On the non-normality of asset classes

Transcription

1 On the non-normality of asset classes Rumi Masih, PhD Managing Director Abdullah Sheikh, FSA Vice President 0 May 5, 2009

2 Agenda Mean Variance as a leap of faith Non-normality in asset returns Serial Correlation Fat left tails Converging Correlations Incorporating non-normality into asset allocations Optimizations in a non-normal framework Appendix 1

3 Unprecedented losses in the markets Year End Performance 2008 U.S. Equity Int l Equity Global Equity Emerging Markets Equity U.S. Fixed Income Int l Fixed Income Global Fixed Income Emerging Markets Fixed Income Hedge Fund of Funds Real Estate 5.24% 8.01% 9.21% (10.91%) (6.46%) (23.25%) (37.00%) (43.38%) (40.71%) (53.33%) 2 Representative index return for asset class US Equity: S&P 500 Global Fixed Income: Citigroup WGBI hedged International Equity: MSCI EAFE Free- ND EM Fixed Income: JPM EMBI Global Global Equity: MSCI World- ND Hedge Fund of Funds: HFRX Global Hedge Fund EM Equity: MSCI EM- ND Real Estate: NCREIF Property Index US Fixed Income: Barclays Capital Aggregate International Fixed Income: Citigroup Non-US WGBI hedged The above chart is shown for illustrative and discusssion purposes only. All benchmarks sourced from evestments as of December 31, 2008, except for HFRX Global Hedge Fund Index which was sourced from HFRI.

4 Traditional mean-variance optimization frameworks are inadequate for risk measurement and management Broadly, two specific weaknesses in conventional mean-variance frameworks lead to quantifiable underestimation of portfolio risk: assuming normal return distributions for asset classes in the modeling and optimization process using standard deviation as the primary quantifier of portfolio risk The latest statistical methods address these shortcomings. Based on the results presented here, a modified risk framework may help investors improve portfolio efficiency and resiliency Key Take-Aways from non-normality Implies Higher Portfolio Risks Different Efficient Asset Allocations 3

5 Forms of non-normality ignored by traditional frameworks A traditional mean-variance framework fails to incorporate three forms of nonnormality: Serial correlation in returns exhibited by many alternative asset classes over time, underestimating the true volatility of these asset classes by using smoothed return series The phenomenon of fat left tails in financial market returns, particularly, equities and alternatives, underestimating the downside risk from asset classes with leptokurtic distributions The observation that correlations converge during periods of high market volatility, overestimating diversification potential at the total portfolio level Conclusion: Relying on traditional mean-variance models for asset allocation or risk management purposes underestimates downside risk. 4

6 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 Aggregate bonds Barclays Capital Aggregate No U.S. Equity S&P 500 Total Return No International Equity MSCI EAFE (hedged) Yes Emerging Market Equity MSCI Emerging Markets Yes Real Estate Investment Trusts (REITs) FTSE / S&P NAREIT No Fund of hedge funds HFRI Fund of Funds Diversified Yes Private Equity Dow Jones Wilshire Microcap TR Yes 5 Source: J.P. Morgan Asset Management. For illustrative purposes only. All return series are U.S. dollar denominated. 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

7 and the differences can be quite high Standard Deviation before and after unsmoothing for Serial Correlation Percentage Annualized before "unsmoothing" 35.00% Annualized after "unsmoothing" 31.4% 30.00% 29.2% 25.00% 24.2% 23.5% 20.00% 18.9% 15.00% 15.3% 10.00% 5.00% 6.5% 10.3% 0.00% International Equity Emerging Markets Fund of Hedge Funds Private Equity 6 Source: J.P. Morgan Asset Management. For illustrative purposes only. Based on 10 years of monthly data to September 30, Please see slide five for asset class descriptions.

