Turbulence, Systemic Risk, and Dynamic Portfolio · PDF file1 RESEARCH Turbulence, Systemic Risk, and Dynamic Portfolio Construction Will Kinlaw, CFA Head of Portfolio and Risk Management

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Turbulence, Systemic Risk,and Dynamic Portfolio Construction

Will Kinlaw, CFAHead of Portfolio and Risk Management Research

State Street Associates

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Outline

Measuring market turbulence

Principal components as a measure of systemic risk

Application I: Market timing

Application II: Dynamic allocation to risk factors

Summary

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Measuring market turbulence

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• 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.

Measuring Turbulence: Better Risk Estimates

Source: State Street Global Markets

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The Turbulence Index

dt = vector distance from multivariate averageyt = return seriesμ = mean vector of return series ytΣ = covariance matrix of return series yt

How we define financial turbulence:

Nyyd ttt /)'()( 1 μμ −Σ−= −

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Two Assets Normal vs. Turbulent


Stocks

Bon

ds

Stocks

Bon

ds

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Turbulence Across Markets (30-day moving avg)

0

2

4

6

8

10

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-10 Jan-11

Global Asset Class

0

2

4

6

8

10


US Equity

0

5

10

15

20


European Equity

0

2

4

6

8

10


Currency

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02468

101214


US Fixed Income

0

2

4

6

8

10


US Treasury

0

5

10

15

20


US Credit

02468

101214


Sovereign Debt


Fixed Income Markets

9/11 Iraq War

Historic Low Volatility

BearStearns

Accounting Scandals

Credit Crisis

Greek Debt Crisis

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* 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 2008. 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 1000 Value minus Russell 1000 Growth (Value Premium), and a naïve carry strategy over the same time period. Monthly hedge fund returns are from HFRI fund of funds composite.

-12.3%

-24.7% -26.4%

-9.8%

7.9%

-40%

-30%

-20%

-10%

0%

10%

20%

World Equity

Small - Large

Value -Growth

Carry HedgeFunds

Full SampleAnnualized Return

90% Non-TurbulentAnnualized Return

10% Most TurbulentAnnualized Return

Turbulence and Market Performance


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How Persistent is Turbulence?

Next 5 Days Next 10 Days Next 20 Days10th 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 1998. Each value in parentheses shows where the average level of turbulence falls, as a percentile from the maximum turbulence value.

• Average level of turbulence following a 10% outlier


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Principal components as a measure of systemic risk

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* Kritzman, M., Y. Li, S. Page and R. Rigobon. “Principal Components as a Measure of Systemic Risk.” Revere Street Working Paper Series: Financial Economics 272-28, updated June 21, 2010.

• 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.

Principal components as a measure of systemic risk*

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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


A brief refresher on principal component analysis

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The Systemic Risk Index

∑∑

=

=N

j E

n

i E

j

i

1

21

2

σσ

AR =

absorption rationumber of assetsnumber of eigenvectors used to calculate absorption ratio

variance of the i-th eigenvector:

: : :AR

2

σ iE

nN

* Variances are estimated using exponentially decayed returns

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• The covariance matrix and eigenvectors are estimated from daily returns over the prior 500 days.• The absorption ratio is estimated from the first 10 eigenvectors.


Absorption ratio and U.S. stocks

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1% Worst 2% Worst 5% Worst

1 Day 81.82% 76.92% 63.98%

1 Week 81.82% 80.00% 70.81%

1 Month 100% 98.46% 86.96%

Fraction of drawdowns preceded by spike in SRI

* 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 1st,1998 through May 5th,2010.

1 Sigma Increase 1 Sigma Decrease Difference

1 Day -6.75% 12.39% -19.14%

1 Week -7.93% 11.45% -19.38%

1 Month -6.16% 8.72% -14.87%

Annualized return after extreme SRI


The Systemic Risk Index and drawdowns

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Application I:Market timing

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The Systemic Risk Index as a market timing signal

Trading Rule

Performance

* 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 one-year time period.

