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
http://www.quantal.com/Research
Outline
My
Asset
Allocation
Model
Failed!!!!
No
Diversification
when I needed
it!!
Black
Swans!!!
25-standard
deviations!!!!
Outline (cont’d.)
BASE
VARIATIONS
CASE
Specify Pre-Crisis Market Environment and
Determine Optimal Allocations for Various
Clientele
Crisis Hits: Allocation Weights Change Because of
Price Declines
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
US Equity
Dev Equity
Em Equity
Bonds
Cash
Market Standard
Weights Deviation
20.00% 18.00%
22.00% 20.00%
18.00% 30.00%
30.00% 10.00%
10.00%
0.00%
US
Equity
1.00
0.65
0.60
0.40
Correlations
Dev
Em
Equity
Equity
0.65
0.60
1.00
0.60
0.60
1.00
0.35
0.30
* Average Risk Tolerance = 0.5
** Borrowing Cost = 3.50%
Bonds
0.40
0.35
0.30
1.00
Equilibrium
Exp Return*
7.11%
7.60%
9.84%
4.71%
3.00%**
Pre-Crisis: Investor Clienteles and Market-Clearing
Allocations (Optimal for each Clientele)
Clientele
Risk Tolerance
% of Total Wealth
Optimal Allocations
% Holdings in Economy
US Equity
Dev Equity
Em Equity
Bonds
Cash
Total
US Equity
Dev Equity
Em Equity
Bonds
Cash
Total
(a)
0.2
5.00%
(b)
0.3
10.00%
(c)
0.4
20.00%
(d)
0.5
30.00%
(e)
0.6
20.00%
(f)
0.7
10.00%
(g)
0.8
5.00%
8.36%
9.07%
7.03%
15.40%
60.13%
100.00%
12.53%
13.61%
10.55%
23.11%
40.20%
100.00%
16.71%
18.14%
14.07%
30.81%
20.27%
100.00%
20.89%
22.68%
17.59%
38.51%
0.34%
100.00%
23.26%
25.84%
21.94%
28.96%
0.00%
100.00%
25.88%
29.19%
26.18%
21.72%
-2.97%
100.00%
29.57%
33.36%
29.92%
24.82%
-17.69%
100.00%
0.42%
0.45%
0.35%
0.77%
3.01%
5.00%
1.25%
1.36%
1.06%
2.31%
4.02%
10.00%
3.34%
3.63%
2.81%
6.16%
4.05%
20.00%
6.27%
6.80%
5.28%
11.55%
0.10%
30.00%
4.65%
5.17%
4.39%
5.79%
0.00%
20.00%
2.59%
2.92%
2.62%
2.17%
-0.30%
10.00%
1.48%
1.67%
1.50%
1.24%
-0.88%
5.00%
Total
20.00%
22.00%
18.00%
30.00%
10.00%
100.00%
Post-Crisis: Realized Allocations After Huge Price
Changes
Clientele
New Level of Risk Tolerance
New % of Total Wealth
Allocations after 40%
Decline in Equity, 10%
Decline in Bonds and 5%
Gain In Riskless
% Holdings after 40%
Decline in Equity, 10%
Decline in Bonds and 5%
Gain In Riskless
(a)
0.1
6.24%
US Equity 5.47%
Dev Equity 5.94%
Em Equity 4.60%
Bonds 15.12%
Cash 68.87%
Total 100.00%
US Equity
Dev Equity
Em Equity
Bonds
Cash
Total
0.34%
0.37%
0.29%
0.94%
4.30%
6.24%
(b)
0.2
11.57%
(c)
0.3
21.32%
(d)
0.4
29.27%
(e)
0.5
18.69%
(f)
0.6
8.87%
(g)
0.7
4.05%
8.85%
9.60%
7.45%
24.46%
49.65%
100.00%
12.80%
13.89%
10.77%
35.38%
27.16%
100.00%
17.48%
18.97%
14.71%
48.34%
0.49%
100.00%
20.32%
22.57%
19.17%
37.94%
0.00%
100.00%
23.82%
26.87%