8 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 Aggregate bonds Barclays Capital Aggregate Yes U.S. Equity S&P 500 Total Return Yes International Equity MSCI EAFE (hedged) Yes Emerging Market Equity MSCI Emerging Markets Yes Real Estate Investment Trusts (REITs) FTSE / S&P NAREIT Yes Fund of hedge funds HFRI Fund of Funds Diversified Yes Private Equity Dow Jones Wilshire Microcap TR Yes 7 Source: J.P. Morgan Asset Management. The above table is shown for illustrative and discussion 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

9 Observed distribution, very different than normal Fatter left tail in International Equity leads to greater likelihood of losses 10.50% Normal Observed 7.75 Density % Return 8 Source: J.P. Morgan Asset Management. The above chart is shown for illustrative and discussion purposes only. Based on 10 years of monthly data to October 31, 2008

10 Converging correlations reduce diversification benefits Occurs during periods of high market volatility and is typically not captured by linear correlation matrices. Correlations over ten years to September 2007 U.S. Bonds U.S. Equity Intl equity EM Equity REITS HFs Private Equity U.S. Bonds 1.00 U.S. Equity Intl Equity EM Equity REITS HFs Private Equity VIX averaged 20.9% Correlations over August 1998 thru September 1999 U.S. Bonds U.S. Equity Intl equity EM Equity REITS HFs Private Equity U.S. Bonds 1.00 U.S. Equity Intl Equity EM Equity REITS HFs Private Equity VIX averaged 30.9% 9 Source: J.P. Morgan Asset Management. The above tables are shown for illustrative and discussion purposes only.

11 How do we allow for each form of non-normality? Serial Correlation Unsmoothing Rx Fat left tails Extreme Extreme Value Value Theory Theory Rx Converging Correlations Copula Theory Rx 10

12 Conditional Value at Risk as a better risk quantifier Standard deviation may not be investors most appropriate measure of portfolio risk because it rewards the desirable upside movements as hard as it punishes the undesirable movements as a risk measure, focus should be on potential loss Standard deviation calculation is only valid under a Mean Variance framework Conditional Value at Risk (CVaR 95 ) overcomes many of the drawbacks of standard deviation as a risk measure: 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 by institutional investors 11

13 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 Expected portfolio gain (loss) at the end of ten years ($ millions) 12 Source: J.P. Morgan Asset Management. The above chart is shown for illustrative and discussion purposes only. Analysis based on J.P. Morgan s Long Term Capital Market s Assumptions.

14 Incorporating non-normality of returns implies significantly higher portfolio risk Efficient frontier based on non-normal distribution of returns 12.0% Expected compound return (% per year) 11.0% 10.0% 9.0% 8.0% 7.0% 6.0% Normal framework Non-normal Mean CVaR framework 5.0% -$200.0 $0.0 $200.0 $400.0 $600.0 $800.0 $1,000.0 Conditional Value At Risk 95 (in $ millions) Significantly higher portfolio risk implies that the efficient frontier shifts to the right 13 Source: J.P. Morgan Asset Management. The above chart is shown for illustrative and discussion purposes only. Analysis based on J.P. Morgan s Long Term Capital Market s Assumptions.

15 and different efficient asset allocations Hypothetical un-constrained optimizations using a Normal and Non-normal framework Normal Non-normal 5.6% 0.0% 8.9% 11.5% 7.6% 1.9% 7.0% 34.5% 11.9% 11.1% 8.5% 64.1% 5.8% 21.7% U.S. Aggregate Bonds U.S. Large Cap Equity International Equity EM Equity REITs Fund of Hedge Funds Private Equity 14 Source: J.P. Morgan Asset Management. The above chart is shown for illustrative and discussion purposes only. Please see slide five for asset class descriptions. Analysis based on J.P. Morgan s Long Term Capital Market s Assumptions.

