Introduction
LC Model
Subprime!
The Theory of Optimal Life-Cycle Saving and
Investing
Paul Willen (joint with Zvi Bodie and Jonathan Treussard)
Federal Reserve Bank of Boston
Q-Group Spring Seminar, March 31, 2008
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
1 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Disclaimer
The views expressed today are mine.
The do not necessarily reflect the views of
The Boston Fed
or the Federal Reserve System
When I say “we”, I mean members of the research
department.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
2 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Disclaimer
The views expressed today are mine.
The do not necessarily reflect the views of
The Boston Fed
or the Federal Reserve System
When I say “we”, I mean members of the research
department.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
2 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Disclaimer
The views expressed today are mine.
The do not necessarily reflect the views of
The Boston Fed
or the Federal Reserve System
When I say “we”, I mean members of the research
department.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
2 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Disclaimer
The views expressed today are mine.
The do not necessarily reflect the views of
The Boston Fed
or the Federal Reserve System
When I say “we”, I mean members of the research
department.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
2 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Disclaimer
The views expressed today are mine.
The do not necessarily reflect the views of
The Boston Fed
or the Federal Reserve System
When I say “we”, I mean members of the research
department.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
2 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Disclaimer
The views expressed today are mine.
The do not necessarily reflect the views of
The Boston Fed
or the Federal Reserve System
When I say “we”, I mean members of the research
department.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
2 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
This paper
Zvi said:
Let’s try to make life-cycle portfolio choice accessible.
Practitioners
Key lessons
Wide audience
I said:
No problem!
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
3 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
There are N states of the world indexed by ω ∈ Ω and T + 1
time period t = 0, 1, 2, ..., T . An event tree describes the
information structure of the economy and {Ft ; t = 0, .., T } is
the sequence of partitions of Ω corresponding to the tree. All
stochastic process are adapted tot he filtration generated by
the {Ft }.
At each date there are K + 1 securities available for trading in
frictionless markets, with K ≥ 0. We use Stk to denote the
price of security k at time t,
{St = (St0 , St1 , ..., StK )′ ; t = 0, 1, ..., T } to denote the price of
securities price pricess and assume that |Stk | < +∞ for
t = 0, 1, ..., T and K = 0, 1, 2, ..., k. For convenience we
assume that the securities pay no dividends. This affects
nothing.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
4 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
There are N states of the world indexed by ω ∈ Ω and T + 1
time period t = 0, 1, 2, ..., T . An event tree describes the
information structure of the economy and {Ft ; t = 0, .., T } is
the sequence of partitions of Ω corresponding to the tree. All
stochastic process are adapted tot he filtration generated by
the {Ft }.
At each date there are K + 1 securities available for trading in
frictionless markets, with K ≥ 0. We use Stk to denote the
price of security k at time t,
{St = (St0 , St1 , ..., StK )′ ; t = 0, 1, ..., T } to denote the price of
securities price pricess and assume that |Stk | < +∞ for
t = 0, 1, ..., T and K = 0, 1, 2, ..., k. For convenience we
assume that the securities pay no dividends. This affects
nothing.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
4 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Zvi said:
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
5 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Zvi said:
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
5 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Brief history
Zvi, Jonathan and I wrote this paper in October of 2006.
Mortgages were just part of my research agenda then...
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
6 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Brief history
Zvi, Jonathan and I wrote this paper in October of 2006.
Mortgages were just part of my research agenda then...
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
6 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Brief history
Zvi, Jonathan and I wrote this paper in October of 2006.
Mortgages were just part of my research agenda then...
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
6 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Brief history
Zvi, Jonathan and I wrote this paper in October of 2006.
Mortgages were just part of my research agenda then...
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
6 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Disclaimer
This paper
Outline of the talk
Today’s presentation
Do two things:
1
Review the basic points of the paper
Describe the model
Focus on the key insights
2
Life-cycle analysis and the subprime crisis
Understanding the crisis
Evaluating policy responses
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
7 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
LC Model
“Life-Cycle” or LC
Not really
No “re-birth”!
“Life Course”
Not just time
Different outcomes
“Contingencies”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
8 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(1) Youth (21-35)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(1) Youth (21-35)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(1) Youth (21-35)
Start
Income: $30,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Start
Income: $30,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Start
Income: $30,000 a year
(L) Low Income
Income: $50,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Start
Income: $30,000 a year
(LG ) Good Health
Expenses: $5,000 a year
(L) Low Income
Income: $50,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Start
Income: $30,000 a year
(LG ) Good Health
Expenses: $5,000 a year
(L) Low Income
Income: $50,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Start
Income: $30,000 a year
(LG ) Good Health
Expenses: $5,000 a year
(L) Low Income
Income: $50,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Start
Income: $30,000 a year
(LG ) Good Health
Expenses: $5,000 a year
(L) Low Income
Income: $50,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consider a portfolio strategy
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consider a portfolio strategy
Don’t care about accumulation, returns.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Consider a portfolio strategy
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Don’t care about accumulation, returns.
