Turbulence, Systemic Risk, and Dynamic Portfolio Construction

Transcription

1 Turbulence, Systemic Risk, and Dynamic Portfolio Construction Will Kinlaw, CFA Head of Portfolio and Risk Management Research State Street Associates 1 Outline Measuring market turbulence Principal components as a measure of systemic risk Application I: Market timing Application II: Dynamic allocation to risk factors Summary 2

2 Measuring market turbulence 3 Measuring Turbulence: Better Risk Estimates We calculate rates of return by subtracting the price at the beginning of the period from the price at the end of the period, adding income, and dividing by the price at the beginning of the period. In many periods, however, there are no significant events that should cause prices to change; hence the returns we observe merely reflect the fact that prices are noisy. In other periods, such as August 1998 and September 2008, prices legitimately shift in response to significant events. Despite this difference in return generation, the formulas we use to calculate standard deviation and correlation assign as much importance to periods with no events as they do to periods with significant events. It is therefore useful to partition historical returns into those that reflect noise and those that are driven by events, and to estimate risk parameters from these sub-samples of quiet and turbulent markets. 4

3 The Turbulence Index How we define financial turbulence: 1 dt = ( yt μ) Σ ( yt μ)' / N d t = vector distance from multivariate average y t = return series μ = mean vector of return series y t Σ = covariance matrix of return series y t 5 Two Assets Normal vs. Turbulent Bonds Bonds Stocks Stocks 6

4 Turbulence Across Markets (30-day moving avg) Global Asset Class Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan-11 8 US Equity Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan European Equity 5 0 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan-11 8 Currency Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan-11 7 Fixed Income Markets US Fixed Income Historic Low Volatility Bear Stearns Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan-11 8 US Treasury 6 4 9/11 Iraq War 2 0 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan US Credit Accounting Scandals Credit Crisis 0 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan Sovereign Debt Greek Debt Crisis Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan- Jan-11 8

5 Turbulence and Market Performance 20% % 7.9% Full Sample Annualized Return 0% -% -20% -12.3% -9.8% 90% Non-Turbulent Annualized Return % Most Turbulent Annualized Return -30% -24.7% -26.4% -40% World Equity Small - Large Value - Growth Carry Hedge Funds * Turbulent periods are identified using USD-denominated daily values of the Turbulence Index constructed for Global Asset Allocation (World Equity), US Sectors (Size Premium and Value Premium), and Developed Currencies (Carry) over the time period 4 January 1993 through 31 December Monthly Turbulence Index values for Global Asset Allocation over the period January 1993 through December 2008 are used for Hedge Funds. Raw turbulence values are multivariate distances using a full-sample covariance matrix. The market returns are daily returns of MSCI World (World Equity), Russell 2000 minus S&P 500 (Size Premium), Russell 00 Value minus Russell 00 Growth (Value Premium), and a naïve carry strategy over the same time period. Monthly hedge fund returns are from HFRI fund of funds composite. 9 How Persistent is Turbulence? Average level of turbulence following a % outlier Next 5 Days Next Days Next 20 Days th Percentile Threshold Global Assets 2.31 (7%) 2.22 (8%) 2.13 (9%) 1.93 US Assets 2.98 (5%) 2.90 (5%) 2.79 (6%) 1.95 US Sectors 3.12 (5%) 3.04 (6%) 2.87 (6%) 2.03 Currency 2.08 (8%) 1.93 (9%) 1.80 (11%) 1.83 US Fixed Income 4.05 (4%) 3.85 (5%) 3.60 (5%) 2.12 US Treasuries 3.19 (5%) 3.13 (6%) 2.96 (6%) 2.00 US Credit 4.17 (4%) 4.09 (4%) 3.69 (4%) 1.61 * Based on all available history for each index. Raw turbulence values are multivariate distances using a full-sample covariance matrix. Global Assets begin 4 January 1993, Domestic Assets begin 1 August 1989, US Sectors begin 3 January 1973, Currency begins 2 January 1975, US Fixed Income begins 11 December 2000, US Treasuries begin 1 September 1998, and US Credit begins 7 August Each value in parentheses shows where the average level of turbulence falls, as a percentile from the maximum turbulence value.