16 seeking to lowering risk, without sacrificing target returns Optimized portfolios Hypothetical Un-constrained Un-constrained allocation Normal Non-normal Total Bonds Total Equity Total Alternatives Total Assets 100% 100% 100% Target expected arithmetic return Expected volatility Expected compound return 8.7% 8.6% 8.7% Sharpe ratio CVaR 95 ($M) allowing for Non-normality $168.0 $206.0 $148.0 CVaR 95 vs. Hypothetical 23% 12% Optimized Portfolio, under a Non-normal framework is more diversified than under a Normal framework Expected return is not reduced, but potential risk (CVAR 95 ) is lowered by12% 15 Source: J.P. Morgan Asset Management. The table chart is shown for illustrative and discussion purposes only. Analysis based on J.P. Morgan s Long Term Capital Market s Assumptions.

17 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 All 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

18 How can you access more information? The Softcopy of the Non-normality of Market Returns paper is being released today, please look for it in your inboxes. There will be two versions of the paper available to you: Short Version with summary of key-takeaways Full Version with all supporting data We look forward to additional discussions with you regarding this topic. Please contact your JPMorgan Client Advisor or other JPMorgan representative for further details. 17

19 Appendix 18

20 The Marginal impact of each form of non-normality on the optimal portfolio solution, compared to an MVO framework IM9459 Phenomenon 1: Serial correlation Phenomenon 2: Fat tails Phenomenon 3: Converging correlations U.S. Bonds U.S. Equity Intl equity EM Equity REITs Fund of Hedge Funds Private Equity Each arrow in the table indicates the broad directional impact of the particular form of non-normality on the allocation to the asset class relative to the allocation implied by a mean-variance approach. For example, an up arrow indicates the allocation to the asset class increases in a non-normal framework, relative to the allocation implied by a traditional framework. Each subsequent column allows for the prior form (or forms) of non-normality hence, the attribution in each case is truly marginal 19 Source: J.P. Morgan Asset Management. The above chart is shown for illustrative and discussion purposes only.

21 Statistical techniques applied to incorporate non-normality Fortunately, there are sophisticated methods that allow us to attempt to correct for the different types of non-normality: Unsmoothing Serial Correlation: Using a variation of Fisher-Geltner-Webb s well established unsmoothing methodology, we can restore independence to single-period returns. The new adjusted return series is better reflective of the risk characteristics of the asset class. The new unsmoothed return stream has the same mean as the original return stream, but shows higher volatility thus higher downside risk Modeling Fat left tails: Using Extreme Value theory, we can create asset return distributions that are a closer fit to the return series that we actually see in the real world much more similar than the normal distribution. Thus, we are better able to estimate the probability of high-risk, low-probability events Simulating Correlation Breakdown: Using Copula theory, we can better model an increased incidence of negative joint returns (when asset class returns move down together) for the total portfolio. By considering joint distributions, we turn our focus on how asset classes behave together, rather than individually. This is a better model of asset class behavior during periods of market stress 20

22 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 21 Source: J.P. Morgan Asset Management. The above chart is shown for illustrative and discussion purposes only.

23 Incorporating the impact of Serial Correlations 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 Where R t represents the return at time t The regressions indicate the following estimates for the serial correlation coefficients, based on monthly returns. Step 1 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 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)) Step 2 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 Evidence of serial Test statistic p-value correlation International Equity No Emerging Markets Equity No Fund of Hedge Funds No Private Equity No 22 * 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 Value Indices of Commercial Real Estate: A Comparison of Index Construction Methods. Also, Fisher, J. and D. Geltner De-Lagging the NCREIF Index: Transaction Prices and Reverse-Engineering.

24 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. 23 Source: J.P. Morgan Asset Management. For illustrative purposes only.

25 Characteristics of U.S. Large Cap Equities S&P 500 monthly returns used as proxy Frequency Series: DLPINDEX_SPX Sample 1960M M06 Observations 534 Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Return Returns are negatively skewed with excess kurtosis using the Jarque-Bera test, we can conclusively reject the null hypothesis of normality 24 Source: J.P. Morgan Asset Management. For illustrative purposes only.