Key is implied consumption flow
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Some situations
Willen (Boston Fed)
(3) Retirement (66-80)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Some situations
lots of consumption...
very little consumption...
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Some situations
lots of consumption...
very little consumption...
Smooth consumption
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Financial assets allow people to move consumption from one
place to another.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
1
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Financial assets allow people to move consumption from one
place to another.
1
Borrowing
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
1
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
2
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(LG ) Good Health
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
2
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Financial assets allow people to move consumption from one
place to another.
1
2
Borrowing
Health insurance
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
1
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(3) Retirement (66-80)
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
2
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
3
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
(LG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
2
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Financial assets allow people to move consumption from one
place to another.
1
2
3
Borrowing
Health insurance
“Income Insurance”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
9 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Brief Overview
Three insights from the LC model:
1
2
3
The role of human capital
Risky assets in the LC model
Portfolio constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
10 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Brief Overview
Three insights from the LC model:
1
2
3
The role of human capital
Risky assets in the LC model
Portfolio constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
10 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Brief Overview
Three insights from the LC model:
1
2
3
The role of human capital
Risky assets in the LC model
Portfolio constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
10 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Brief Overview
Three insights from the LC model:
1
2
3
The role of human capital
Risky assets in the LC model
Portfolio constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
10 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Brief Overview
Three insights from the LC model:
1
2
3
The role of human capital
Risky assets in the LC model
Portfolio constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
10 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
The role of human capital
How much money does an investor have to invest?
Financial wealth
+ using financial assets, he can transfer all his future labor
income to the present
We call that human wealth
Total wealth
Total wealth = Financial wealth + Human wealth
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
11 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
The role of human capital
How much money does an investor have to invest?
Financial wealth
+ using financial assets, he can transfer all his future labor
income to the present
We call that human wealth
Total wealth
Total wealth = Financial wealth + Human wealth
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
11 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
The role of human capital
How much money does an investor have to invest?
Financial wealth
+ using financial assets, he can transfer all his future labor
income to the present
We call that human wealth
Total wealth
Total wealth = Financial wealth + Human wealth
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
11 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
The role of human capital
How much money does an investor have to invest?
Financial wealth
+ using financial assets, he can transfer all his future labor
income to the present
We call that human wealth
Total wealth
Total wealth = Financial wealth + Human wealth
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
11 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
The role of human capital
How much money does an investor have to invest?
Financial wealth
+ using financial assets, he can transfer all his future labor
income to the present
We call that human wealth
Total wealth
Total wealth = Financial wealth + Human wealth
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
11 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
The role of human capital
How much money does an investor have to invest?
Financial wealth
+ using financial assets, he can transfer all his future labor
income to the present
We call that human wealth
Total wealth
Total wealth = Financial wealth + Human wealth
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
11 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Human wealth is...
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
12 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Human wealth is...
1
huge
35
25.9
Men with high school degree
(=
Men with high school degree
19.1
(=
Women with college degree
629,378
33,005 )
20.1
(=
Willen (Boston Fed)
1,483,295
57,264 )
792,354
39,424 )
Life-Cycle Theory
March 31, 2008
12 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Human wealth is...
1
2
huge
differs across people
25
47.4
Men with high school degree
(=
Men with high school degree
(=
29.7
(=
Women with college degree
718,530
24,199 )
881,762
26,808 )
1,483,295
57,264 )
45
15.9
(=
19.1
(=
32.9
(=
Willen (Boston Fed)
1,483,412
31,297 )
35
25.9
629,378
33,005 )
792,354
39,424 )
Life-Cycle Theory
(=
691,057
79,566 )
(=
219,269
26,814 )
(=
266,430
38,064 )
12.8
(=
20.1
(=
1,212,542
76,385 )
55
8.7
439,494
34,301 )
8.2
13.3
(=
580,133
43,506 )
7.0
March 31, 2008
12 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Human wealth is...
1
2
huge
differs across people
25
47.4
Men with high school degree
(=
Men with high school degree
1,483,412
31,297 )
35
25.9
(=
29.7
(=
Women with college degree
718,530
24,199 )
881,762
26,808 )
(=
19.1
(=
32.9
(=
1,483,295
57,264 )
45
15.9
629,378
33,005 )
792,354
39,424 )
(=
691,057
79,566 )
(=
219,269
26,814 )
(=
266,430
38,064 )
12.8
(=
20.1
(=
1,212,542
76,385 )
55
8.7
439,494
34,301 )
8.2
13.3
(=
580,133
43,506 )
7.0
How should we view a $250,000 portfolio?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
12 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Human wealth is...
