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Mortgage Composition and 

Risk Evaluation

Taylor J. Wilson

Economist

Division of Consumer Expenditure Surveys

George Mason University Seminar

21 February 2017
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Introduction

1. Mortgages in the CE Survey.

2. A conceptual analysis of risk.

3. Connecting mortgages to risk. 

4. Risk abatement strategies.

5. Modeling risk with insurance proxies.
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Terms and Definitions

 Mortgage Composition: The number of various mortgage 

instruments reported in the sample as a proportion of the 

total number of reported mortgages.

 Mortgage Choice: The decision to select one type of 

mortgage over another. 

 Risk Preference: The type of behavior a consumer unit 

exhibits.

 Risk Evaluation: Understanding the sources of risk and how 

they apply to the various instruments. 

 FRM: Fixed Rate Mortgage

 ARM: Adjustable Rate Mortgage
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Mortgage Composition in CE

30yr FRM 15yr FRM Other Term FRM Non-FRM

Number of 

Mortgages

107,991

(61.49)

25,717

(14.64)

17,221

(9.81)

24,685

(14.06)

Source: 2004-2014 CE Pooled Sample - Percentage of Sample in Parentheses

 Term

 Interest rate type 

(i.e. Fixed Rate or 

Non-Fixed Rate)

 30yr FRM

 15yr FRM

 Other term FRM

 Non-FRM

CE Variables Mortgage Instruments
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Mortgage Choice
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Risk Preferences

 Risk Averse

Concave utility of 

wealth function

 Risk Neutral

Linear utility of 

wealth function

 Risk Loving

Convex utility of 

wealth function
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Risk Preferences

 There is good reason to believe that most 

consumer units will be risk averse. Friend and 

Blume (1957) and Latane (1959)

 Concavity, negative second derivative, along 

all values of w assumes absolute risk aversion 

(i.e. Well behaved utility functions).

∂U2

∂w2

< 0
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Risk Preferences

 Utility functions are not estimable. 

 General shape inferred based on behavior of 

the consumer units. 

Concave Utility of Wealth Function
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Risk Evaluation

 How do the mortgage instruments fit onto a utility of wealth 

function?

 Why would risk averse individuals ever select an ARM?

ARM FRM vs. ARM
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Risk Evaluation

E U w = α1U w1 + α2U(w2)

If α1 = α2
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Risk Evaluation

 w3 represents the guaranteed wealth from an FRM in this 

forward looking period. 

 Utility Floor at U(w3)
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Risk Evaluation

E U w = α1U w1 + α2U(w2)

If α1<< α2 such that E U w ε A then 

E U w > U E w

A
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Mortgage Choice
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Mortgage Choice

 2008 is a large shock 

to the mortgage 

market. 

 Size of the market 

shrunk.

 Non-Fixed Rate 

Mortgages diminished 

as a share of the 

market.

 How did consumer 

choice change before 

and after the shock?
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Mortgage Choice

 Risk preferences changed in the sample.

Perhaps risk loving people became more risk 

averse.

Risk loving people chose not to buy houses 

anymore. 

 E U w = α1U w1 + α2U(w2)

α1<< α2 turned into α1>>α2

Individuals moved from ARMs into FRMs.
Contact Information

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Taylor J. Wilson

Economist

Division of Consumer Expenditure Surveys

www.bls.gov/cex

202-691-6550

wilson.taylor@bls.gov