Financial Modeling & the Crisis

Terry MarshQuantal International Inc.

19th Annual Conference of the PBFEAM

Friday, July 8 , 2011Taipei

Joint Work, Background Papers

Work is with Paul Pfleiderer

http://www.quantal.com/Research

Outline

MyAsset

Allocation Model

Failed!!!!

No Diversification when I needed

it!!

Black Swans!!!

25-standard deviations!!!!

Outline (cont’d.)

BASECASE

VARIATIONSCrisis 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

Market Standard US Dev Em EquilibriumWeights Deviation Equity Equity Equity Bonds Exp Return*

US Equity 20.00% 18.00% 1.00 0.65 0.60 0.40 7.11%

Dev Equity 22.00% 20.00% 0.65 1.00 0.60 0.35 7.60%Em Equity 18.00% 30.00% 0.60 0.60 1.00 0.30 9.84%

Bonds 30.00% 10.00% 0.40 0.35 0.30 1.00 4.71%

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 0.2 0.3 0.4 0.5 0.6 0.7 0.8

% of Total Wealth 5.00% 10.00% 20.00% 30.00% 20.00% 10.00% 5.00%

US Equity 8.36% 12.53% 16.71% 20.89% 23.26% 25.88% 29.57%

Dev Equity 9.07% 13.61% 18.14% 22.68% 25.84% 29.19% 33.36%

Em Equity 7.03% 10.55% 14.07% 17.59% 21.94% 26.18% 29.92%

Bonds 15.40% 23.11% 30.81% 38.51% 28.96% 21.72% 24.82%

Cash 60.13% 40.20% 20.27% 0.34% 0.00% -2.97% -17.69%

Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%

Optimal Allocations

Total

US Equity 0.42% 1.25% 3.34% 6.27% 4.65% 2.59% 1.48% 20.00%

Dev Equity 0.45% 1.36% 3.63% 6.80% 5.17% 2.92% 1.67% 22.00%

Em Equity 0.35% 1.06% 2.81% 5.28% 4.39% 2.62% 1.50% 18.00%

Bonds 0.77% 2.31% 6.16% 11.55% 5.79% 2.17% 1.24% 30.00%

Cash 3.01% 4.02% 4.05% 0.10% 0.00% -0.30% -0.88% 10.00%

Total 5.00% 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 0.1 0.2 0.3 0.4 0.5 0.6 0.7

New % of Total Wealth 6.24% 11.57% 21.32% 29.27% 18.69% 8.87% 4.05%

US Equity 5.47% 8.85% 12.80% 17.48% 20.32% 23.82% 29.83%Dev Equity 5.94% 9.60% 13.89% 18.97% 22.57% 26.87% 33.65%

Em Equity 4.60% 7.45% 10.77% 14.71% 19.17% 24.10% 30.18%

Bonds 15.12% 24.46% 35.38% 48.34% 37.94% 29.99% 37.56%

Cash 68.87% 49.65% 27.16% 0.49% 0.00% -4.79% -31.22%

Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%

Allocations after 40%

Decline in Equity, 10%

Decline in Bonds and 5%

Gain In Riskless

Total

US Equity 0.34% 1.02% 2.73% 5.12% 3.80% 2.11% 1.21% 16.33%Dev Equity 0.37% 1.11% 2.96% 5.55% 4.22% 2.38% 1.36% 17.96%

Em Equity 0.29% 0.86% 2.30% 4.31% 3.58% 2.14% 1.22% 14.69%

Bonds 0.94% 2.83% 7.55% 14.15% 7.09% 2.66% 1.52% 36.74%

Cash 4.30% 5.74% 5.79% 0.14% 0.00% -0.42% -1.26% 14.29%

Total 6.24% 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

Market Standard US Dev Em Equilibrium

Weights Deviation Equity Equity Equity Bonds Exp Return*

US Equity 20.00% 18.00% 1.00 0.65 0.60 0.40 7.11%

Dev Equity 22.00% 20.00% 0.65 1.00 0.60 0.35 7.60%

Em Equity 18.00% 30.00% 0.60 0.60 1.00 0.30 9.84%

Bonds 30.00% 10.00% 0.40 0.35 0.30 1.00 4.71%

Cash 10.00% 0.00% 3.00%**

** Borrowing Cost = 3.50%

Correlations

* Average Risk Tolerance = 0.5

BEFORE

Market Standard US Dev Em Equilibrium

Weights Deviation Equity Equity Equity Bonds Exp Return*

US Equity 16.33% 30.00% 1.00 0.75 0.70 0.50 13.53%

Dev Equity 17.96% 30.00% 0.75 1.00 0.70 0.50 13.63%

Em Equity 14.69% 40.00% 0.70 0.70 1.00 0.45 17.37%

Bonds 36.73% 15.00% 0.50 0.50 0.45 1.00 6.40%

Cash 14.29% 0.00% 1%**

** Borrowing Cost = 1.50%

Correlations

* Average Risk Tolerance = 0.385

AFTER

Optimal Allocations and TurnoverClientele (a) (b) (c) (d) (e) (f) (g)