Systemic Risk Index* Stock / Bond Exposure

-1σ ≤ ∆Index ≤ +1σ 50 / 50

∆Index > +1σ 0 / 100

∆Index < -1σ 100 / 0

Dynamic Static (50/50)

Return 10.49% 5.84%

Risk 12.05% 10.74%

Return/Risk 0.87 0.54

Max. Drawdown 12.46% 26.26%

9th Dec 1997 through 31st Dec 2010, 2.22 trades per year, 110% turnover

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The Systemic Risk Index as a market timing signal

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Application II:Dynamic allocation to risk factors

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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.

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In-sample Markov-Switching results

Regime 1 Regime 2 (“event regime”)

Persistence* Mu Sigma Persistence* Mu Sigma

Equity Turbulence 92% 0.65 0.28 90% 1.89 1.13

Currency Turbulence 92% 0.88 0.33 68% 2.14 1.22

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.


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Probability that the event regime prevails

0%20%40%60%80%

100%

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

0%20%40%60%80%

100%

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

Equity Turbulence

Currency Turbulence

End of energy crisis

Recession of early 1980s

1987 stock market crash


Dot-com bubble / collapse

Recent financial crisis

ERM crisis

Asian financial

crisis

Russian defaultSept 11, 2001


Brief run on USD

NZD begins to float and USD/GBP

speculationPlaza

Accord


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Probability that the event regime prevails

0%20%40%60%80%

100%

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

0%20%40%60%80%

100%

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

Inflation Rate

Economic Growth

Post-Korean war

Vietnam war / high

Government spending

Energy crisis and stagflation

Brief oil price shock

2007-2008 oil shock

Recession of 1947 Recession

of 1953

Recession of 1957 Oil crisis


Recession of early 1990s Recession

of early 2000s



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Risk premia: in-sample performance*

(Event Mean - Non-Event Mean) / Full Sample Standard Deviation

-2.00-0.26

-1.68-1.13

-0.34-1.70

-2.37-1.02

-1.880.45

0.900.78

-1.13-1.44

-1.31-2.38

Global Stocks - BondsEquity Mkt Neutral HF - CashEmerging - Developed Equity

Small Cap PremiumEquity Momentum

Credit SpreadHigh Yield Spread

Emerging Market Bond SpreadFX Carry Strategy**

FX Valuation Strategy**Gold - Cash

TIPS - Nominal BondsUS Yield Curve (10y-2y)

Global Stocks - BondsUS 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 Source: State Street Global Markets

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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.

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Risk premia tiltsEvent Regime Tilts

Risk Premia Default Exposure Turbulence Recession Inflation

Global Stocks – Bonds 10% - 5% - 5%

Small Cap Premium 10% - 5%

Equity Momentum 10% - 5%

Equity Mk Neutral HF – Cash 10% - 5%

Emerging – Developed Equity 10% - 5%

Credit Spread 10% - 5%

High Yield Spread 10% - 5%

US Yield Curve (10y-2y) 10% - 5%

Emerging Market Bond Spread 10% - 5%

FX Carry Strategy* 10% - 5%

Defensive Trades

Gold – Cash 0% +10%

TIPS – Nominal Bonds 0% +10%

US Non-Cyclical – Cyclical Stocks 0% +10%

FX Valuation Strategy 0% +10%

Total Notional Exposure 100% 55% 15% 25%


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Out-of-sample performance*

[Feb 1978 - Dec 2009] Static Dynamic

Annualized Excess Return 5.99% 6.28%

Annualized Volatility 8.37% 6.83%

Information Ratio 0.72 0.92

Skewness -1.56 -1.01

5% Value-at-Risk -3.39% -2.72%

Maximum Drawdown -41.48% -32.69%

* Includes transaction costs of 40 basis points. The dynamic strategy turns over approximately 1.5 times per year.


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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.


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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 272-28, updated June 21, 2010.

Kritzman, M. and Y. Li. “Skulls, Financial Turbulence, and Risk Management.” The Financial Analysts Journal, May/June 2010.

Kritzman, M., S. Page, and D. Turkington. “Dynamic Portfolio Construction.” Revere Street Working Paper Series.

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Turbulence, Systemic Risk, and Dynamic Portfolio · PDF file1 RESEARCH Turbulence, Systemic Risk, and Dynamic Portfolio Construction Will Kinlaw, CFA Head of Portfolio and Risk Management