26 Incorporating the impact of Converging Correlations Copulas, based on Sklar s theorem (1959), are functions that allow us to choose the joint distribution of return series without compromising on the choice of marginal distributions in other words, we can model the underlying equity and alternative distributions using EVT, while still imposing an overall joint distribution to allow for converging correlations used extensive in industry to price Collateralized Debt Obligations (CDOs) In addition, copulas capture contagion risk better because they use rank correlations rather than linear correlations (such as Pearson s) For our purposes, we use a Student t-copula, which allows calibration using the correlation matrix and the degrees of freedom parameters it allows for converging correlations during market downturns in line with our capital market assumptions we run 2,500 simulations for each asset class Copulas are very intuitive and perfect for portfolio applications 25

27 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 10.0% 10.0% Monthly simulated Fund of Hedge Fund returns Monthly simulated Fund of Hedge Fund returns % -15.0% -10.0% -5.0% 0.0% 5.0% 10.0% 15.0% 20.0% % -15.0% -10.0% -5.0% 0.0% 5.0% 10.0% 15.0% 20.0% 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 26 Source: J.P. Morgan Asset Management. For illustrative purposes only.

28 Glossary of terms Converging correlations: A reference to the tendency of correlations between different asset classes to increase significantly (towards one) during periods of high market volatility. Hence, diversification benefits associated with lowly correlated asset classes do not necessarily materialize when needed most Copula theory: We can address the issue of correlation breakdown using copula theory a body of work that explicitly looks at the impact of contagion or converging correlations at the total portfolio level. Copulas are mathematical functions that allow us to model the joint distribution of asset returns separately from the marginal (i.e., individual asset class) distributions By considering joint distributions, we turn our focus to how asset classes behave together rather than individually. In particular, copulas allow us to model an increased incidence of joint negative returns (i.e. the fatter joint left tails) in our simulation results, just as we observe empirically in real-world market data. And again, using a more accurate proxy for observed data results in recognizing higher downside portfolio risk, specifically due to increased dependence of asset returns during periods of market stress 27

29 Glossary of terms Extreme Value theory: A body of work specifically designed to look at the probability of high-risk, but lowprobability, events such as floods, earthquakes and large insurance losses. In other words, it is focused on estimating tail risk. By applying Extreme Value theory we can create asset return distribution models that are closer to the return series we observe empirically, much more similar than normal distributions. The result that it better accounts for the frequency of observed extreme negative events also increases the portfolio s overall downside risk profile Fat (left or right) tails: A form of non-normality that relates to observing negative (or positive) returns in greater magnitude and with a higher probability than implied by the normal distribution. This phenomenon is commonly referred to as fat left (or right) tails a reference to the higher probability observed at the left (or right) tail of the empirical probability density function, relative to that implied by a normal distribution Fisher-Geltner unsmoothing procedure: A procedure by which serial correlations can be removed from the raw data. That is, we can correct for the influence of prior-period returns and restore independence to single period returns. Our new adjusted return series should be more reflective of the risk characteristics of the underlying data generating process. Notably, the new unsmoothed return series shows higher volatility, and thus higher downside risk 28

30 Glossary of terms Kernel (or empirical) density function: The probability density function implied by actual observed historical data. The kernel density function is often plotted against the assumed distribution in our model to gauge goodness of fit. In other words, we compare our model with the observed data to see how well the model fits the data. The better the fit, the more realistic our model can be considered to be Linear (or Pearson) correlation matrix: The simple correlations often used in traditional asset allocation models assume a linear relationship between asset classes i.e., assume that the relationship between the variables at the extremes is similar to their relationship at less extreme values. Using simple linear correlations is the equivalent of assuming that the joint distribution of asset returns is (multivariate) normal Conditional Value at Risk: We define Conditional Value at Risk (CVaR 95 ) as the average real portfolio loss (or gain) at the end of ten years relative to the starting portfolio value in the worst five percent of scenarios, based on our 10,000 Monte Carlo simulations. It is simply the average real loss (or gain) in the worst 500 (5% of 10,000) scenarios i.e. the left tail of the portfolio loss (gain) distribution Conditional Value at Risk (CVaR 95 ) overcomes many of the drawbacks of standard deviation as a risk measure. Primarily, as it only measures risk on the downside, it captures both the asymmetric risk preferences of investors and the incidence of fatter left tails induced by skewed and leptokurtic return distributions. Further, given the widespread use by major institutional investors and regulators of its first cousin Value at Risk we judge it to be the most appropriate risk measure to incorporate it into our framework 29