Risk Tolerance 0.1 0.2 0.3 0.4 0.5 0.6 0.7% of Total Wealth 6.24% 11.57% 21.32% 29.27% 18.69% 8.87% 4.05%

US Equity 4.27% 8.54% 12.81% 17.08% 20.98% 25.18% 29.37%Dev Equity 4.69% 9.39% 14.08% 18.77% 23.10% 27.72% 32.34%Em Equity 3.75% 7.49% 11.24% 14.99% 19.45% 23.34% 27.23%

Bonds 10.55% 21.11% 31.66% 42.21% 41.52% 49.82% 58.13%Cash 76.74% 53.48% 30.21% 6.95% -5.05% -26.07% -47.08%Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%

New Optimal Allocations

TotalUS Equity 0.27% 0.99% 2.73% 5.00% 3.92% 2.23% 1.19% 16.33%

Dev Equity 0.29% 1.09% 3.00% 5.49% 4.32% 2.46% 1.31% 17.96%Em Equity 0.23% 0.87% 2.40% 4.39% 3.64% 2.07% 1.10% 14.69%

Bonds 0.66% 2.44% 6.75% 12.35% 7.76% 4.42% 2.35% 36.73%Cash 4.79% 6.19% 6.44% 2.03% -0.94% -2.31% -1.91% 14.29%Total 6.24% 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%Cash 7.87% 3.83% 3.05% 6.46% -5.05% -21.27% -15.86%Total 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Change in Allocations

TotalUS Equity -0.07% -0.04% 0.00% -0.12% 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%Cash 0.49% 0.44% 0.65% 1.89% -0.94% -1.89% -0.64% 0.00%Total 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

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

BeforeAverage Risk Tol 0.500

US Equity 7.11%

Dev Equity 7.60%Em Equity 9.84%

Bonds 4.71%

Cash 3.00%

Sharpe Ratio 0.274

AfterAverage Risk Tol 0.385

US Equity 13.53%

Dev Equity 13.63%

Em Equity 17.37%

Bonds 6.40%

Cash 1.00%

Sharpe Ratio 0.481

Total Turnover 7.44%

No

Leverage

(A)

0.500

7.20%

7.68%9.93%

4.79%

3.00%

0.280

0.387

14.21%

14.30%

18.03%

7.11%

1.00%

0.513

1.68%

EqualWealth

Clienteles

(B)

0.500

7.23%

7.72%9.96%

4.82%

3.00%

0.282

0.371

14.09%

14.19%

18.08%

6.68%

1.00%

0.503

8.62%

No Decreasein Risk

Tolerance

(C)

0.500

7.11%

7.60%9.84%

4.71%

3.00%

0.274

0.485

10.96%

11.04%

14.01%

5.30%

1.00%

0.382

5.64%

High

Correlations

(D)

0.500

7.11%

7.60%9.84%

4.71%

3.00%

0.274

0.385

16.14%

16.18%

21.22%

8.09%

1.00%

0.533

5.79%

Naïve

Rebalancing

(E)

0.500

7.11%

7.60%9.84%

4.71%

3.00%

0.274

0.385

13.02%

13.11%

16.67%

6.34%

1.00%

0.464

8.23%

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

0

10

20

30

40

50

60

70

80

90

1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009

VIX Index Level

0

200

400

600

800

1000

1200

1400

1600

1800

1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009

S&P 500 Index Level

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

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009

S&P 500 Returns Scaled by Standard Deviation Measured Over Entire Period

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

1/2/1990 9/28/1992 6/25/1995 3/21/1998 12/15/2000 9/11/2003 6/7/2006 3/3/2009

S&P 500 Returns Scaled by Level of VIX on Preceding Day

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

S&P 500 Returns Scaled byStandard Deviation Measured over Entire Period

Mean 0.018302

Median 0.044372

Standard Deviation 1.000000

Sample Variance 1.000000

Kurtosis 11.963779

Skewness -0.200296

Minimum -8.059105

Probability of Seeing Minimum or Less if Normal

0.00000000017166268407%

Maximum 9.325208

Probability of Seeing Maximum or More if Normal

0.00000000000000000000%

S&P 500 Returns Scaled byVIX on Preceding Day

0.017289

0.048046

0.776764

0.603362

4.473268

-0.361824

-5.031819

0.12512451075820100000%

3.307484

91.16557201094780%

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.