6 Principal components as a measure of systemic risk 11 Principal components as a measure of systemic risk* It is unlikely that we can directly observe the explicit linkages of financial institutions due to many factors such as the opacity of private transactions, the complexity of securitization, and flexible accounting. As an alternative, we introduce a measure of implied systemic risk based on market price behavior. The Systemic Risk Index represents the fraction of the total variance of a set of asset returns explained or absorbed by a finite number of eigenvectors. A high index value implies that markets are compact or tightly coupled. Compact markets are relatively fragile in that shocks propagate more quickly and broadly than when markets are loosely linked. * Kritzman, M., Y. Li, S. Page and R. Rigobon. Principal Components as a Measure of Systemic Risk. Revere Street Working Paper Series: Financial Economics , updated June 21,

7 A brief refresher on principal component analysis 1. Scatter plot returns, and draw all possible vectors through the data set 2. Project data points onto each vector 3. Identify the vector associated with the greatest volatility as the first eigenvector 4. Repeat this process for the second eigenvector, searching only in a plane perpendicular to the first eigenvector 13 The Systemic Risk Index AR = n 2 i= 1σ Ei N 2 j= 1σ E j AR : N n : 2 σ E i : : absorption ratio number of assets number of eigenvectors used to calculate absorption ratio variance of the i-th eigenvector * Variances are estimated using exponentially decayed returns 14

8 Absorption ratio and U.S. stocks The covariance matrix and eigenvectors are estimated from daily returns over the prior 500 days. The absorption ratio is estimated from the first eigenvectors. 15 The Systemic Risk Index and drawdowns Fraction of drawdowns preceded by spike in SRI 1% Worst 2% Worst 5% Worst 1 Day 81.82% 76.92% 63.98% 1 Week 81.82% 80.00% 70.81% 1 Month 0% 98.46% 86.96% Annualized return after extreme SRI 1 Sigma Increase 1 Sigma Decrease Difference 1 Day -6.75% 12.39% % 1 Week -7.93% 11.45% % 1 Month -6.16% 8.72% % * We first compute the moving average of the Systemic Risk Index over 15 days and subtract it from the moving average of the index over one year. We then divide this difference by the standard deviation of the index over the one-year time period. Results cover the period from January 1 st,1998 through May 5 th,20. 16

9 Application I: Market timing 17 The Systemic Risk Index as a market timing signal Trading Rule Systemic Risk Index* Stock / Bond Exposure -1σ Index +1σ 50 / 50 Index > +1σ 0 / 0 Index < -1σ 0 / 0 Performance Dynamic Static (50/50) Return.49% 5.84% Risk 12.05%.74% Return/Risk Max. Drawdown 12.46% 26.26% 9th Dec 1997 through 31st Dec 20, 2.22 trades per year, 1% turnover * We compute a standardized shift to construct this trading rule. We first compute the moving average of the Systemic Risk Index over 15 days and subtract it from the moving average of the index over one year. We then divide this difference by the standard deviation of the index over the oneyear time period. 18

10 The Systemic Risk Index as a market timing signal 19 Application II: Dynamic allocation to risk factors 20

11 Motivation Harvey and Dalquist (2001) suggest that if economic conditions are (1) persistent and (2) strongly linked to asset performance, then a dynamic asset allocation process should add value. We employ Maximum Likelihood Estimation to build a simple regime-switching model for the following variables: FX market turbulence [December 1977 through December 2009] Equity market turbulence [December 1975 through December 2009] Inflation (CPI) [February 1947 through December 2009] Gross National Product [April 1947 through December 2009] We then measure the conditional performance of a variety of risk premia and asset classes during each regime. 21 In-sample Markov-Switching results Regime 1 Regime 2 ( event regime ) Persistence* Mu Sigma Persistence* Mu Sigma Equity Turbulence 92% % Currency Turbulence 92% % Inflation Rate 98% 2.62% 0.70% 95% 6.66% 1.81% Economic Growth 90% 1.09% 0.84% 68% -0.14% 0.96% *Persistence is defined as the estimated transition probability of staying in the current regime. 22

