HedgeSPA November 2014 Sophisticated Investment Analytics | Trusted Market Insights White Paper: A Pragmatically-Modified Black-Litterman Approach to Help Multi-Asset Portfolios to Cope with Low-Probability “Black Swan” Scenarios Overview: Portfolio manager John manages an institutional fund of $45 billion. The fund has no explicit liability profile to match and does not contain any investment with a near-term maturity date. It is a partially illiquid fund, but historically only a minor percentage of its holdings may need to be withdrawn based on the needs of its sponsors. Therefore, its investments cannot be wholly illiquid. The strategic allocation of the fund can be modeled by a U.S. multi-asset portfolio, which produces a desirable historical portfolio return of 7.79%, as shown in Figure 1. John’s goal is to generate a steady absolute return over the medium to long term. The sponsor is well aware that markets may swing up and down in the short term, and that artificially creating an absolute return vehicle may be very costly and hurt returns without achieving the sponsor’s longer-term investment objectives. Figure 1: US Multi-Asset Funds Investment Problem: In order to reach his investment goal, John faces several significant limitations associated with the characteristics of any multi-asset portfolio. Firstly, it is common knowledge among professional investors that most institutional-sized portfolios derive their returns from beta instead of alpha [1] due to their massive size. Secondly, any significant change to the portfolio will result in high transaction costs in terms of market impact, which will offset the benefits from trying to achieve meaningful returns[2]. In addition, hedging[3] may not be a practical strategy for a large portfolio as [1] Alpha is a risk-adjusted measure of active return on an investment. A positive alpha of 1.0 means the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha would indicate an underperformance of 1%. [2] An active return is the difference between the benchmark and the actual return. It can be positive or negative and is typically used to assess performance. [3] Hedging is to make an investment to reduce the risk of adverse price movement in an asset. 1 1 HedgeSPA November 2014 Sophisticated Investment Analytics | Trusted Market Insights such, because the massive size of any short positions required by the hedge may artificially induce a market crash. Finally, there is always some portion of investments in any portfolio that may be difficult to sell en masse, such as those in real estate investment trusts. After the financial crisis in 2008, the sponsor of the fund introduced the mandate to account for potential “Black Swan” scenarios in its routine portfolio construction reviews, because it may be impossible to make any sudden, major changes to such a large portfolio or put on any hedge even with, say, 6 months of visibility in the event that such a “Black Swan” event does happen. At the same time, the fund cannot and will not generate a healthy medium to long-term return if it is “permanently” positioned to avoid extreme events. John wants to find an optimal asset allocation that can take into account low-probability extreme events for a multi-asset portfolio. John’s “Black Swan” Scenarios: On July 30th 2014, Argentina defaulted again by not paying its bondholders after its last default 12 years ago. (See Appendix Sec I.1) John is concerned that Argentina’s default can trigger ripple effects in the global financial markets and may significantly impact his portfolio’s performance. In order to protect the sponsor’s wealth from excessive risk exposures and potential devaluation impacts, John wants to estimate what needs to be done to rebalance such a portfolio. Therefore, he comes up with three possible market outcomes from Argentina’s default, which he describes as “Selective Default”, “Managed Default”, and “Destructive Default” scenarios with different shocks on Figure 2: Three Argentina default scenarios with market shocks chosen market indices (Figure 2). Practical Criteria John starts with the classic approach of maximizing portfolio Sharp Ratio. He first obtains the expected return of each asset under each scenario (See Appendix Sec II 4). Based