1
2
huge
differs across people
25
47.4
Men with high school degree
(=
Men with high school degree
1,483,412
31,297 )
35
25.9
(=
29.7
(=
Women with college degree
718,530
24,199 )
881,762
26,808 )
(=
19.1
(=
32.9
(=
1,483,295
57,264 )
45
15.9
629,378
33,005 )
792,354
39,424 )
(=
691,057
79,566 )
(=
219,269
26,814 )
(=
266,430
38,064 )
12.8
(=
20.1
(=
1,212,542
76,385 )
55
8.7
439,494
34,301 )
8.2
13.3
(=
580,133
43,506 )
7.0
How should we view a $250,000 portfolio?
As almost 40% of a 45-year old high-school grad’s total
wealth?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
12 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Human wealth is...
1
2
huge
differs across people
25
47.4
Men with high school degree
(=
Men with high school degree
1,483,412
31,297 )
35
25.9
(=
29.7
(=
Women with college degree
718,530
24,199 )
881,762
26,808 )
(=
19.1
(=
32.9
(=
1,483,295
57,264 )
45
15.9
629,378
33,005 )
792,354
39,424 )
(=
691,057
79,566 )
(=
219,269
26,814 )
(=
266,430
38,064 )
12.8
(=
20.1
(=
1,212,542
76,385 )
55
8.7
439,494
34,301 )
8.2
13.3
(=
580,133
43,506 )
7.0
How should we view a $250,000 portfolio?
As almost 40% of a 45-year old high-school grad’s total
wealth?
As < 20% of a 45-year old college grad’s?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
12 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Risky assets in the LC model
Risky assets not about accumulation – transfers across time
Transfer money across outcomes.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
13 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Risky assets in the LC model
Risky assets not about accumulation – transfers across time
Transfer money across outcomes.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
13 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Risky assets in the LC model
Risky assets not about accumulation – transfers across time
Transfer money across outcomes.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
13 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
This year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
This year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
This year
Start
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
“Good Times”
This year
Start
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
“Good Times”
This year
Start
“Bad Times”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
“Good Times”
This year
Start
Bond
“Bad Times”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
“Good Times”
This year
Bond
+5%
Start
Bond
“Bad Times”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
“Good Times”
This year
Bond
+5%
Start
Bond
“Bad Times”
Bond
Willen (Boston Fed)
Life-Cycle Theory
+5%
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Bond
+5%
1
“Bad Times”
Bond
1
+5%
Bonds allow you to move money across time
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Bond
+5%
1
“Bad Times”
Bond
1
+5%
Bonds allow you to move money across time
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Bond
Stock
+5%
+30%
1
“Bad Times”
Bond
1
+5%
Bonds allow you to move money across time
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Bond
Stock
+5%
+30%
1
“Bad Times”
Bond
Stock
1
+5%
−5%
Bonds allow you to move money across time
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Bond
Stock
+5%
+30%
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
−$100
Bond
Stock
+5%
+30%
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
−$100
$100
Bond
Stock
+5%
+30%
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
+5%
+30%
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
+5%
+30%
−$105
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
+5%
+30%
−$105
+$130
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
−$105
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
1
2
+5%
−5%
−$105
+$95
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
1
2
+5%
−5%
−$105
+$95
= −$10
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
1
2
+5%
−5%
−$105
+$95
= −$10
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Much better than fair odds.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
1
2
+5%
−5%
−$105
+$95
= −$10
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Much better than fair odds.
Move money the “wrong” way (from “bad times” to “good
times”)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
1
2
+5%
−5%
−$105
+$95
= −$10
Bonds allow you to move money across time
Stocks allow you to move money across outcomes
Much better than fair odds.
Move money the “wrong” way (from “bad times” to “good
times”)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
+5%
−5%
−$105
+$95
= −$10
LC model views risky assets not as transfers across times but
across outcomes.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
+5%
−5%
−$105
+$95
= −$10
LC model views risky assets not as transfers across times but
across outcomes.
Makes sense for people if
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
+5%
−5%
−$105
+$95
= −$10
LC model views risky assets not as transfers across times but
across outcomes.
Makes sense for people if
Bad times aren’t that bad – bankruptcy lawyer
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Introduction
LC Model
Subprime!