31 Glossary of terms Normal distribution: A widely used statistical distribution often used to model future asset class returns in traditional Mean Variance Optimization frameworks. The probability density function of a normal distribution is a symmetric bell shaped curve. The normal distribution is completely defined by its mean and standard deviation. It s popularity stems from statistical properties associated with the underlying distribution and transformations to variables that are normally distributed. In reality, asset class returns are not normally distributed demonstrating amongst other things fatter left tails. Hence, a direct consequence of assuming future asset returns are normally distributed is a systematic underestimation of downside portfolio risk Serial (or auto) correlation of returns: This occurs when one period s return is correlated to the previous period s return, inducing dependence over time A critical pillar of many traditional asset allocation frameworks is the assumption that asset returns from period to period are independent. However, if one month s return is influenced by the previous month s return, then the returns are serially correlated. There may also be a need to account for this effect in future asset projections. Traditional asset allocation frameworks do not allow for serial correlation, but our tests reveal the presence of serial correlation in many asset class returns particularly alternatives Standard deviation: A measure of risk (or uncertainty) associated with an asset class or portfolio, as defined in traditional mean-variance optimization frameworks Standard deviation is not a robust measure of risk when assuming non-normality. This is because standard deviation places an equal weight on portfolio gains and portfolio losses. This is generally inconsistent with investor risk preferences primarily as it relates to observations in the field of behavioral finance. It is, however, widely used due to the ease with which it can be calculated and its analytical properties under the assumption of normality 30

32 Glossary of terms Mean-variance optimization (MVO): An industry standard framework used to develop asset allocation solutions. MVO frameworks assume that future asset class returns will be independent and normally distributed. Despite being widely recognized as overly simplistic, the assumption of normality has broad appeal due to the ease with which it can be implemented To implement a MVO framework based on normal asset return distributions, practitioners need only make two assumptions for each asset class (mean and standard deviation) and one assumption for each pair (co-variance). The latter applies because one approximates the relationship between each pair of asset classes as being linear Non-linear correlations: Empirically, we find that in many cases correlations under extreme conditions are quite different than under normal conditions. In other words, the expected linear correlations breakdown and asset classes exhibit quite different joint behavior. The relationships, in fact, are not linear, and the assumption of linearity (by using linear correlation matrices) underestimates the probability of joint negative returns under extreme conditions 31

