Table of Contents


File

optimal_gap_thresholds.m

Name

optimal_gap_thresholds

Synopsis

optimal_gap_thresholds - Calculates the optimal gap thresholds according to nts ratio and true positive rate based on Borio et al. (2009).

Introduction

NOTE: PART OF A SET OF 2 RELATED FILES:

Borio (2009) construct macroeconomic early warning indicators to predict banking sector crises by extending the framework of Borio and Lowe (2004). The three indicators used are the property price gap, the (real) equity price gap, and the credit gap. This approach is grounded in the endogenous-cycle view of financial instability. The authors argue that the coexistence of unusually rapid credit growth and asset prices indicate the build-up of financial imbalances that raise the likelihood of subsequent financial distress.

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

indicators_series
Name:
indicators_series
Description:

The joint signal indicators yearly time series. (>=10 years data).

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

Tx2 matrix

  1. Rows represent dates.
  2. Columns represent signal indicators.

is_crisis_series
Name:
is_crisis_series
Description:

Indicates occurence of crisis with value 1. Note: values are yes/no flags, represented as 1/0 values, respectively.

Type:
float
Range:
{0, 1}
Dimensions:

Tx1 matrix

  1. Rows represent dates. In the paper it is set 1 to 3 years

max_thresholds
Name:
max_thresholds
Description:

Matrix with the maximum thresholds for the two indicators.

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

2x1 matrix

  1. Rows represent indicators.

Outputs

nts_thresholds
Name:
nts_thresholds
Description:

The optimal thresholds for the two indicators when the objective function is nts.

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

2x1 matrix

  1. Rows represent indicators.

true_positive_thresholds
Name:
true_positive_thresholds
Description:

The optimal thresholds for the two indicators when the objective function is true_positive rate.

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

2x1 matrix

  1. Rows represent indicators.

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.']);




% We check only integer thresholds as in the paper
nts = zeros(max_thresholds(1), max_thresholds(2));
true_positives = zeros(max_thresholds(1), max_thresholds(2));;


for i=1:max_thresholds(1)
    for j=1:max_thresholds(2)
        thresholds = [i;j];
        [noise_to_signal num_predicted_crises] = joint_gap_indicators( ...
        indicators_series, thresholds, is_crisis_series, horizon);
        nts(i,j) = noise_to_signal;
        true_positives(i,j) = num_predicted_crises;
    end
end


% Find the optimal thresholds for the nts objective
[vals ind] =  min(nts);
[val index] = min(vals);
nts_thresholds = [ind(index);index];

% Find the optimal thresholds fpr the true positive objective
[vals ind] =  max(true_positives);
[val index] = max(vals);
true_positive_thresholds = [ind(index);index];

Examples

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

 indicators_series = ...
 [1.7 1.8 1.5 3.0 4.2 5.3 3.2 3.6 3.4 2.3 2.1 8.0 1.0 0.5 2.2; ...
 130 132 120 124 130 124 140 165 180 140 130 120 132 129 110]';

 max_thresholds = [1; 20];

 horizon = 3;

 is_crisis_series = [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]'

 [nts_thresholds, true_positive_thresholds] ... 
 = optimal_gap_thresholds(indicators_series, is_crisis_series,horizon, ...
 max_thresholds);

References

Borio et al. (2009). Towards an operational framework for financial stability:" fuzzy" measurement and its consequences. Documentos de Trabajo (Banco Central de Chile), (544), 1.

Bisias et al. (2012). A survey of systemic risk analytics (Working paper #0001). Washington, DC: Office of Financial Research, 53-54.