Next year
“Good Times”
This year
Start
Bond
Stock
Investment
−$100
$100
= $0
Bond
Stock
Payoff
+5%
+30%
−$105
+$130
= $25
1
2
“Bad Times”
Bond
Stock
Payoff
+5%
−5%
−$105
+$95
= −$10
LC model views risky assets not as transfers across times but
across outcomes.
Makes sense for people if
Bad times aren’t that bad – bankruptcy lawyer
No free lunch.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
14 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Realistic constraints
Assume move resources around at will.
Healthy to sick ⇐ actuarially fair insurance
Good times to bad times ⇐ unlimited short sales
Prime working years to youth ⇐ unlimited borrowing
Can we do this in real life? No.
Research on portfolio choice with constaints
Short-sale constraints
Borrowing constraints
Collateral constraints
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
15 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
(2) Prime Earning Years
(36-65)
(1) Youth (21-35)
(H) High Income
1
Income: $100,000 a year
Advice: Save $20,000 a year
Consumption: $80,000 a year
(HG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
2
(HB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Start
Income: $30,000 a year
Advice: Save $10,000 a year
Consumption: $20,000 a year
(3) Retirement (66-80)
3
(L) Low Income
Income: $50,000 a year
Advice: Save $20,000 a year
Consumption: $30,000 a year
(LG ) Good Health
Expenses: $5,000 a year
Advice: Withdraw $50,000 a year
Consumption: $45,000 a year
2
(LB) Bad Health
Expenses: $15,000 a year
Advice: Withdraw $50,000 a year
Consumption: $35,000 a year
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
16 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Key issue: Cost of funds
Source of funds:
Liquid assets
Cost = return on investments
Borrowing
Cost = borrowing interest rate
Reduced consumption
Cost = relative value of consumption today and consumption
in the future.
Cost of funds impacts everything.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
17 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
This year
“Good Times”
“Funds”
Stock
Payoff
Start
“Funds”
Stock
Investment
−$100
$100
= $0
−$105
+$130
= $25
“Bad Times”
“Funds”
Stock
Payoff
Willen (Boston Fed)
+5%
+30%
Life-Cycle Theory
+5%
−5%
−$105
+$95
= −$10
March 31, 2008
18 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
This year
“Good Times”
“Funds”
Stock
Payoff
Start
“Funds”
Stock
Investment
−$100
$100
= $0
−$120
+$130
= $10
“Bad Times”
“Funds”
Stock
Payoff
Willen (Boston Fed)
+20%
+30%
Life-Cycle Theory
+5%
−5%
−$105
+$95
= −$10
March 31, 2008
18 / 50
Introduction
LC Model
Subprime!
Overview
The role of human capital
Risky assets in the LC model
Importance of portfolio constraints
Next year
This year
“Good Times”
“Funds”
Stock
Payoff
Start
“Funds”
Stock
Investment
−$100
$100
= $0
−$120
+$130
= $10
“Bad Times”
“Funds”
Stock
Payoff
Willen (Boston Fed)
+20%
+30%
Life-Cycle Theory
+20%
−5%
−$120
+$95
= −$25
March 31, 2008
18 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Subprime!
Do three things:
1
2
3
Causes of the subprime crisis
Life-cycle analysis of foreclosure decision
Policy analysis
Analysis from
“Subprime Outcomes” by Gerardi, Shapiro and Willen.
Available on the Boston Fed website (www.bos.frb.org)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
19 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Caveat
Everything I’m about to say could be wrong:
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
20 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Caveat
Everything I’m about to say could be wrong:
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
20 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
We are learning new things every day
“Why, just fifty years ago, they thought a disease like
your daughter’s was caused by demonic possession or
witchcraft. But nowadays we know that Isabelle is
suffering from an imbalance of bodily humors, perhaps
caused by a toad or a small dwarf living in her stomach.”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
21 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
We are learning new things every day
Figure: Theodoric of York, Medieval Barber (and intellectual)
“Why, just fifty years ago, they thought a disease like
your daughter’s was caused by demonic possession or
witchcraft. But nowadays we know that Isabelle is
suffering from an imbalance of bodily humors, perhaps
caused by a toad or a small dwarf living in her stomach.”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
21 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
We are learning new things every day
Figure: Theodoric of York, Medieval Barber (and intellectual)
“Why, just fifty years ago, they thought a disease like
your daughter’s was caused by demonic possession or
witchcraft. But nowadays we know that Isabelle is
suffering from an imbalance of bodily humors, perhaps
caused by a toad or a small dwarf living in her stomach.”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
21 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Do borrowers default at ARM reset?