33 J.P. Morgan s Long-term Capital Market Return Assumptions Expected year annualized compound returns 1,2 Rationale U.S. Inflation 2.75% Inflation to be extremely low in the near term, but today s aggressive policy stimulusmakes inflation likely to rise on the other side of the recession. U.S. Real GDP 2.75% Private sector de-leveraging and a tighter future credit environment to place constraints on economic growth. U.S. Cash 4.00% Fed policymakers to raise the Fed funds rate to 4% as growth rebounds. This is a lower target funds rate than we expected prior to the 2008 downturn. U.S. 10-yr Treasury 4.00% Yields to rise towardsa higher assumed equilibrium of 5.5% given future inflation risk and increased bond issuance to fund fiscal expansion. The resulting capital loss to reduce total return. U.S. Aggregate 5.50% U.S. Long Duration Govt./Corp. 6.25% Current wide spreads are offset by low risk-free rates. Total return close to equilibrium yield. U.S. TIPS (nominal) 5.25% Relatively high real yields and future inflation risk increase expected returnsrelative to nominal Treasuriesgiven current low nominal yields. U.S. High Yield 11.00% Current yieldswell above assumed long-term equilibrium. Spread tightening to provide a significant boost to future returns. Haircut to returns from expected defaults. World Govt. Bond Index (local) 3.25% Non-U.S. World Govt. Bond Index (local) 3.00% Government bond yields to rise globally from current low levels leading to capital losses during the convergence period. Non-U.S. World Govt. Bond Index (USD) 4.25% Dollar depreciation against the major constituent currencies of the World Govt. Bond Index (WGBI) expected to boost returnsto U.S. investors. Emerging Market Debt 9.25% Current wide spreads are offset by low risk-free rates. Total return closeto equilibrium yield. Municipal 4.25% Slight increase in yieldsexpected as state funding problems outweigh potential boost to demand from higher Federal income tax rates. U.S. Large Cap 9.00% Sum of below building blocks (U.S. Large Cap EPS Growth (nominal) + Dividend Yield +P/ Ereturn impact). U.S. Large Cap EPS Growth (nominal) 6.00% Slight premium to GDP maintained, reflecting both increased cost-cutting and partial recovery from current depressed rates of earnings growth. U.S. Large Cap Dividend Yield 2.50% Companies to increase dividends as a means of maintaining investor confidence given more risk-averse future environment. U.S. Large Cap P/ EReturn Impact 0.50% Equity valuationsto recover only partially, reflecting the likelihood of more frequent recessionsand increased government regulation. U.S. Mid Cap 9.25% U.S. Small Cap 9.25% Moderate premium to large cap assumed for both. Tighter credit availability and limited scope for valuation improvement to restrain return advantage. U.S. Large Cap Growth 8.75% U.S. Large Cap Value 9.25% Value expected to outperform growth over time, especially given increased demand for return through yield. Europe ex-u.k. Large Cap (local) 9.00% Earnings premium to GDP, with dividend yields to remain above global average. Valuationsto recover by lessthan other developed markets given less supportive central bank policy. Japan Large Cap (local) 7.00% Earnings premium to GDP, with companiesto increase dividendsasa means of maintaining investor confidence. Valuationsto recover from current depressed levels. U.K. Large Cap (local) 9.25% Earnings premium to GDP, with dividend yields to remain above global average. Valuationsto recover from current depressed levels. EAFE (local) 8.50% Market capitalization-weighted average of expectationsfor regional equity returns. EAFE (USD) 9.25% Dollar depreciation against the major constituent currencies of the EAFE index to boost returnsto U.S. investors. Emerging Market Equity (USD) 10.25% Slightly reduced premium to developed market returns, reflecting pressure on Asia from Western consumer de-leveraging, and reduced boost from commodities for Latin America and Emerging Europe. Asia ex-japan Equity (USD) 10.25% Higher productivity growth relative to other emerging regions offset by Asian exposure to Western consumer and developed market-type returnsin large constituent countries. Pr ivate Equit y % Moderation in premium to public marketsgiven tighter access to financing is offset by likelihood of weaker managers exiting industry. Sizeable divergences expected between managers. U.S. Direct Real Estate (unlevered) % Delivered returns assumed to be between equity and fixed income. U.S. Value Added Real Estate % 125 bps premium assumed for specialized acquisition and management expertise. European Direct Real Estate (unlevered, local) % Slight return premium to the U.S given lower liquidity. U.S. REITs 8.00% REITreturn between publicequity and direct real estate. Hedge Fund - (arbitrage/non-directional) % Non-directional returns reflect expected premium to bond returns. Directional returns expected to be below public equity given reduced leverage vs. prior years. Fund of fundsreturn reflects Hedge Fund - (directional) % expected 60% exposure to developed world equity and 40% to U.S. bond market. Sizeable divergencesexpected between managers. Hedge Fund - (fund of funds) % Commodities 7.00% Returnsin line with expected global nominal GDP growth Return estimates are on a compound or internal rate of return (IRR) basis. Equivalent arithmetic averages, as well as further information, are shown below. 2 All asset class assumptions are in total return terms, including equity return assumptions. All returns are in U.S. dollar terms unless otherwise indicated. 3 Private Equity, Hedge Funds and Direct Real Estate are unlike other asset classes shown above in that there is no underlying investible index. Exchange traded funds may be used to gain exposure to REITs. 4 The return estimates shown for these asset classes are our estimates of industry medians the dispersion of returns among managers in these asset classes is typically far wider than for traditional asset classes. See additional notes on page below.

