Financial Modeling & the Crisis Terry Marsh Quantal International Inc. 19th Annual Conference of the PBFEAM Friday, July 8, 2011 Taipei

Joint Work, Background Papers Work is with Paul Pfleiderer

Outline My Asset Allocation Model Failed!!!! No Diversification when I needed it!! Black Swans!!! 25-standard deviations!!!!

Outline (cont’d.) BASE CASE VARIATIONS Crisis Hits: Allocation Weights Change Because of Price Declines Specify Pre-Crisis Market Environment and Determine Optimal Allocations for Various Clientele Solve for Post-Crisis Market-Clearing Equilibrium and Optimal Allocations Calculate Turnover caused by the Crisis

Pre-Crisis: Market Environment: Assumed Risk-Return Structure, Market Index Weights MarketStandardUSDevEmEquilibrium WeightsDeviationEquity BondsExp Return* US Equity 20.00%18.00% % Dev Equity 22.00%20.00% % Em Equity 18.00%30.00% % Bonds 30.00%10.00% % Cash 10.00%0.00%3.00%** ** Borrowing Cost = 3.50% Correlations * Average Risk Tolerance = 0.5

Pre-Crisis: Investor Clienteles and Market-Clearing Allocations (Optimal for each Clientele) Clientele(a)(b)(c)(d)(e)(f)(g) Risk Tolerance % of Total Wealth5.00%10.00%20.00%30.00%20.00%10.00%5.00% US Equity8.36%12.53%16.71%20.89%23.26%25.88%29.57% Dev Equity9.07%13.61%18.14%22.68%25.84%29.19%33.36% Em Equity7.03%10.55%14.07%17.59%21.94%26.18%29.92% Bonds15.40%23.11%30.81%38.51%28.96%21.72%24.82% Cash60.13%40.20%20.27%0.34%0.00%-2.97%-17.69% Total100.00% Optimal Allocations Total US Equity0.42%1.25%3.34%6.27%4.65%2.59%1.48%20.00% Dev Equity0.45%1.36%3.63%6.80%5.17%2.92%1.67%22.00% Em Equity0.35%1.06%2.81%5.28%4.39%2.62%1.50%18.00% Bonds0.77%2.31%6.16%11.55%5.79%2.17%1.24%30.00% Cash3.01%4.02%4.05%0.10%0.00%-0.30%-0.88%10.00% Total5.00%10.00%20.00%30.00%20.00%10.00%5.00%100.00% % Holdings in Economy

Post-Crisis: Realized Allocations After Huge Price Changes Clientele(a)(b)(c)(d)(e)(f)(g) New Level of Risk Tolerance New % of Total Wealth6.24%11.57%21.32%29.27%18.69%8.87%4.05% US Equity5.47%8.85%12.80%17.48%20.32%23.82%29.83% Dev Equity5.94%9.60%13.89%18.97%22.57%26.87%33.65% Em Equity4.60%7.45%10.77%14.71%19.17%24.10%30.18% Bonds15.12%24.46%35.38%48.34%37.94%29.99%37.56% Cash68.87%49.65%27.16%0.49%0.00%-4.79%-31.22% Total100.00% Allocations after 40% Decline in Equity, 10% Decline in Bonds and 5% Gain In Riskless Total US Equity0.34%1.02%2.73%5.12%3.80%2.11%1.21%16.33% Dev Equity0.37%1.11%2.96%5.55%4.22%2.38%1.36%17.96% Em Equity0.29%0.86%2.30%4.31%3.58%2.14%1.22%14.69% Bonds0.94%2.83%7.55%14.15%7.09%2.66%1.52%36.74% Cash4.30%5.74%5.79%0.14%0.00%-0.42%-1.26%14.29% Total6.24%11.57%21.32%29.27%18.69%8.87%4.05%100.00% % Holdings after 40% Decline in Equity, 10% Decline in Bonds and 5% Gain In Riskless

Market Environment Before and After: Assumed Risk-Return Structure, Market Index Weights MarketStandardUSDevEmEquilibrium WeightsDeviationEquity BondsExp Return* US Equity20.00%18.00% % Dev Equity22.00%20.00% % Em Equity18.00%30.00% % Bonds30.00%10.00% % Cash10.00%0.00%3.00%** ** Borrowing Cost = 3.50% Correlations * Average Risk Tolerance = 0.5 BEFORE MarketStandardUSDevEmEquilibrium WeightsDeviationEquity BondsExp Return* US Equity16.33%30.00% % Dev Equity17.96%30.00% % Em Equity14.69%40.00% % Bonds36.73%15.00% % Cash14.29%0.00%1%** ** Borrowing Cost = 1.50% Correlations * Average Risk Tolerance = AFTER