Subprime 2/28s just in MA, CT and RI.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
22 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
ARMs more generally
Data from MBA
Servicer data
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
23 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
ARMs more generally
Data from MBA
Servicer data
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
23 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
ARMs more generally
Data from MBA
Servicer data
20
18
16
Subprime ARMs ց
% of loans
14
12
10
8
2005
Willen (Boston Fed)
2006
Life-Cycle Theory
2007
March 31, 2008
23 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
ARMs more generally
Data from MBA
Servicer data
20
18
16
Subprime ARMs ց
% of loans
14
12
Subprime Fixed ց
10
8
2005
Willen (Boston Fed)
2006
Life-Cycle Theory
2007
March 31, 2008
23 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
What is this number?
“Percentage of Loans Past Due”
=
Loans Past Due ⇐
Total Loans ⇐
What could make this number go up?
Higher delinquencies
Lower number of loans
Problem here
Suppose a current borrower with a subprime ARM
refinances into a subprime FRM
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
24 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Total Number of Loans
3
2.8
տSubprime ARMs
2008.5
# of loans in millions
2.6
2.4
2.2
2
1.8
1.6
2005
Willen (Boston Fed)
2006
Life-Cycle Theory
2007
March 31, 2008
25 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Total Number of Loans
3
2.8
տSubprime ARMs
2008.5
# of loans in millions
2.6
2.4
2.2
2
տSubprime Fixed
1.8
1.6
2005
Willen (Boston Fed)
2006
Life-Cycle Theory
2007
March 31, 2008
25 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Simple adjustment
Correct for the changing denominator
By just looking at the numerator
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
26 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Total number of past due loans
500
2008
# of loans in thousands
400
300
տSubprime ARMs
200
2005
Willen (Boston Fed)
2006
Life-Cycle Theory
2007
March 31, 2008
27 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Total number of past due loans
500
2008
# of loans in thousands
400
300
տSubprime ARMs
Subprime Fixedց
200
2005
Willen (Boston Fed)
2006
Life-Cycle Theory
2007
March 31, 2008
27 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
It’s the house prices
Figure: Foreclosures and house prices in Mass., 1989-present. Source:
Boston Fed and The Warren Group.
% of homes foreclosed
0.8
0.6
0.4
ւ Foreclosure rate
0.2
0
Willen (Boston Fed)
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
Life-Cycle
Year Theory
March 31, 2008
28 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
It’s the house prices
Figure: Foreclosures and house prices in Mass., 1989-present. Source:
Boston Fed and The Warren Group.
0.6
0.4
ւ Foreclosure rate
0.2
0
15
10
5
0
-5
տ House price growth
Willen (Boston Fed)
-10
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
Life-Cycle
Year Theory
% growth at annual rates
% of homes foreclosed
0.8
March 31, 2008
28 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Causality
Figure: Foreclosures and 30-day delinquency rates in Mass.,
1989-present. Source: Boston Fed, the MBA and The Warren Group.
% of homes foreclosed
0.8
0.6
0.4
ւ Foreclosure rate
0.2
0
Willen (Boston Fed)
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
Life-Cycle
Year Theory
March 31, 2008
29 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Causality
Figure: Foreclosures and 30-day delinquency rates in Mass.,
1989-present. Source: Boston Fed, the MBA and The Warren Group.
0.6
0.4
ւ Foreclosure rate
0.2
0
ւ 30-day Delinquency rate
2.8
2.6
2.4
2.2
2
Willen (Boston Fed)
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
Life-Cycle
Year Theory
% of borrowers delinquent
% of homes foreclosed
0.8
March 31, 2008
29 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Foreclosure Hazards
0.8
Quarterly default hazard, in %
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
Years after purchase
10
12
14
HPA>20%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
30 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Foreclosure Hazards
0.8
Quarterly default hazard, in %
0.7
0.6
0.5
0.4
0.3
0.2
0% < HPA ≤ 20% ց
0.1
0
0
2
4
6
8
Years after purchase
10
12
14
HPA>20%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
30 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Foreclosure Hazards
0.8
Quarterly default hazard, in %
0.7
0.6
0.5
0.4
ւ −20% < HPA ≤ 0%
0.3
0.2
0% < HPA ≤ 20% ց
0.1
0
0
2
4
6
8
Years after purchase
10
12
14
HPA>20%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
30 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Foreclosure Hazards
0.8
ւ HPA ≤ −20%
Quarterly default hazard, in %
0.7
0.6
0.5
0.4
ւ −20% < HPA ≤ 0%
0.3
0.2
0% < HPA ≤ 20% ց
0.1
0
0
2
4
6
8
Years after purchase
10
12
14
HPA>20%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
30 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Bottom Line
Quarterly default hazard, in %
0.5
0.4
0.3
0.2
0.1
2002↓
0
0
Willen (Boston Fed)
5
10
15
20
Months after purchase
Life-Cycle Theory
25
30
March 31, 2008
31 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Bottom Line
Quarterly default hazard, in %
0.5
0.4
2005ց
0.3
0.2
0.1
2002↓
0
0
Willen (Boston Fed)
5
10
15
20
Months after purchase
Life-Cycle Theory
25
30
March 31, 2008
31 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Bottom Line
Quarterly default hazard, in %
0.5
0.4
2005ց
0.3
0.2
↓2005 with 2002 prices
0.1
2002↓
0
0
Willen (Boston Fed)
5
10
15
20
Months after purchase
Life-Cycle Theory
25
30
March 31, 2008
31 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
House prices and default
Why does default when house prices fall?