34 J.P. Morgan s Long-term Capital Market Return Assumptions (cont d.) 33 Expect ed annualized volatility Expected compound return 2 Expected arithmeticreturn 2 U.S. Inflation Correlation Matrix U.S. Cash U.S. 10-yr Treasury U.S. Aggregate U.S. Long Duration Govt./Corp. U.S. Inflation 2.76% 2.75% 1.50% U.S. Cash 4.00% 4.00% 0.50% U.S. 10-yr Treasury 4.22% 4.00% 6.75% U.S. Aggregate 5.59% 5.50% 4.25% U.S. Long Duration Govt./Corp. 6.67% 6.25% 9.50% U.S. TIPS(nominal) 5.48% 5.25% 7.00% U.S. High Yield 11.61% 11.00% 11.75% WGBI hedged 4.30% 4.25% 3.25% WGBI unhedged 4.55% 4.25% 8.00% WGBI ex-u.s. hedged 4.29% 4.25% 2.75% WGBI ex-u.s. unhedged 4.68% 4.25% 9.50% Emerging Market Debt 10.04% 9.25% 13.25% Municipal 4.35% 4.25% 4.50% U.S. Large Cap 10.36% 9.00% 17.50% U.S. Mid Cap 10.97% 9.25% 19.75% U.S. Small Cap 11.55% 9.25% 23.00% U.S. Large Cap Growth 10.87% 8.75% 22.00% U.S. Large Cap Value 10.46% 9.25% 16.50% Europe ex-u.k. Large Cap 11.65% 9.50% 22.25% Japan Large Cap 10.98% 9.00% 21.25% U.K. Large Cap 10.69% 9.25% 18.00% EAFEunhedged 10.80% 9.25% 18.75% EAFE hedged 10.61% 9.25% 17.50% Emerging Market Equity 13.44% 10.25% 27.50% Asia ex-japanequity 13.39% 10.25% 27.25% Private Equity 13.09% 10.00% 27.00% U.S. Direct Real Estate (unlevered) 7.60% 7.25% 8.75% U.S. Value Added Real Estate 9.27% 8.50% 13.00% U.S. REITs 9.95% 8.00% 21.00% Hedge Fund (non-directional) 6.82% 6.50% 8.25% Hedge Fund - (directional) 8.75% 8.25% 10.50% Hedge Fund - (fund of funds) 8.12% 7.75% 9.00% Commodities 10.44% 7.00% 28.25% U.S. TIPS (nominal) U.S. High Yield WGBI hedged WGBI unhedged WGBI ex-u.s. hedged WGBI ex-u.s. unhedged Emerging Market Debt Municipal Note: Given the complex risk-reward trade-offs involved, we advise clients to rely on judgment as well as quantitative optimization approaches in setting strategic allocations to all the above asset classes. Please note that all information shown is based on qualitative analysis. Exclusive reliance on the above is not advised. This information is not intended as a recommendation to invest in any particular asset class or as a promise of future performance. Note that these asset class assumptions are passive only they do not consider the impact of active management. References to future returns for either asset allocation strategies or asset classes are not promises or even estimates of actual returns a client portfolio may achieve. See footnotes on page above. Assumptions, opinions and estimates are provided for illustrative purposes only. They should not be relied upon as recommendations to buy or sell securities. Forecasts of financial market trends that are based on current market conditions constitute our judgment and are subject to change without notice. We believe the information provided here is reliable, but do not warrant its accuracy or completeness. This material has been prepared for information purposes only, and is not intended to provide, and should not be relied on for, accounting, legal or tax advice. J.P. Morgan Asset Management is the marketing name for the asset management businesses of JPMorgan Chase & Co. Those businesses include, but are not limited to, J.P. Morgan Investment Management Inc., J.P. Morgan Investment Advisors Inc., Security Capital Research & Management Inc. and J.P. Morgan Alternative Asset Management Inc. Copyright 2008 JPMorgan Chase & Co. J.P. Morgan Asset Management 245 Park Avenue, New York, NY jpmorgan.com/insight U.S. Large Cap U.S. Mid Cap U.S. Small Cap U.S. Large Cap Growth U.S. Large Cap Value Europe ex-u.k. LargeCap Japan Large Cap U.K. Large Cap EAFEunhedged EAFE hedged Emerging Market Equity Asia ex-japan Equity Private Equity U.S. Direct Real Estate (unlevered) U.S. Value Added Real Estate U.S. REITs Hedge Fund - (non-di rectional) Hedge Fund - (directional) HedgeFund - (fund of funds) Commodities