24.10%
29.99%
-4.79%
100.00%
29.83%
33.65%
30.18%
37.56%
-31.22%
100.00%
1.02%
1.11%
0.86%
2.83%
5.74%
11.57%
2.73%
2.96%
2.30%
7.55%
5.79%
21.32%
5.12%
5.55%
4.31%
14.15%
0.14%
29.27%
3.80%
4.22%
3.58%
7.09%
0.00%
18.69%
2.11%
2.38%
2.14%
2.66%
-0.42%
8.87%
1.21%
1.36%
1.22%
1.52%
-1.26%
4.05%
Total
16.33%
17.96%
14.69%
36.74%
14.29%
100.00%
Market Environment Before and After: Assumed Risk-Return
Structure, Market Index Weights
BEFORE
US Equity
Dev Equity
Em Equity
Bonds
Cash
Market Standard
Weights Deviation
20.00%
18.00%
22.00%
20.00%
18.00%
30.00%
30.00%
10.00%
10.00%
0.00%
US
Equity
1.00
0.65
0.60
0.40
Correlations
Dev
Em
Equity
Equity
0.65
0.60
1.00
0.60
0.60
1.00
0.35
0.30
Bonds
0.40
0.35
0.30
1.00
Equilibrium
Exp Return*
7.11%
7.60%
9.84%
4.71%
3.00%**
Bonds
0.50
0.50
0.45
1.00
Equilibrium
Exp Return*
13.53%
13.63%
17.37%
6.40%
1%**
* Average Risk Tolerance = 0.5
** Borrowing Cost = 3.50%
AFTER
US Equity
Dev Equity
Em Equity
Bonds
Cash
Market Standard
Weights Deviation
16.33%
30.00%
17.96%
30.00%
14.69%
40.00%
36.73%
15.00%
14.29%
0.00%
US
Equity
1.00
0.75
0.70
0.50
Correlations
Dev
Em
Equity
Equity
0.75
0.70
1.00
0.70
0.70
1.00
0.50
0.45
* Average Risk Tolerance = 0.385
** Borrowing Cost = 1.50%
Optimal Allocations and Turnover
Clientele
Risk Tolerance
% of Total Wealth
New Optimal Allocations
New % Holdings in
Economy
Change in Allocations
Change in % Holdings
in Economy
(a)
0.1
6.24%
US Equity 4.27%
Dev Equity 4.69%
Em Equity 3.75%
Bonds 10.55%
Cash 76.74%
Total 100.00%
(b)
0.2
11.57%
(c)
0.3
21.32%
(d)
0.4
29.27%
(e)
0.5
18.69%
(f)
0.6
8.87%
(g)
0.7
4.05%
8.54%
9.39%
7.49%
21.11%
53.48%
100.00%
12.81%
14.08%
11.24%
31.66%
30.21%
100.00%
17.08%
18.77%
14.99%
42.21%
6.95%
100.00%
20.98%
23.10%
19.45%
41.52%
-5.05%
100.00%
25.18%
27.72%
23.34%
49.82%
-26.07%
100.00%
29.37%
32.34%
27.23%
58.13%
-47.08%
100.00%
US Equity
Dev Equity
Em Equity
Bonds
Cash
Total
0.27%
0.29%
0.23%
0.66%
4.79%
6.24%
0.99%
1.09%
0.87%
2.44%
6.19%
11.57%
2.73%
3.00%
2.40%
6.75%
6.44%
21.32%
5.00%
5.49%
4.39%
12.35%
2.03%
29.27%
3.92%
4.32%
3.64%
7.76%
-0.94%
18.69%
2.23%
2.46%
2.07%
4.42%
-2.31%
8.87%
1.19%
1.31%
1.10%
2.35%
-1.91%
4.05%
US Equity
Dev Equity
Em Equity
Bonds
Cash
Total
-1.20%
-1.24%
-0.86%
-4.57%
7.87%
0.00%
-0.31%
-0.22%
0.05%
-3.35%
3.83%
0.00%
0.01%
0.19%
0.47%
-3.73%
3.05%
0.00%
-0.40%
-0.20%
0.27%
-6.13%
6.46%
0.00%
0.66%
0.53%
0.29%
3.58%
-5.05%
0.00%
1.36%
0.85%
-0.76%
19.83%
-21.27%
0.00%
-0.45%
-1.31%
-2.95%
20.57%
-15.86%
0.00%
US Equity
Dev Equity
Em Equity
Bonds
Cash
Total
-0.07%
-0.08%
-0.05%
-0.28%
0.49%
0.00%
-0.04%