House price falls reduce equity:
Equity = House Price − Mortgage Balance
Theory says:
Positive equity ⇒ No foreclosures
borrower can sell the house
Almost no borrowers with positive equity default (< 0.1% at
quarterly frequency)
Does negative equity ⇒ foreclosure?
NO!
Recall < 1% at quarterly frequency
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
32 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Table: Negative Equity Homeowners and Subsequent Foreclosures
# Negative Equity Homeowners in Q4, 1991
who ended up in foreclosure in...
1
Q1
2
Q2
1992
3
Q3
4
Q4
5
Q1
6
Q2
1993
7
Q3
8
Q4
9
Q1
10
Q2
1994
11
Q3
12
Q4
Total
% of Negative Equity Homeowners
Willen (Boston Fed)
Life-Cycle Theory
100,288
618
542
610
606
606
535
490
516
490
543
480
417
6,453
6.4
March 31, 2008
33 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Price of House
Mortgage balance
Willen (Boston Fed)
$200K
−$225K
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
Willen (Boston Fed)
$200K
−$225K
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
Willen (Boston Fed)
Irrational
Attachment to
house
$200K
−$225K
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
Irrational
Attachment to
house
$200K
−$225K
Hit to credit score
or report
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
Irrational
Attachment to
house
$200K
−$225K
Hit to credit score
or report
Stigma
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
Irrational
Attachment to
house
$200K
−$225K
Hit to credit score
or report
Stigma
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
You have a
zero-percent
interest only
mortgage
Irrational
Attachment to
house
$200K
−$225K
Hit to credit score
or report
Stigma
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Why would someone with negative equity keep a house?
Moving costs
Price of House
Mortgage balance
$200K
−$225K
Irrational
Attachment to
house
Hit to credit score
or report
You have a
zero-percent
interest only
mortgage
50% chance that
the the price rises
by 25% to $250K
in next year
Stigma
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
34 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Willen (Boston Fed)
2013
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
Willen (Boston Fed)
2013
$200K
−$225K
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
2013
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Price of House
Mortgage balance
Willen (Boston Fed)
$200K
−$225K
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
2013
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Price of House
Mortgage balance
$200K
−$225K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
Willen (Boston Fed)
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Life-Cycle Theory
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Constructing “Asset K ” (“K”eep the house)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
Willen (Boston Fed)
$50K
$35K
$15K
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance $200K
Payoff
$50K
$50K
$35K
$15K
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
Willen (Boston Fed)
$50K
$35K
$15K
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance $200K
Payoff
$50K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance $200K
Payoff
$0K
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
“Asset K ”
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
Willen (Boston Fed)
$50K
$35K
$15K
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance $200K
Payoff
$50K
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance $200K
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
35 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Eric Rosengren’s Homeownership Experience
Eric Rosengren is the President of the Boston Fed.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
36 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Eric Rosengren’s Homeownership Experience
Eric Rosengren is the President of the Boston Fed.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
36 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Eric Rosengren’s Homeownership Experience
Eric Rosengren is the President of the Boston Fed.
He bought his house in the summer of 1988.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
36 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Eric Rosengren’s Homeownership Experience
Figure: Cumulative appreciation for Massachusetts homeowner who
bought in Q3, 1988.
100
80
60
40
20
0
-20
88
Willen (Boston Fed)
90
92
94
96
98
00
Life-Cycle Theory
02
04
06
08
March 31, 2008
37 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Eric Rosengren’s Homeownership Experience
Figure: Cumulative appreciation for Massachusetts homeowner who
bought in Q3, 1988.