35 J.P. Morgan Asset Management 34 This document is intended solely to report on various investment views held by J.P. Morgan Asset Management. Opinions, estimates, forecasts, and statements of financial market trends that are based on current market conditions constitute our judgment and are subject to change without notice. We believe the information provided here is reliable but should not be assumed to be accurate or complete. The views and strategies described may not be suitable for all investors. References to specific securities, asset classes and financial markets are for illustrative purposes only and are not intended to be, and should not be interpreted as, recommendations. Indices do not include fees or operating expenses and are not available for actual investment. The information contained herein employs proprietary projections of expected returns as well as estimates of their future volatility. The relative relationships and forecasts contained herein are based upon proprietary research and are developed through analysis of historical data and capital markets theory. These estimates have certain inherent limitations, and unlike an actual performance record, they do not reflect actual trading, liquidity constraints, fees or other costs. References to future net returns are not promises or even estimates of actual returns a client portfolio may achieve. The forecasts contained herein are for illustrative purposes only and are not to be relied upon as advice or interpreted as a recommendation. The value of investments and the income from them may fluctuate and your investment is not guaranteed. Past performance is no guarantee of future results. Please note current performance may be higher or lower than the performance data shown. Please note that investments in foreign markets are subject to special currency, political, and economic risks. Exchange rates may cause the value of underlying overseas investments to go down or up. Investments in emerging markets may be more volatile than other markets and the risk to your capital is therefore greater. Also, the economic and political situations may be more volatile than in established economies and these may adversely influence the value of investments made. Performance results are gross of investment management fees. The deduction of an advisory fee reduces an investor s return. Actual account performance will vary depending on individual portfolio security selection and the applicable fee schedule. Fees are available upon request. The following is an example of the effect of compounded advisory fees over a period of time on the value of a client s portfolio: A portfolio with a beginning value of $100 million, gaining an annual return of 10% per annum would grow to $259 million after 10 years, assuming no fees have been paid out. Conversely, a portfolio with a beginning value of $100 million, gaining an annual return of 10% per annum, but paying a fee of 1% per annum, would only grow to $235 million after 10 years. The annualized returns over the 10 year time period are 10.00% (gross of fees) and 8.91% (net of fees). If the fee in the above example was 0.25% per annum, the portfolio would grow to $253 million after 10 years and return 9.73% net of fees. The fees were calculated on a monthly basis, which shows the maximum effect of compounding. Illustration showing impact of investment management fees: An investment of USD $1,000,000 under the management of JPMFAM achieves a 10% compounded gross annual return for 10 years. If a management fee of 0.75% of average assets under management were charged per year for the 10-year period, the annual return would be 9.25% and the value of assets would be USD $2,422,225 net of fees, compared with USD $2,593,742 gross of fees. Therefore, the investment management fee, and any other expenses incurred in the management of the portfolio, will reduce the client s return. The securities mentioned throughout the presentation are shown for illustrative purposes only and should not be interpreted as recommendations to buy or sell. A full list of firm recommendations for the past year are available upon request. J.P. Morgan Asset Management is the marketing name for the asset management businesses of JPMorgan Chase & Co and its affiliates worldwide. Copyright 2009 JPMorgan Chase & Co.