Measuring Risk in Canadian Portfolios: Is There a Better Way?

J.P. Morgan Asset Management (Canada) Measuring Risk in Canadian Portfolios: Is There a Better Way? May 2010 On the Non-Normality of Asset Classes Serial Correlation Fat left tails Converging Correlations Rumi Masih, Head of Strategic Investment Advisory Group, Managing Director, 212-648-1723, rumi.x.masih@jpmorgan.com Ian Ngo, Strategic Investment Advisory Group, Vice President, 212-648-1562, ngo_ian@jpmorgan.com Mark Doyle, Client Advisor, Vice President, 416-981-9109, mark.x.doyle@jpmorgan.com

Asset allocation for Canadian pension plans: 2000-2008 Increasing diversification over time Total assets (C$bn): 100 80 Pe ercent 60 40 $524.3 $645.2 $815.6 5.2 27.0 27.9 0.8 1.4 1.5 3.4 2.7 1.4 6.4 5.7 3.6 2.5 10.0 28.3 24.6 23.9 14.5 20 37.5 35.9 35.8 0 2000 2004 2008 Fixed income Series1 PE/VC Canadian equities Global equities Real estate Infrastructure Hedge funds Other Source: Pension Investment Association of Canada Note: Includes Canadian corporate, public and multi-employer plans >C$100mm in assets 1

Allocation to alternatives fell to 17% at year-end 2009 after equities rebounded However largest plans are much more diversified Top 5 plans 1 ($335bn) Ex-Top 5 plans ($585bn) Fixed income Infrastructure Canadian equities Hedge funds Global equities PE/VC Real estate Other Alternatives 27.3% 6.1% 3.3% 6.5% 3.6% 24.0% 2 Alternatives 1.3% 2.2% 10.6% 1.0% 6.1% 2.1% 38.9% 11.4% 26.7% 16.4% 28.7% Source: Canadian Institutional Investment Network Note: Includes plans >C$100mm in assets 1 Includes the 5 largest pension plans in Canada CPPIB, OTPPB, OMERS, QGPERP and PSP. 2 Includes net negative cash positions of -1.6% 21.6% 2

Unprecedented losses in the markets Year end performance 2008 10 6.4 0-10 -6.5 Percent -20-30 -21.6-13.2-40 -50 Canada Bonds -33.0 Canada Equity -39.0 U.S. Equity -41.6-41.5 International Equity Emerging Markets Equity -42.8 U.S. Private Equity U.S. Hedge Fund of Funds Commodities U.S. Real Estate Representative index return for asset class: Canada Bonds: DEX Universe Bond U.S. Hedge Fund of Funds: HFRI Fund of Funds Canada Equity: S&P/TSX Composite Commodities: Dow Jones UBS Spot U.S. Equity: S&P 500 U.S. Real Estate: NCREIF Property Index International Equity: MSCI EAFE Emerging Markets Equity: MSCI EM U.S. Private Equity: Wilshire U.S. Micro Cap For illustrative purposes only. All benchmarks sourced from Morningstar Encorr (Ibbotson), Bloomberg, HFRI, and JPMorgan as of December 31, 2008 3

Traditional mean-variance optimization frameworks are inadequate for risk measurement and management Two specific weaknesses underestimate portfolio risk: assumption of normal distributions standard deviation as primary risk quantifier Key Take-Aways from non-normality Implies Higher Portfolio Risks Different Efficient Asset Allocations 4

Forms of non-normality ignored by traditional frameworks A traditional mean-variance framework fails to incorporate three forms of non-normality: serial correlation fat left tails correlations converge Conclusion: Relying on traditional mean-variance models for asset allocation or risk management purposes underestimates downside risk 5

Serial Correlation leads to underestimation of true risk Occurs when one period s return is correlated to the previous period s return, inducing dependence over time one month s return is influenced by the previous month s return Benchmark index Evidence of serial correlation Canadian Aggregate Bond DEX Universe Bond No Canadian Large Cap Equity S&P/TSX Composite Yes U.S. Large Cap S&P 500 No International Equity MSCI EAFE Yes Emerging Markets Equity MSCI EM Yes U.S. Private Equity Wilshire U.S. Micro Cap Yes U.S. Hedge Fund of Funds HFRI Fund of Funds Yes Commodities Dow Jones UBS Spot No Source: J.P. Morgan Asset Management. For illustrative purposes only. For asset classes that do not show evidence of serial correlation, we show the Q-statistic and associated p-value at lag six. For asset classes that do exhibit serial correlation, we show the Q-statistic and associated p-value at the statistically significant lag level. Note: All return series are CAD dollar denominated. Hedged asset classes, assumes buying a 1month Forward contract on CAD/USD to lock in exchange rate implied by the Forward Curve in the FX market. 6