100
80
60
40
20
0
-20
88
Willen (Boston Fed)
90
92
94
96
98
00
Life-Cycle Theory
02
04
06
08
March 31, 2008
37 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
1 Mr. Savings
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
1 Mr. Savings
Cost of funds is 5%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
1 Mr. Savings
Cost of funds is 5%
Over five years, 30%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
1 Mr. Savings
Cost of funds is 5%
Over five years, 30%
2
No savings (spendthrift, life event)
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
1 Mr. Savings
Cost of funds is 5%
Over five years, 30%
2
No savings (spendthrift, life event)
Cost of funds is 20%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
And the “Cost of funds”
Two people
1 Mr. Savings
Cost of funds is 5%
Over five years, 30%
2
No savings (spendthrift, life event)
Cost of funds is 20%
Over five years, 150%
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
38 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Asset K ”
Start
“Asset K ”
+$333
2
$100
“Bad Times”
“Asset K ”
Willen (Boston Fed)
+233%
Life-Cycle Theory
−100%
+$0
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Asset K ”
Start
“Funds”
“Asset K ”
Investment
+$333
2
−$100
$100
= $0
“Bad Times”
“Asset K ”
Willen (Boston Fed)
+233%
Life-Cycle Theory
−100%
+$0
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Funds”
“Asset K ”
Payoff
Start
“Funds”
“Asset K ”
Investment
−$100
$100
= $0
−$130
+$333
= $203
2
“Bad Times”
“Asset K ”
Willen (Boston Fed)
+30%
+233%
Life-Cycle Theory
−100%
+$0
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Funds”
“Asset K ”
Payoff
Start
“Funds”
“Asset K ”
Investment
−$100
$100
= $0
+30%
+233%
−$130
+$333
= $203
2
“Bad Times”
“Funds”
“Asset K ”
Payoff
+30%
−100%
−$130
+$0
= −$130
Expected Payoff = $120
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Funds”
“Asset K ”
Payoff
Start
“Funds”
“Asset K ”
Investment
−$100
$100
= $0
+100%
+233%
−$250
+$333
= $83
2
“Bad Times”
“Funds”
“Asset K ”
Payoff
+30%
−100%
−$130
+$0
= −$130
Expected Payoff = $120
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Funds”
“Asset K ”
Payoff
Start
“Funds”
“Asset K ”
Investment
−$100
$100
= $0
+100%
+233%
−$250
+$333
= $83
2
“Bad Times”
“Funds”
“Asset K ”
Payoff
+100%
−100%
−$250
+$0
= −$250
Expected Payoff = $120
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Next year
This year
“Good Times”
“Funds”
“Asset K ”
Payoff
Start
“Funds”
“Asset K ”
Investment
−$100
$100
= $0
+100%
+233%
−$250
+$333
= $83
2
“Bad Times”
“Funds”
“Asset K ”
Payoff
+100%
−100%
−$250
+$0
= −$250
Expected Payoff = −$1
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
39 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Policy Analysis
Many policy proposals floating around
Basic idea
Choose a group of people
All
All
All
All
subprime borrowers
people with negative equity
borrowers
delinquent borrowers
Offer a new mortgage
Do two things:
Basic logic
Evaluate some schemes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
40 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The cruel arithmetic of principal reduction
Let
m = the outstanding balance on the mortgage.
p H = the price of the house
λ = deadweight loss of foreclosure
a = principal reduction
Logic for principal reduction
a
< m − (p H − λ)
|{z}
| {z }
principal
expected
reduction
recovery
a < m − (p H − λ)
So long as condition holds, principal reduction is win/win.
If recovery value m − (p H − λ) =50%, then lender can forgive
50% and win/win.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
41 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The problem: Only α% of the people actually default
Condition becomes
H
a
< m − α(p − λ) + (1 − α)m
|{z}
|
{z
}
principal
Expected
reduction
repayment
Or:
a < α · [m − (p H − λ)]
Suppose recovery is 50% but foreclosure probability is 10%,
then a < 5%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
42 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The problem: Only α% of the people actually default
Condition becomes
H
a
< m − α(p − λ) + (1 − α)m
|{z}
|
{z
}
principal
Expected
reduction
repayment
Or:
a < α · [m − (p H − λ)]
Suppose recovery is 50% but foreclosure probability is 10%,
then a < 5%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
42 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
The problem: Only α% of the people actually default
Condition becomes
H
a
< m − α(p − λ) + (1 − α)m
|{z}
|
{z
}
principal
Expected
reduction
repayment
Or:
a < α · [m − (p H − λ)]
Suppose recovery is 50% but foreclosure probability is 10%,
then a < 5%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
42 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
This is a moral hazard problem.
If you can’t tell who “needs” principal reduction, everyone will
take it.
To design a program that works, you need to:
Make α as high as possible
I.e. make a program attractive only to people who need it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
43 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
This is a moral hazard problem.
If you can’t tell who “needs” principal reduction, everyone will
take it.
To design a program that works, you need to:
Make α as high as possible
I.e. make a program attractive only to people who need it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
43 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
This is a moral hazard problem.
