Actuarial Financial Scenario Generator Project

Sponsored by the Casualty Actuarial Society and the Society of Actuaries

Kevin Ahlgrim, ASA, Bradley UniversityStephen D’Arcy, FCAS, University of Illinois

Richard Gorvett, FCAS, Zurich North America

Presented at Victoria UniversityWellington, New Zealand

February 2003

Overview of Project

CAS/SOA Request for Proposals on:

Economic Scenario Generators for Dynamic Financial Analysis and Cash Flow Testing

Goal is to provide actuaries a model for projecting economic and financial indices with realistic interdependencies among the variables.

Scope of Project

• Literature review

• Develop economic (financial) scenario generator model

• Generate scenarios over 50 year time horizon

• Document and facilitate use of model

Components of Model• Inflation

• Real interest rates

• Nominal interest rates

• Equity returns– Large stocks– Small stocks

• Equity dividend yields

• Real estate returns

• Unemployment

Inflation

One factor mean reverting process

Speed of reversion: .4

Mean reversion level: 4.8%

qtqt dBdtqdq )( (1)

Real Interest Rates

• Two factor Vasicek term structure model

• Short term rate and long term mean are both stochastic variables

222

111

)(

)(

dBdtldl

dBdtrldr

tt

ttt

r r r l l 6.1 2.8% 10.0% 5.1 10.0%

Nominal Interest Rates

Combines inflation and real interest rates

i = (1+q)x(1+r)-1

i = nominal interest rate

q = inflation

r = real interest rate

Equity Returns

• Excess equity returns (over the nominal interest rate)

• Empirical “fat tails” issue

• Regime switching model– Low volatility regime– High volatility regime

Excess Monthly Returns (1988 – 2001)

Low Volatility Regime High Volatility Regime

Large Stocks

Small Stocks Large Stocks

Small Stocks

Mean 0.6% 0.9% 0.4% -0.7%

Variance 2.2% 3.8% 4.7% 7.1%

Probability of Switching

2.7% 1.0% 2.3% 3.7%

Excess Monthly Returns (1982 – 2001) – Large Stocks Only

Low Volatility Regime High Volatility Regime

Mean 0.7% -9.0%

Variance 3.9% 8.4%

Probability of Switching

2.4% 70.4%

Unemployment

• Phillips curve– Inverse relationship between unemployment and

inflation

• First order autoregressive process

utututuut dqdtudu )(

Results• Funnel of doubt plots

• Histograms of Actual Values vs. Model Values – Inflation– Nominal interest rates

• 3 month• 1 year• 10 year

– Equity returns• Large stocks• Small stocks

• Unemployment rate

Figure 51 Year Inflation Rate (L4 to L30)

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

L4 L6 L8 L10 L12 L14 L16 L18 L20 L22 L24 L26 L28 L30

Cell

Figure 7 Actual Inflation Rates (1913-2001)

versus Model Values

0.00

0.05

0.10

0.15

0.20

-0.1

2

-0.0

9

-0.0

6

-0.0

3

0.00

0.03

0.06

0.09

0.12

0.15

0.18

Inflation Rate

Model

Actual

Figure 11Actual 3 Month Interest Rates (1/31-6/02)

versus Model 1 Month Values

00.050.1

0.150.2

0.25

-0.2

-0.1

-0.1

-0.1 -0 0

0.03

0.06

0.09

0.12

0.15

0.18

0.21

0.24

Interest Rate

Model

Actual

Figure 12 Actual 1 Year Interest Rates (4/53-6/02)

versus Model 1 Year Interest Rates

0

0.05

0.1

0.15

0.2

-0.1 -0 -0

0.01

0.03

0.05

0.07

0.09

0.11

0.13

0.15

0.17

0.19

Interest Rate

Model

Actual

Figure 13 Actual 10 Year Interest Rates (4/54-6/02)

versus Model 20 Year Rates

00.10.20.30.40.50.6

0

0.02

0.04

0.06

0.08 0.1

0.12

0.14

0.16

0.18

Interest Rate

Model

Actual

Figure 16Actual Large Stock Returns (1871-2002)

versus Model Large Stock Returns

0

0.010.02

0.03

0.04

0.050.06

0.07

0.080.09

0.1

0.110.12

0.13

0.14

0.150.16

0.17

-0.8

-0.6

-0.5

-0.3

-0.2 0

0.15 0.3

0.45 0.6

0.75 0.9

1.05 1.2

1.35 1.5

1.65 1.8

1.95 2.1

2.25 2.4

Actual

Model

Figure 17Actual Small Stock Returns (1926-1999)

versus Model Small Stock Returns

00.020.040.060.080.1

0.120.14

-0.8

-0.5

-0.3 0

0.25 0.5

0.75 1

1.25 1.5

1.75 2

2.25

Model

Actual

Figure 21Actual Unemployment (1/48-1/02) versus Model

Unemployment Rates

0

0.05

0.1

0.15

0.2

0.25

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09 0.1

0.11

0.12

Model

Actual