-0.02%
0.01%
-0.39%
0.44%
0.00%
0.00%
0.04%
0.10%
-0.79%
0.65%
0.00%
-0.12%
-0.06%
0.08%
-1.79%
1.89%
0.00%
0.12%
0.10%
0.05%
0.67%
-0.94%
0.00%
0.12%
0.08%
-0.07%
1.76%
-1.89%
0.00%
-0.02%
-0.05%
-0.12%
0.83%
-0.64%
0.00%
Total
16.33%
17.96%
14.69%
36.73%
14.29%
100.00%
Total
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
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
No
Leverage
(A)
Equal
Wealth
Clienteles
(B)
No Decrease
in Risk
Tolerance
(C)
High
Correlations
(D)
Naïve
Rebalancing
(E)
Average Risk Tol
0.500
0.500
0.500
0.500
0.500
0.500
US Equity
Dev Equity
Em Equity
Bonds
Cash
7.11%
7.60%
9.84%
4.71%
3.00%
7.20%
7.68%
9.93%
4.79%
3.00%
7.23%
7.72%
9.96%
4.82%
3.00%
7.11%
7.60%
9.84%
4.71%
3.00%
7.11%
7.60%
9.84%
4.71%
3.00%
7.11%
7.60%
9.84%
4.71%
3.00%
Sharpe Ratio
0.274
0.280
0.282
0.274
0.274
0.274
Average Risk Tol
0.385
0.387
0.371
0.485
0.385
0.385
13.53%
13.63%
17.37%
6.40%
1.00%
14.21%
14.30%
18.03%
7.11%
1.00%
14.09%
14.19%
18.08%
6.68%
1.00%
10.96%
11.04%
14.01%
5.30%
1.00%
16.14%
16.18%
21.22%
8.09%
1.00%
13.02%
13.11%
16.67%
6.34%
1.00%
Sharpe Ratio
0.481
0.513
0.503
0.382
0.533
0.464
Total Turnover
7.44%
1.68%
8.62%
5.64%
5.79%
8.23%
Before
Equilibriu
m
Expected
Returns
After
Equilibriu
m
Expected
Returns
US Equity
Dev Equity
Em Equity
Bonds
Cash
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”
90
VIX Index Level
80
70
60
50
40
30
20
10
0
1/2/1990
9/28/1992
6/25/1995
1800
3/21/1998
12/15/2000
9/11/2003
6/7/2006
3/3/2009
9/11/2003
6/7/2006
3/3/2009
S&P 500 Index Level
1600
1400
1200
1000
800
600
400
200
0
1/2/1990
9/28/1992
6/25/1995
3/21/1998
12/15/2000
Example: Conditional Variance-Covariance = Control for “Black Swans” (cont’d.)
12
10
S&P 500 Returns Scaled by Standard Deviation Measured Over Entire Period
8
6
4
2
0
-2
-4
-6
-8
-10
-12
1/2/1990
12
10
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
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
S&P 500 Returns Scaled by
VIX on Preceding Day
Mean
0.018302
0.017289
Median
0.044372
0.048046
Standard Deviation
1.000000
0.776764
Sample Variance
1.000000
0.603362
Kurtosis
11.963779
4.473268
Skewness
-0.200296
-0.361824
Minimum
-8.059105
-5.031819
Probability of Seeing Minimum
or Less if Normal
Maximum
0.00000000017166268407%
9.325208
Probability of Seeing Maximum 0.00000000000000000000%
or More if Normal
0.12512451075820100000%
3.307484
91.16557201094780%
Interesting Questions re “Black Swans”?

Who buys insurance against “black swan”
events, who supplies this insurance, who selfinsures, when does the insurance market “break
down”….etc.