on these expected returns, he calculates the optimal asset allocation under each scenario. The absolute changes in portfolio positions total from 139% to 166%, and the resulting portfolios concentrate on a few assets (See Appendix Sec II 3 & 4). The key disadvantages of this naïve 2 2 HedgeSPA November 2014 Sophisticated Investment Analytics | Trusted Market Insights approach are: a) not knowing which scenario to choose in advance and b) the potentially high transaction costs if he changes his views. John is also concerned about several practical considerations before choosing a specific implementation: 1. If the portfolio is structured based on any specific black swan scenario, it will result in a “corner solution” concentrated in a few assets, rather than a full range of diversified assets. From one corner solution to the next (after a change in investment view) will result in yet another major change in weights; this approach may not be practical because no one knows exactly which scenario may happen. 2. The existing market views should be medium to long term in order to be consistent with investment goal. Otherwise, the high transaction costs from dramatic moves from existing scenarios will exceed any expected benefits from portfolio rebalancing. 3. There should be some evidence of appropriate trade-offs between risks and return. Solution In order to address the practical criteria above, John is going to use the Black-Litterman model to obtain an optimal asset allocation. He picks the Argentina Managed Default scenario and defines four user inputs for this model (See Appendix Section II 5). By varying only the confidence level, John compares the different sets of optimal asset allocation and believes that the confidence level of 80-95%, resulting in a total weight change of a few percentages, may keep the overall weight adjustments to be relatively reasonable (See Figure 3). CL 0% (Tau =0.01) 20% (Tau =0.01) 40% (Tau =0.01) 60% (Tau =0.01) 80% (Tau =0.01) 95% (Tau =0.01) 100% (Tau =0.01) 95% (Tau =0.1) Asset Weight Abs Weight Abs Weight Abs Weight Abs Weight Abs Weight Abs Weight Abs Weight Abs Chg Chg Chg Chg Chg Chg Chg Chg 1 10.29% 0.00% 10.29% 0.00% 10.27% 0.02% 10.26% 0.03% 10.20% 0.09% 9.93% 0.36% 3.38% 6.91% 8.15% 2.14% 2 4.84% 0.00% 4.84% 0.00% 4.85% 0.01% 4.86% 0.02% 4.90% 0.06% 5.10% 0.26% 0.00% 4.84% 4.05% 0.79% 3 4.88% 0.00% 4.86% 0.02% 4.83% 0.05% 4.77% 0.11% 4.58% 0.30% 3.58% 1.30% 0.00% 4.88% 0.00% 4.88% 4 4.09% 0.00% 4.09% 0.00% 4.10% 0.01% 4.11% 0.02% 4.15% 0.06% 4.33% 0.24% 9.95% 5.86% 6.07% 1.98% 5 5.97% 0.00% 5.97% 0.00% 5.98% 0.01% 5.99% 0.02% 6.01% 0.04% 6.14% 0.17% 6.50% 0.53% 6.20% 0.23% 6 7.24% 0.00% 7.25% 0.01% 7.26% 0.02% 7.28% 0.04% 7.36% 0.12% 7.74% 0.50% 7.16% 0.08% 6.70% 0.54% 7 5.17% 0.00% 5.16% 0.01% 5.15% 0.02% 5.13% 0.04% 5.07% 0.10% 4.73% 0.44% 0.00% 5.17% 0.42% 4.75% 8 2.39% 0.00% 2.40% 0.01% 2.41% 0.02% 2.42% 0.03% 2.48% 0.09% 2.77% 0.38% 7.37% 4.98% 4.40% 2.01% 9 8.10% 0.00% 8.09% 0.01% 8.09% 0.01% 8.07% 0.03% 8.02% 0.08% 7.76% 0.34% 6.47% 1.63% 7.54% 0.56% 10 5.74% 0.00% 5.73% 0.01% 5.73% 0.01% 5.71% 0.03% 5.66% 0.08% 5.39% 0.35% 0.00% 5.74% 3.39% 2.35% 11 22.10% 0.00% 22.10% 0.00% 22.07% 0.03% 22.05% 0.05% 21.96% 0.14% 21.53% 0.57% 13.45% 8.65% 18.25% 3.85% 12 8.33% 0.00% 8.35% 0.02% 8.38% 0.05% 8.44% 0.11% 8.62% 0.29% 9.58% 1.25% 25.22% 16.89% 13.23% 4.90% 13 6.74% 0.00% 6.75% 0.01% 6.76% 0.02% 6.79% 0.05% 6.86% 0.12% 7.28% 0.54% 14.83% 8.09% 17.25% 10.51% 14 4.12% 0.00% 4.12% 0.00% 4.12% 0.00% 4.12% 0.00% 4.13% 0.01% 4.14% 0.02% 5.66% 1.54% 4.36% 0.24% Total 100.00% 0.00% 100.00% 0.10% 100.00% 0.28% 100.00% 0.58% 100.00% 1.58% 100.00% 6.72% 100.00% 75.80% 100.00% 39.73% Portfolio Change Figure 3: Optimal Asset Weight Allocation by Black-Litterman Model with Different Confidence Level (tau = 0.01) Note: Last column is calculated with tau =0.1 and confidence level 95% 3 12 HedgeSPA November 2014 Sophisticated Investment Analytics | Trusted Market Insights Multiple Scenarios Asset New Original Abs Weights Weights Chg Even though John can use the Black-Litterman model to get the 1 2.04% 10.29% 8.3% 2 3.27% 4.84% 1.6% desired outcome for one particular scenario, the textbook 3 42.08% 4.88% 37.2% 4 1.15% 4.09% 2.9% approach may not give him a pragmatic solution.