12 Probability that the event regime prevails End of energy crisis Recession of early 1980s 1987 stock market crash Equity Turbulence Recession of early 1990s Dot-com bubble / collapse Recent financial crisis 0% 80% 60% 40% 20% 0% 12/75 12/77 12/79 12/81 12/83 12/85 12/87 12/89 12/91 12/93 12/95 12/97 12/99 12/01 12/03 12/05 12/07 12/09 Brief run on USD NZD begins to float and USD/GBP speculation Plaza Accord Currency Turbulence ERM crisis Asian financial crisis Russian default Sept 11, 2001 Recent financial crisis 0% 80% 60% 40% 20% 0% 12/77 12/79 12/81 12/83 12/85 12/87 12/89 12/91 12/93 12/95 12/97 12/99 12/01 12/03 12/05 12/07 12/09 23 Probability that the event regime prevails Post-Korean war Vietnam war / high Government spending Inflation Rate Energy crisis and stagflation Brief oil price shock oil shock 0% 80% 60% 40% 20% 0% 02/47 02/52 02/57 02/62 02/67 02/72 02/77 02/82 02/87 02/92 02/97 02/02 02/07 0% 80% 60% 40% 20% 0% Recession Recession of 1947 Recession of 1957 of 1953 Economic Growth Oil crisis Recession of early 1980s Recession of early 1990s Recession of early 2000s Recent financial crisis 04/47 04/52 04/57 04/62 04/67 04/72 04/77 04/82 04/87 04/92 04/97 04/02 04/07 24

13 Risk premia: in-sample performance* (Event Mean - Non-Event Mean) / Full Sample Standard Deviation Global Stocks - Bonds Equity Mkt Neutral HF - Cash Emerging - Developed Equity Small Cap Premium Equity Momentum Credit Spread High Yield Spread Emerging Market Bond Spread FX Carry Strategy** FX Valuation Strategy** Gold - Cash TIPS - Nominal Bonds US Yield Curve (y-2y) Global Stocks - Bonds US Cyclical - Non-Cyclical Stocks Turbulence Inflation Economic Growth * Time period ends in December 2009 and starts at various points (as early as 1947) depending on data availability. ** Based on Currency Turbulence 25 Backtest procedure: Investable risk premia At the beginning of each month in the backtest, we: 1.Calibrate our Markov-Switching model using a growing window of data available up to that point in time. 2.Tilt our risk premia allocation defensively when the model indicates a high probability that an event regime is imminent. 3.Compare the performance of the dynamic risk premia portfolio with the performance of the constant risk premia portfolio. 4.Roll the backtest forward one month and repeat. 26

14 Risk premia tilts Event Regime Tilts Risk Premia Default Exposure Turbulence Recession Inflation Global Stocks Bonds % -5% -5% Small Cap Premium % -5% Equity Momentum % -5% Equity Mk Neutral HF Cash % -5% Emerging Developed Equity % -5% Credit Spread % -5% High Yield Spread % -5% US Yield Curve (y-2y) % -5% Emerging Market Bond Spread % -5% FX Carry Strategy* % -5% Defensive Trades Gold Cash 0% +% TIPS Nominal Bonds 0% +% US Non-Cyclical Cyclical Stocks 0% +% FX Valuation Strategy 0% +% Total Notional Exposure 0% 55% 15% 25% 27 Out-of-sample performance* [Feb Dec 2009] Static Dynamic Annualized Excess Return 5.99% 6.28% Annualized Volatility 8.37% 6.83% Information Ratio Skewness % Value-at-Risk -3.39% -2.72% Maximum Drawdown % % * Includes transaction costs of 40 basis points. The dynamic strategy turns over approximately 1.5 times per year. 28

15 Summary We introduce a measure of financial turbulence that captures periods characterized by extreme returns, the convergence of uncorrelated assets, or the divergence of correlated assets. We provide evidence that (1) there is a link between turbulence and the performance of key risk premia, and (2) turbulence is persistent. We present a method for inferring systemic risk from asset prices, which we call the absorption ratio. A high absorption ratio implies that markets are relatively compact. Compact markets are fragile, because shocks propagate more quickly and broadly. We show how an investor might employ the absorption ratio signal to time exposure to stocks versus bonds. We show how an investor might exploit the turbulence signal along with regime switching models to dynamically allocate exposure across a range of investable risk premia. 29 References Kritzman, M., Y. Li, S. Page and R. Rigobon. Principal Components as a Measure of Systemic Risk. Revere Street Working Paper Series: Financial Economics , updated June 21, 20. Kritzman, M. and Y. Li. Skulls, Financial Turbulence, and Risk Management. The Financial Analysts Journal, May/June 20. Kritzman, M., S. Page, and D. Turkington. Dynamic Portfolio Construction. Revere Street Working Paper Series. 30

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