and the differences can be quite high Standard deviation before and after unsmoothing for Serial Correlation Annualized before "unsmoothing" Annualized after "unsmoothing" 35 33.2 Percent 30 25 20 15 21.9 16.7 16.1 20.9 20.8 27.6 25.2 10 5 0 Canadian Large Cap Equity International Equity Emerging Markets Equity U.S. Private Equity Source: J.P. Morgan Asset Management. For illustrative purposes only. Based on 10 years of monthly data to October 2009. 7

Fat left tails leads to increased downside risk Occurs when extreme negative returns are observed, with a greater magnitude and frequency than implied by the normal distribution specifically the left tail of the probability density function Benchmark index Fat left tail compared to normal Canadian Aggregate Bond DEX Universe Bond No Canadian Large Cap Equity S&P/TSX Composite Yes U.S. Large Cap S&P 500 Yes International Equity MSCI EAFE Yes Emerging Markets Equity MSCI EM Yes U.S. Private Equity Wilshire U.S. Micro Cap No U.S. Hedge Fund of Funds HFRI Fund of Funds Yes Commodities Dow Jones UBS Spot No Source: J.P. Morgan Asset Management. For illustrative purposes only. We formally tested for departure from normality of a sample by applying the Jarque-Bera (J-B) test. The J-B test statistic is defined as Jarque-Bera = N/6 * (S2 + (K-3)2 / 4) where S is the skewness, and K is the kurtosis. Note: All return series are CAD dollar denominated. Hedged asset classes, assumes buying a 1month Forward contract on CAD/USD to lock in exchange rate implied by the Forward Curve in the FX market. 8

Observed distribution, very different than normal Fatter left tail in Canadian Large Cap Equity leads to greater likelihood of losses 12 10 %) 8 Observed Density ( 6 4 Fat left tail Normal 2 0-0.20-0.15-0.10-0.05 0.00 0.05 0.10 0.15 0.20 Return (%) Source: J.P. Morgan Asset Management. For illustrative purposes only. Based on 10 years of monthly data to October 2009. 9

Converging correlations reduce diversification benefits Correlations over seven years ending December 2007 7 Years 1 2 3 4 5 6 7 8 1. Aggregate Bonds 1.00 2. Canadian Equity -0.06 1.00 3. U.S. Large Equity -0.16 0.76 1.00 4. International -0.18 0.75 0.85 1.00 5. Emerging Markets Equity -0.09 0.71 0.66 0.72 1.00 6. U.S. Private Equity 0.01 0.71 0.59 0.63 0.64 1.00 7. U.S. Hedge FOFs 0.09 0.69 0.43 0.54 0.63 0.78 1.00 8. Commodities 0.02 0.14-0.10-0.02 0.14-0.09 0.07 1.00 Correlations over one year ending December 2008 1 Years 1 2 3 4 5 6 7 8 1. Aggregate Bonds 1.00 2. Canadian Equity 0.34 1.00 3. U.S. Large Equity 0.33 0.81 1.00 4. International 0.38 0.83 0.93 1.00 5. Emerging Markets Equity 0.58 0.81 0.82 0.90 1.00 6. U.S. Private Equity 0.25 0.77 0.93 0.85 0.77 1.00 7. U.S. Hedge FOFs 0.32 0.97 0.73 0.80 0.81 0.72 1.00 8. Commodities 0.13 0.63 0.15 0.18 0.33 0.15 0.67 1.00 Source: J.P. Morgan Asset Management. For illustrative purposes only. All return series are CAD dollar denominated. Hedged asset classes, assumes buying a 1month Forward contract on CAD/USD to lock in exchange rate implied by the Forward Curve in the FX market. 10

How do we allow for each form of non-normality? Serial Correlation Unsmoothing Rx Fat left tails Extreme Value Extreme Value Theory Theory Rx Converging Correlations Copula Theory Rx 11

