 2013, 68(6): 2309-2340.

[15] Gârleanu N, Pedersen L H. Dynamic portfolio choice with frictions. Journal of Economic Theory, 2016, 165: 487-516.

[16] Glasserman P, Xu X. Robust portfolio control with stochastic factor dynamics. Operations Research, 2013, 61(4): 874-893.

[17] Herskovic B, Kelly B, Lustig H, Van Nieuwerburgh S. The common factor in idiosyncratic volatility: Quantitative asset pricing implications. Journal of Financial Economics, 2016, 119(2): 249-283.

[18] Li D, Ng W L. Optimal dynamic portfolio selection: Multiperiod mean-variance formulation. Mathematical Finance, 2000, 10(3): 387-406.

[19] Li X, Zhou X Y, Lim A E. Dynamic mean-variance portfolio selection with no-shorting constraints. SIAM Journal on Control and Optimization, 2002, 40(5): 1540-1555.

[20] Liu H. Optimal consumption and investment with transaction costs and multiple risky assets. The Journal of Finance, 2004, 59(1): 289-338.

[21] Lynch A W, Balduzzi P. Predictability and transaction costs: The impact on rebalancing rules and behavior. The Journal of Finance, 2000, 55(5): 2285-2309.

[22] Merton R C. Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Economics and Statistics, 1969, 51(3): 247-257.

[23] Moreira A, Muir T. Volatility-managed portfolios. The Journal of Finance, 2017, 72(4): 1611-1644.

[24] Moreira A, Muir T. Should long-term investors time volatility?. Journal of Financial Economics, 2019, 131(3): 507-527.

[25] Mossin J. Optimal multiperiod portfolio policies. The Journal of Business, 1968, 41(2): 215-229.

[26] Stambaugh R F, Yu J, Yuan Y. Arbitrage asymmetry and the idiosyncratic volatility puzzle. The Journal of Finance, 2015, 70(5): 1903-1948.

[27] Stoll H R. The supply of dealer services in securities markets. The Journal of Finance, 1978, 33(4): 1133-1151.

[28] Zhang J, Jin Z, An Y. Dynamic portfolio optimization with ambiguity aversion. Journal of Banking & Finance, 2017, 79: 95-109.

[29] Zhou X, Li D. Continuous-time mean-variance portfolio selection: A stochastic LQ framework. Applied Mathematics and Optimization, 2000, 42: 19-33.