How to Measure Systematic Risk

Transcription

1 W WINDHAM the windham systemic risk index Windham Investment Review Mark Kritzman May, 2010 Windham Capital Management, LLC 5 Revere Street Cambridge, MA

2 the windham systemic risk index In the wake of the near collapse of the world financial system, both regulators and investors have become intensely interested in monitoring systemic risk. Yet, in order to monitor systemic risk first we must know how to measure it, and this task has proved unusually challenging. Securitization, for example, obscures connections among stakeholders. Private transacting leads to opacity. Complexity reduces transparency.¹ And flexible accounting² hides financial linkages. These impediments prevent us from directly observing the explicit linkages among financial institutions and across the broader economy. As an alternative, Windham has developed a method for inferring systemic risk from asset prices. Our method measures the degree to which a market is tightly coupled or compact. Compact markets are fragile because they enable shocks to spread more quickly and broadly than when markets are loosely linked. Consider, for example, an unanticipated jump in energy prices that occurs when markets are loosely connected. It is likely that airline stocks and other companies that are highly dependent on fuel consumption will fall in price. But it is unlikely that industries less dependent on energy prices will experience a significant selloff. However, when markets are highly unified an unanticipated jump in energy prices is more likely to impact a wide range of disparate industries not fundamentally connected to energy prices, leading to a broad market selloff. Windham s methodology captures the extent to which a market is tightly or loosely coupled by measuring the fraction of market variability explained by a fixed number of factors. If a set of factors explains a large fraction of total variability, a market is compact and more vulnerable to shocks. If the same set of factors explains only a small fraction of total variability, a market is more diversified and less vulnerable to specific shocks. ¹Lehman Brothers, for example, had 900,000 derivative contracts on its books when it defaulted. 2Euphemism for accounting practices such as Lehman Brothers use of repurchase agreements to conceal $50 billion of debt shortly before its demise. 1

3 01 Systemic Risk and Stock Prices measures the current level of systemic risk relative to a long-term average level of systemic risk, based on the daily returns of over 50 industries. This particular construction of systemic risk captures shifts in systemic risk, which is more informative than the absolute level of systemic risk. Exhibit 1 offers persuasive evidence that the Windham Systemic Risk Index serves as a reliable indicator of market fragility. It reports the fraction of major stock market selloffs that were preceded by a spike in the index. Exhibit 1: Fraction of drawdowns preceded by spike in WSRI Fraction of drawdowns preceded by spike in WSRI January 1, January 31, % Worst 2% Worst 5% Worst 1 Day 87.50% 84.13% 73.42% 1 Week 81.25% 80.95% 76.58% 1 Month % 98.41% 89.81% For example, all of the 1% worst monthly drawdowns were preceded by a spike in the index. Furthermore, a very high percentage of other significant drawdowns occurred after the index spiked. Although most major drawdowns followed spikes in the Windham Systemic Risk Index, not all spikes were followed by drawdowns. There were a number of false positives, which should be expected given that the index captures the stock market s vulnerability. Major drawdowns typically require both a vulnerable market and a negative shock. Nonetheless, average stock market performance is much lower following a spike up in the index than when the index falls sharply. 2

4 Exhibit 2 shows the annualized one-day, one-week, and one-month returns following spikes and sharp drops in the index. Exhibit 2: Annualized Return after Spikes and Declines These differences in performance following spikes and declines in systemic risk suggest that investors may be able to improve performance by varying exposure to stocks in accordance with signals from the index. We test this notion by applying the following trading rule: following a spike in the Windham Systemic Risk Index we reduce the stock exposure of an otherwise equally weighted portfolio of stocks and government bonds to 0%, and we increase it to 100% following a sharp decline. The results of this experiment are shown in Exhibit 3. 3

5 Exhibit 3: Cumulative Wealth All-stock Dynamic Not only did this dynamic trading rule generate substantially more wealth than both a 50/50 stock/ bond portfolio and an all stock portfolio, it did so with much less volatility, as evidenced by the steadier progression of wealth accumulation. 4

6 Exhibit 4 sheds more light on how this trading rule added value. It shows the stock exposure of the dynamic trading rule coincident with the level of the MSCI USA stock index. Exhibit 4 Stock Exposure MSCI USA Price Index MSCI USA Price Index Stock Exposure As one should expect, the Windham Systemic Risk Index produced several false positives throughout the period, but not nearly enough to offset the signals to reduce stock exposure throughout most of the Dot Com meltdown and all of the global financial crisis. Moreover, the index led investors back to stocks in time to capture the long bull market between these two major selloffs and to participate in the post crisis recovery. We do not have daily industry returns to test the index in earlier periods, but we are able to test its efficacy in other stock markets. Exhibit 5 shows that this trading rule improved performance in foreign markets as well. 5

7 Exhibit 5: WSRI Global Performance 02 Systemic Risk and Financial Turbulence In the Winter 2008 edition of the Windham Investment Review, we discussed a statistical procedure for measuring financial turbulence, which captures the unusualness of a contemporaneous set of returns, taking into account extreme price moves, decoupling of correlated assets, and convergence of uncorrelated assets. We showed that these statistically unusual returns tended to coincide with widely recognizable turbulent events, such as the 1987 stock market crash, the Gulf war, Russia s default on its sovereign debt, and the global financial crisis. In related research we offered strong evidence that returns to risk were much lower during turbulent periods than non-turbulent periods, indicating that investors might benefit from an early warning signal of financial turbulence.³ Our evidence suggests that the Windham Systemic Risk Index would have provided such a signal. We next describe how we came to this conclusion. We first identified the 10% most turbulent 30-day periods, based on the average daily turbulence of the MSCI USA stock index from January 1, 1997 through January 10, We then synchronized these 30-day turbulent periods and examined the average behavior of the Windham Systemic Risk Index in the days leading up to the beginning of turbulent periods, throughout the turbulent periods, and in the days following the turbulent periods. 3See, for example, Kritzman, M. and Y. Li, Skulls, Financial Turbulence, and Risk Management, forthcoming, Financial Analysts Journal. 6

8 Exhibit 6 Turbulence WSRI steadily retreats WSRI rises 40 days prior to beginning of turblence Time (in days) Exhibit 6 reveals that the Windham Systemic Risk Index rose sharply about 40 days prior to the beginning of the turbulent periods, and continued to rise throughout the turbulent episodes. Shortly after the conclusion of the turbulent periods, the index peaked and then steadily retreated. This experiment suggests that systemic risk is a reliable precursor of financial turbulence. 03 Summary measures the extent to which a market is more or less compact. Compact markets are fragile because they enable shocks to propagate more quickly and broadly than markets that are highly diverse. We have provided persuasive evidence that this index is related to changes in stock prices both in the U.S. and in foreign markets, as well as financial turbulence. Although high index values were not always followed by price depreciation and financial turbulence, most major stock market selloffs were preceded by spikes in systemic risk. We think that systemic risk, as we measure it, is a reliable indicator of market vulnerability which, along with other signals of market stress, could help investors to avoid episodes of substantial market weakness. 7