Conditional value at risk as a better risk quantifier Standard deviation may not be appropriate desirable upside movements equally compared to undesirable downside movements only valid under a Mean Variance framework Conditional Value at Risk (CVaR 95 ) overcomes many standard deviation drawbacks captures asymmetric risk preferences investors prefer to avoid large losses than making large gains incorporates the incidence of fat left tails closely related to Value at Risk a measure already widely used 12

and it s intuitive We define CVaR 95 as simply the average real loss in the worst 5% of 10,000 Monte Carlo simulations the left tail of the portfolio distribution Histogram of projected cumulative portfolio loss assuming non-normality Frequency 1,100 1,000 900 800 700 600 500 400 300 200 100 0 Portfolio CVaR 951 : Initial value: Normal: $1,000mm $43mm -548-104 341 785 1,230 1,674 2,119 2,563 3,008 3,452 3,897 4,341 4,786 5,230 5,675 Source: J.P. Morgan Asset Management. For illustrative purposes only. 1 Asset mix of average plan for year-end 2009 Expected portfolio gain (loss) at the end of ten years ($mm) Non-normal: $269mm % difference: 522% 13

Incorporating non-normality of returns implies significantly higher portfolio risk Hypothetical efficient frontier based on non-normal distribution of returns Expected compound return (% per year) Normal framework Non-normal Mean CVaR framework Conditional value at risk 95 ($mm) Significantly higher portfolio risk implies that the efficient frontier shifts to the right Source: J.P. Morgan Asset Management. For illustrative purposes only. 14

Reducing portfolio risk: Examples Canadian pension plans (non-normal framework) (%) Non-normal portfolio example #1 (%) Non-normal portfolio example #2 (%) Fixed Income 33.9 30.0 35.0 Canadian Equity U.S. Equity International Equity Emerging Markets Equity Total Equity 20.2 13.4 13.4 1.5 48.5 15.0 15.0 15.0 5.0 50.0 10.0 10.0 10.0 5.0 35.0 Private Equity Hedge Funds Commodities Real Estate & Infrastructure Total Alternatives 4.0 2.2 0.0 11.5 17.7 5.0 5.0 5.0 5.0 20.0 5.0 10.0 5.0 10.0 30.0 Total Assets 100.0 100.0 100.0 Expected Arithmetic Return Expected Volatility Expected Compound Return Sharpe Ratio CVaR95 ($mm) Allowing for Non-normality Risk Reduction 7.6 8.0 7.3 0.45 $269 7.8 8.5 7.5 0.45 $236-12.2 7.5 7.0 7.3 0.50 $185-31.0 Source: J.P. Morgan Asset Management, Canadian Institutional Investment Network. For illustrative purposes only. Allocation to Other has been prorated. 1 Average Canadian pension fund -2009. As of 12/31/2009 for Canadian pension plans >C$100mm in assets. Analysis based on J.P. Morgan s long-term Capital Market s Assumptions. Sharpe Ratio calculated by using a 10Yr T-Bill value of 4% as the risk free rate. 15

Summary Risk assessment and modeling tools, based on Mean Variance Theory, need to better account for the different forms of non-normality serial correlations fat left tails converging correlations Risk measures (standard deviation) that rely on Mean Variance Theory tend to underestimate risk within a portfolio Most asset classes (not just alternatives) display some form of non-normality J.P. Morgan Asset Management has developed a framework to attempt to account for the phenomena of non-normality using theoretical approaches that have been vetted by academia and other industry practitioners 16

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Strategic Investment Advisory Group (SIAG) Investment and pension finance expertise Rumi Masih, SIAG Group Head Perspective Share experiences best practices Over 10 years industry experience PhD in Econometrics, University of Cambridge Published over 60 articles in the fields of macroeconomics, development economics, and empirical finance Fellow to the Financial Management Association, and the Royal Statistical Society Recipient of three best paper prizes at internationally reputed annual finance conferences sponsored by the Chicago Stock Exchange, Financial Mgmt Association and SWFA Listen to our clients understand their needs Strategic thinking, with tactical application What does the future hold? Uncover new opportunities Thoughts on solving problems Competitive Intelligence Market Commentary Research & Thought Leadership Produce compelling, market driven publications: the Case for Asia more than a growth story an assessment of the Unique Nature of OPEB obligations non-normality of Market Returns how adding an asset manager with fewer constraints may improve the risk/return of your portfolio Deliver intellectual capital Generate new ideas for clients Distill research for practical use Client Analyses Portfolio reviews Asset Class and Manager optimizations Risk budgeting Capital Markets Calculator Surplus optimizations Asset/liability analysis Liability & required return analysis Corporate Finance and Peer Group Analysis 18 18

