Abstracts

Black and Litterman (1992) developed a framework that produces more accurate and stable assets' returns estimates as inputs to Markowitz's (1952) mean-variance portfolio optimization (MV). Within the Black-Litterman (BL) model, investors combine a prior vector, based on market equilibrium returns obtained through MV reverse optimization, and their views on the future returns of the assets to arrive at a posterior vector. Previous studies have demonstrated that BL helps to overcome the shortcomings of traditional MV.
Das et al (2010) proposed a mental accounting (MA) framework in which they integrate MV and behavioral portfolio theory (BPT) from Shefrin and Statman (2000). In MA investors divide their wealth in subportfolios, each having a different goal stated as a threshold return and maximum probability of not reaching it. Hence, instead of specifying a single risk-aversion coefficient, in MA investors can intuitively set multiple VaR-like constraints for their mental accounts.
We integrate BL and MA to achieve a full integration between standard and behavioral portfolio theory starting from parameter specification to optimization and to monitoring. The objective is to build portfolios that deliver a strong risk-adjusted performance as a consequence of sensible and intuitive processes. We compute the prior vector by reverse optimization using the MA equations, with market capitalization weights and a market threshold return and probability as inputs. The level of confidence on the views is treated as in Idzorek (2004). Once the posterior vector is computed through the BL equation, the weights of each subportfolio are calculated constrained by the investor's goals. Finally, we obtain the aggregated portfolio with the selected distribution of wealth.
A preliminary out-of-sample analysis with the 10 S&P 500 Sector Indices from Jan/2001 until Sep/2013 indicated that the performance of the proposed strategy is superior compared to the market portfolio. The investor's views were set as the historical means of each asset (with a 50\% confidence) and we used three mental accounts. The BL-MA strategy produced an annualized Sharpe ratio and 5\% monthly VaR and CVaR of 0.33, -6.44\%, and -9.22\%, while the market portfolio returned 0.24, -7.81\%, and -10.09\%. The break-even transaction cost of the BL-MA strategy was 0.3\%. The BL-MA strategy is then capable of overperforming its prior even in the presence of naïve views and when a high confidence level is assigned to them.