If you can’t tell who “needs” principal reduction, everyone will
take it.
To design a program that works, you need to:
Make α as high as possible
I.e. make a program attractive only to people who need it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
43 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
This is a moral hazard problem.
If you can’t tell who “needs” principal reduction, everyone will
take it.
To design a program that works, you need to:
Make α as high as possible
I.e. make a program attractive only to people who need it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
43 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
This is a moral hazard problem.
If you can’t tell who “needs” principal reduction, everyone will
take it.
To design a program that works, you need to:
Make α as high as possible
I.e. make a program attractive only to people who need it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
43 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Recreating HOLC
Created in 1933.
Offered new mortgages to everyone.
In 1934
43 percent of all first mortgages were in default
Arrears an average of eighteen months
In other words, α was 43% (at least)
Worst forecasts right now put population α at 3%.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
44 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Barney Frank’s scheme
Offers to “subprime” borrowers with negative equity
“short-repayment”
new mortgage for 85% of current balance
current lender accepts that as payoff for current loan.
So for our borrower
Mortgage
House value
Equity
Everyone will take it...
Before
$225K
$200K
-$25K
After
$170K
$200K
+$30K
∆
-$55K
0
α = 20%
Has potential to increase dramatically the losses
My guess is that lenders will not go for it.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
45 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Appreciating America
Many variations on the same theme
This plan:
Borrower gets new loan for 97.5% of appraised value of house
(FHA mortgage)
New second mortgage for balance
Principal stays the same
No periodic payments on second mortgage.
Interest accrues.
Will this work?
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
46 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $50K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$50K
$35K
$15K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance
$200
Payoff
$50
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance
$200
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $40K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$50K
$35K
$15K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $200K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $200K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance
$200
Payoff
$50
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance
$200
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $40K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$50K
$35K
$15K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $215K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $215K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance
$200
Payoff
$50
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance
$200
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $40K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$40K
$35K
$5K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $215K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $215K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance
$200
Payoff
$50
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance
$200
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $40K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$40K
$35K
$5K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $215K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $215K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance $215K
Payoff
$50
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance $215K
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $40K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$40K
$35K
$5K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $215K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $215K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance $215K
Payoff
$35K
Return ≈ 233%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance $215K
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
2008
Price of House
Mortgage balance
$200K
−$225K
2013
Costs
(over five years)
Mortgage $40K
Rent
$35K
Constructing “Asset K ” (“K”eep the house)
Mortgage
−Rent
Investment
$40K
$35K
$5K
Willen (Boston Fed)
Good times (75% prob.)
+25%HPA
Price of House
$250K
Mortgage Balance $215K
Bad times (25% prob.)
−10%HPA
Price of House
$180K
Mortgage Balance $215K
Good times (75% prob.)
+25%HPA
Price of House
$250K
−Mortgage Balance $215K
Payoff
$35K
Return ≈ 600%
Bad times (25% prob.)
−10%HPA
Price of House
$180K
−Mortgage Balance $215K
Payoff
$0K
Return = −100%
Life-Cycle Theory
March 31, 2008
47 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
So not attractive to most people
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
So not attractive to most people
makes α higher
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
So not attractive to most people
makes α higher
Increases the effective return on “Asset K ”
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
So not attractive to most people
makes α higher
Increases the effective return on “Asset K ”
Makes borrower want to keep house
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
So not attractive to most people
makes α higher
Increases the effective return on “Asset K ”
Makes borrower want to keep house
Intuition
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Principal balance stays the same
So not attractive to most people
makes α higher
Increases the effective return on “Asset K ”
Makes borrower want to keep house
Intuition
Higher leverage makes asset attractive to borrower with high
cost of funds
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
48 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Conclusions
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
49 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Conclusions
Life-cycle approach makes us look at implied consumption.
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
49 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Conclusions
Life-cycle approach makes us look at implied consumption.
Think about financial assets as transferring resources across
time and outcomes
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
49 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Conclusions
Life-cycle approach makes us look at implied consumption.
Think about financial assets as transferring resources across
time and outcomes
Can help with all financial decisions
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
49 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Conclusions
Life-cycle approach makes us look at implied consumption.
Think about financial assets as transferring resources across
time and outcomes
Can help with all financial decisions
Including whether to “walk away” from a mortgage
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
49 / 50
Introduction
LC Model
Subprime!
The causes of the subprime crisis
Foreclosure decision
Policy Analysis
Contact Information
Paul S. Willen
Senior Economist and Policy Advisor
Federal Reserve Bank of Boston
paul.willen@bos.frb.org
Willen (Boston Fed)
Life-Cycle Theory
March 31, 2008
50 / 50