Foreign exchange between Canadian Dollar and U.S. Dollar CAD/USD exchange rate 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Jun-94 Jun-96 Jun-98 Jun-00 Jun-02 Jun-04 Jun-06 Jun-08 Source: DataStream, J.P. Morgan 19

Statistical techniques applied to incorporate non-normality Sophisticated methods allow us to attempt to correct for non-normality Unsmoothing serial correlation (Fisher-Geltner-Webb methodology variation) restore independence to single-period returns adjusted return series is more reflective of asset class risk characteristics unsmoothed return stream has the same mean as the original return stream, but shows higher volatility thus higher downside risk Modeling Fat left tails (Extreme Value theory) create asset return distributions that are a closer fit to real world return series better estimates the probability of high-risk, low-probability events Simulating correlation breakdown (Copula theory) improved model of the increased incidence of negative joint returns (when asset class returns move down together) turning focus to how asset classes behave together, rather than individually more accurate model of asset class behavior during periods of market stress 20

Incorporating non-normality Summary of model Step 1: Input historical data Step 2: Remove serial correlation from returns Unsmoothed data Step 3: fit marginal distributions (using Extreme Value theory) to allow for fat left tails Step 4: Calibrate Student t copula to allow for joint fat tails i.e. increased dependence during periods of market stress Source: J.P. Morgan Asset Management. For illustrative purposes only. 21

Incorporating the impact of Serial Correlations Step 1 We determine the correlation coefficient at lag one 21 (i.e., previous month s return) for each return series, by running the following regression: R t = a + br t-1 + E Where R t represents the return at time t The regressions indicate the following estimates for the serial correlation coefficients, based on monthly returns Correlation coefficients at lag one b (hat) Statistically significant* International Equity 0.21 Yes Emerging Markets Equity 0.25 Yes Fund of Hedge Funds 0.42 Yes Private Equity 0.21 Yes Step 2 We then produce our unsmoothed return series as follows, based on the serial correlation coefficient already derived: R t (corrected) = (R t b (hat)r t-1 ) / (1 b (hat)) After applying the methodology outlined above, we obtain a new data series (Rt) that should display no serial correlation. Once again we use the Q statistic to test the unsmoothed data for serial correlation. The results are shown below Tests for serial correlation on corrected data for up to six lags Test statistic p-value Evidence of serial correlation International Equity 0.03 0.86 No Emerging Markets Equity 0.06 0.80 No Fund of Hedge Funds 0.04 0.85 No Private Equity 0.05 0.82 No * Statistically significant at the 5% level Source: J.P. Morgan Asset Management. Note the coefficient b reflects the strength of the autocorrelation. 21 Note International Equity, Emerging Markets Equity, Fund of Hedge Funds and Private Equity returns test positive for serial correlation at lag one. For a more detailed treatment, please refer to Fisher, J., D. Geltner, and B. Webb 1994. Value Indices of Commercial Real Estate: A Comparison of Index Construction Methods. Also, Fisher, J. and D. Geltner. 2000. De-Lagging the NCREIF Index: Transaction Prices and Reverse-Engineering. 22

Incorporating the impact of Fat left tails Examining the distribution in pieces Left Tail Interior Right Tail We segment each return distribution into three parts the left tail, right tail, and interior. We then fit each segment of the distribution separately. The left and right tails are fitted using the Generalized Pareto distribution (GPD). This is done by calibrating the tail of the GPD to extreme values in the sample using the Method of Maximum Likelihood. The interior is fitted using a non-parametric empirical approach. In aggregate, we derive a semi-parametric probability density function to describe the data generating process. Source: J.P. Morgan Asset Management. For illustrative purposes only. 23 23

Modeling joint dependence in asset returns using Copulas Hedge Fund of Fund (HFOF) returns vs Equity return in 2,500 simulations Traditional linear correlations Increased joint dependence through Copulas 10 10 Monthly simulated Fund of Hedge Fund returns (%) -20-15 -10-5 8 6 4 2 0 0-2 -4-6 5 10 15 20 Monthly simulated Fund of Hedge Fund returns (%) -20-15 -10-5 8 6 4 2 0 0-2 -4-6 5 10 15 20-8 -8-10 -10 Monthly simulated U.S. Equity returns (%) Monthly simulated U.S. Equity returns (%) The Copula increases the incidence of negative HFOF returns accompanied by negative Equity returns, i.e. the effect of Converging Correlations Source: J.P. Morgan Asset Management. For illustrative purposes only. 24

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