Table of Contents


File

loan_to_value.m

Name

loan_to_value

Synopsis

Calculates the loan-to-value ratio at time t for a home initially purchased in vintage i.

Introduction

NOTE: PART OF A SET OF 8 RELATED FILES:

Khandani, Lo, and Merton (2009) posit that rising home prices, declining interest rates, and near-frictionless refinancing opportunities led to vastly increased systemic risk in the financial system. A simultaneous occurrence of these factors imposes an unintentional synchronization of homeowner leverage. This synchronization, coupled with the indivisibility of residential real estate that prevents homeowners from deleveraging when property values decline and homeowner equity deteriorates, conspire to create a "ratchet" effect in which homeowner leverage is maintained or increased during good times without the ability to decrease leverage during bad times. To measure the systemic impact of this ratchet effect, the U.S. housing market is simulated with and without equity extractions, and the losses absorbed by mortgage lenders is estimated by valuing the embedded put option in non-recourse mortgages. The proposed systemic risk indicator for the housing market is the dollar-delta of this embedded put option.

License

=============================================================================

Copyright 2011, Dimitrios Bisias, Andrew W. Lo, and Stavros Valavanis

COPYRIGHT STATUS: This work was funded in whole or in part by the Office of Financial Research under U.S. Government contract TOSOFR-11-C-0001, and is, therefore, subject to the following license: The Government is granted for itself and others acting on its behalf a paid-up, nonexclusive, irrevocable, worldwide license to reproduce, prepare derivative works, distribute copies to the public, perform and display the work.
All other rights are reserved by the copyright owner.

THIS SOFTWARE IS PROVIDED "AS IS". YOU ARE USING THIS SOFTWARE AT YOUR OWN RISK. ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS, CONTRIBUTORS, OR THE UNITED STATES GOVERNMENT BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

=============================================================================

Inputs

i
Name:
i
Description:

The vintage when the house was purchased.

Type:
integer
Range:
[1,+inf)
Dimensions:

scalar


t
Name:
t
Description:

The time at which we calculate the loan-to-value ratio.

Type:
integer
Range:
[1,+inf)
Dimensions:

scalar


mortgage_rate
Name:
mortgage_rate
Description:

The fixed rate for a conventional 30-yr fixed-rate mortgage.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


ltv_initial
Name:
ltv_initial
Description:

The initial loan-to-value ratio.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


value_house
Name:
value_house
Description:

The value of the house.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


hpi
Name:
hpi
Description:

The Home Price Index monthly timeseries indicates increases in the value of existing homes.

Type:
float
Range:
(0,+inf)
Dimensions:

Tx1 matrix

  1. Rows represent Months (dates are ascending).

Outputs

ltv
Name:
ltv
Description:

The loan-to-value ratio at time t.

Type:
float
Range:
(0,+inf)
Dimensions:

scalar


Code

% Run warning message
warning('OFRwp0001:UntestedCode', ...
    ['This version of the source code is very preliminary, ' ...
     'and has not been thoroughly tested. Users should not rely on ' ...
     'these calculations.']);




current_loan = balance_loan(i,t,mortgage_rate, ltv_initial, value_house);


current_value = value_house*hpi(t)/hpi(i);
ltv = current_loan/current_value;

Examples

NOTE: Numbers used in the examples are arbitrary valid values.
They do not necessarily represent a realistic or plausible scenario.

 i = 2;
 t = 10; 
 mortgage_rate = 0.07;
 ltv_initial = 0.8;
 value_house = 10;
 hpi = ...
 [0.3, 0.9, 1, 1.1, 0.8, 1, 0.6, 0.7, 0.5, 0.9, 1.2, 1, 1.3, 1.1, 1.0];

 ltv = loan_to_value(i,t, mortgage_rate, ltv_initial, value_house, hpi);

References

Khandani, A. E., Lo, A. W., & Merton, R. C. (2012). Systemic risk and the refinancing ratchet effect. Journal of Financial Economics.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 89-94.