Optimal Allocations and Turnover Clientele(a)(b)(c)(d)(e)(f)(g) Risk Tolerance % of Total Wealth6.24%11.57%21.32%29.27%18.69%8.87%4.05% US Equity4.27%8.54%12.81%17.08%20.98%25.18%29.37% Dev Equity4.69%9.39%14.08%18.77%23.10%27.72%32.34% Em Equity3.75%7.49%11.24%14.99%19.45%23.34%27.23% Bonds10.55%21.11%31.66%42.21%41.52%49.82%58.13% Cash76.74%53.48%30.21%6.95%-5.05%-26.07%-47.08% Total100.00% New Optimal Allocations Total US Equity0.27%0.99%2.73%5.00%3.92%2.23%1.19%16.33% Dev Equity0.29%1.09%3.00%5.49%4.32%2.46%1.31%17.96% Em Equity0.23%0.87%2.40%4.39%3.64%2.07%1.10%14.69% Bonds0.66%2.44%6.75%12.35%7.76%4.42%2.35%36.73% Cash4.79%6.19%6.44%2.03%-0.94%-2.31%-1.91%14.29% Total6.24%11.57%21.32%29.27%18.69%8.87%4.05%100.00% New % Holdings in Economy US Equity-1.20%-0.31%0.01%-0.40%0.66%1.36%-0.45% Dev Equity-1.24%-0.22%0.19%-0.20%0.53%0.85%-1.31% Em Equity-0.86%0.05%0.47%0.27%0.29%-0.76%-2.95% Bonds-4.57%-3.35%-3.73%-6.13%3.58%19.83%20.57% Cash7.87%3.83%3.05%6.46%-5.05%-21.27%-15.86% Total0.00% Change in Allocations Total US Equity-0.07%-0.04%0.00%-0.12%0.12% -0.02%0.00% Dev Equity-0.08%-0.02%0.04%-0.06%0.10%0.08%-0.05%0.00% Em Equity-0.05%0.01%0.10%0.08%0.05%-0.07%-0.12%0.00% Bonds-0.28%-0.39%-0.79%-1.79%0.67%1.76%0.83%0.00% Cash0.49%0.44%0.65%1.89%-0.94%-1.89%-0.64%0.00% Total0.00% Change in % Holdings in Economy

Variations on Base Case No Leverage Wealth Equally Distributed Across Clienteles No Decrease in Risk Tolerance in Crisis Very High Correlations among Asset Class Returns “Target Weight” Allocation Policy => Naïve Rebalancing

Variations on Base Case Base case Before Average Risk Tol0.500 US Equity7.11% Dev Equity7.60% Em Equity9.84% Bonds4.71% Cash3.00% Sharpe Ratio0.274 After Average Risk Tol0.385 US Equity13.53% Dev Equity13.63% Em Equity17.37% Bonds6.40% Cash1.00% Sharpe Ratio0.481 Total Turnover7.44% No Leverage (A) % 7.68% 9.93% 4.79% 3.00% % 14.30% 18.03% 7.11% 1.00% % Equal Wealth Clienteles (B) % 7.72% 9.96% 4.82% 3.00% % 14.19% 18.08% 6.68% 1.00% % No Decrease in Risk Tolerance (C) % 7.60% 9.84% 4.71% 3.00% % 11.04% 14.01% 5.30% 1.00% % High Correlations (D) % 7.60% 9.84% 4.71% 3.00% % 16.18% 21.22% 8.09% 1.00% % Naïve Rebalancing (E) % 7.60% 9.84% 4.71% 3.00% % 13.11% 16.67% 6.34% 1.00% % Equilibriu m Expected Returns Equilibriu m Expected Returns

Points of Emphasis Flight to Quality  “Flight to Risk” Optimal Investor Response = f (Risk Tolerance relative to Average) Turnover: Between 1.5% and 8%, depending on assumptions Extensions: Liquidity, relative to Average Investment Horizon, relative to Average Taxes, relative to Average

Related Points Good Companies ≠ Good Investments Low Property Taxes ≠ Low House Prices Publicly Listed Private Equity Firms ≠ “Private Equity for Everyman” …..

Popular Sentiment-based Recommendations Generate Some of the Same Actions as Here? Popular Wisdom: “Be greedy when others are fearful, and fearful when others are greedy” (Warren Buffet) Risk premiums are “high” when uncertainty is high (and perhaps liquidity is low), and low when uncertainty is low “Stocks look attractive when they have been oversold” Stock prices have decreased ‘a lot’ => risk premiums have increased a lot => stocks are “attractive” (to a risk-tolerant investor)

Black Swans Point 1: Serial Persistence in Stock Market Uncertainty: Make Decisions using Conditional Variance-Covariance Matrix Subordinated Stochastic Process Model Hidden Markov Model Substantially reduced Black-Swan problem with Conditional Probability Distribution => Provide Simple Illustration Institutional Risk Management Problem: Better Conditional Probability Model  Less Transparent

Example: Conditional Variance-Covariance = Control for “Black Swans”

Example: Conditional Variance-Covariance = Control for “Black Swans” (cont’d.)

S&P 500 Returns Scaled by Standard Deviation Measured over Entire Period Mean Median Standard Deviation Sample Variance Kurtosis Skewness Minimum Probability of Seeing Minimum or Less if Normal % Maximum Probability of Seeing Maximum or More if Normal % S&P 500 Returns Scaled by VIX on Preceding Day % %

Interesting Questions re “Black Swans”? Who buys insurance against “black swan” events, who supplies this insurance, who self- insures, when does the insurance market “break down”….etc.