A Geometric Approach To Multiperiod Mean Variance Optimization of Assets and Liabilities

By Markus Leippold, Fabio Trojani, P. Vanini. 2004

188 citations recorded by the source corpus.

We present a geometric approach to discrete time multiperiod mean variance portfolio optimization that largely simplifies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decomposed in an orthogonal set of basis strategies, each having a clear economic interpretation. This implies that the corresponding multiperiod mean variance frontiers are spanned by an orthogonal basis of dynamic returns. Specifically, in a k-period model the optimal strategy is a linear combination of a single k-period global minimum second moment strategy and a sequence of k local excess return strategies which expose the dynamic portfolio optimally to each single-period asset excess return. This decomposition is a multi period version of Hansen and Richard (Econometrica (1987)) orthogonal representation of single-period mean variance frontiers and naturally extends the basic economic intuition of the static Markowitz model to the multiperiod context. Using the geometric approach to dynamic mean variance optimization we obtain closed form solutions in the i.i.d. setting for portfolios consisting of both assets and liabilities (AL), each modelled by a distinct state variable. As a special case, the solution of the mean variance problem for the asset only case in Li and Ng (Mathematical Finance 10 (2000)) follows directly and can be represented in terms of simple products of some single period orthogonal returns. We illustrate the usefulness of our geometric representation of multiperiods optimal policies and mean variance frontiers by discussing specific issues related to AL portfolios: The impact of taking liabilities into account on the implied mean variance frontiers, the quantification of the impact of the rebalancing frequency and the determination of the optimal initial funding ratio.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/8e09e31dd793b82a30b8ad2e14ff4eb96a1a0aaf

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In Economics and Econometrics

1. Yang Shen
2. Xiangyu Cui
3. Danping Li
4. Yan Zeng
5. Shouyang Wang
6. Shushang Zhu
7. Duan Li
8. Huyen Pham

In Finance

1. Yang Shen
2. Xiangyu Cui
3. Yan Zeng
4. Shouyang Wang
5. Danping Li
6. Duan Li
7. Shushang Zhu
8. Xun Yu Zhou

Citations in the corpus

• BETTER THAN DYNAMIC MEAN‐VARIANCE: TIME INCONSISTENCY AND FREE CASH FLOW STREAM (2012, background): “…and Zhou (2002), Zhou and Yin (2003), Hu and Zhou (2005), Bielecki et al. (2005), Li and Zhou (2006), Chiu and Li (2006), Xiong and Zhou (2007) in continuous-time settings and Leippold, Trojani, and Vanini (2004), Zhu, Li, and Wang (2004), and Liang, Zhang, and Li (2008) in discrete-time settings.”
• Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility (2018, background): “Chen et al. (2008) and Chen and Yang (2011) extended the works of Chiu and Li (2006) and Leippold et al. (2004) to ∗Corresponding author.”
• Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation (2010, unknown): “We should point out here that the optimal mean variance strategy in (Zhou and Li, 2000; Li and Ng, 2000; Nguyen and Portrai, 2002; Leippold et al., 2004; Bielecki et al., 2005; Chiu and Li, 2006; Wang et al., 2007; Hojgaard and Vigna, 2007) is the pre-commitment strategy, i.e. once the initial…”