Obtain Climate Scenario Data

This example uses climate scenarios developed by MIT in collaboration with the Bank of Canada. The scenarios are described as:

The Climate Transition Scenario data is provided by the Bank of Canada and is available free of charge at www.bankofcanada.ca. [1]

The data is converted to a MAT file and is loaded from BankOfCanadaClimateScenarioData.mat.

Compute Market Share Shocks

Load the data file for the Climate Transition Scenario provided by the Bank of Canada. This data set contains energy information of different sectors for various geographies around the world. The CL_VARIABLE column in the data set contains both input information used to model the different climate scenarios, as well as, output information of energy usage. This example focuses on the different forms of primary energy, that is: bioenergy, coal, gas, hydro, nuclear, oil, and renewables (wind and solar). The example computes the market shares for each of the different energy forms and uses this information to calculate climate shocks. The different geographies in the data set are Africa, Canada, China, Europe, India, Japan, the United States, and the rest of the world.

load BankOfCanadaClimateScenarioData.mat
head(ClimateTransitionScenarioData)

    k    CL_GEOGRAPHY    CL_SECTOR              CL_VARIABLE                    CL_UNIT                CL_SCENARIO           CL_YEAR    CL_VALUE
    _    ____________    _________    _______________________________    ___________________    ________________________    _______    ________

    1       Canada       National     Carbon price                       US$2014/tCO2e          Baseline (2019 policies)     2020       12.106 
    2       Canada       National     Carbon price                       US$2014/tCO2e          Below 2°C immediate          2020       12.106 
    3       Canada       National     Emissions | total GHG (scope 1)    Million tonnes CO2e    Baseline (2019 policies)     2020       781.04 
    4       Canada       National     Emissions | total GHG (scope 1)    Million tonnes CO2e    Below 2°C immediate          2020       781.04 
    5       Canada       National     Input price | Coal                 Index (2014 = 1)       Baseline (2019 policies)     2020       1.2875 
    6       Canada       National     Input price | Coal                 Index (2014 = 1)       Below 2°C immediate          2020       1.2875 
    7       Canada       National     Input price | Crops                Index (2014 = 1)       Baseline (2019 policies)     2020       1.0031 
    8       Canada       National     Input price | Crops                Index (2014 = 1)       Below 2°C immediate          2020       1.0031 

Trim and preprocess the original data set for what is required for this example.

% This example uses only the Primary Energy variables to compute market
% shares for different geographies.
VariableSubset = {'Primary Energy | Bioenergy', 'Primary Energy | Coal', 'Primary Energy | Gas', ...
'Primary Energy | Hydro', 'Primary Energy | Nuclear', 'Primary Energy | Oil', ...
'Primary Energy | Renewables (wind&solar)', 'Primary Energy | Total'};
ClimateTransitionScenarioData = ClimateTransitionScenarioData(ismember(ClimateTransitionScenarioData.CL_VARIABLE, VariableSubset),:);

% Remove columns 'k','CL_SECTOR' and 'CL_UNIT' and then sort the rows.
ClimateTransitionScenarioData = removevars(ClimateTransitionScenarioData,{'k','CL_SECTOR','CL_UNIT'});
ClimateTransitionScenarioData = sortrows(ClimateTransitionScenarioData);

% Pull market share data out according to climate scenario.
baseline = ClimateTransitionScenarioData(ismember(ClimateTransitionScenarioData.CL_SCENARIO, 'Baseline (2019 policies)'),:);
b2delayed = ClimateTransitionScenarioData(ismember(ClimateTransitionScenarioData.CL_SCENARIO, 'Below 2°C delayed'),:);
b2immediate = ClimateTransitionScenarioData(ismember(ClimateTransitionScenarioData.CL_SCENARIO, 'Below 2°C immediate'),:);
netzero2050 = ClimateTransitionScenarioData(ismember(ClimateTransitionScenarioData.CL_SCENARIO, 'Net-zero 2050 (1.5°C)'),:);

% Compile all the scenarios into one data set.
MarketShareData = baseline;
MarketShareData = removevars(MarketShareData, "CL_SCENARIO");
MarketShareData.Properties.VariableNames(4) = "BASELINE";
MarketShareData.BELOW_2C_IMMEDIATE = b2immediate.CL_VALUE;
MarketShareData.BELOW_2C_DELAYED = b2delayed.CL_VALUE;
MarketShareData.NETZERO_2050 = netzero2050.CL_VALUE;
head(MarketShareData)

    CL_GEOGRAPHY           CL_VARIABLE            CL_YEAR    BASELINE    BELOW_2C_IMMEDIATE    BELOW_2C_DELAYED    NETZERO_2050
    ____________    __________________________    _______    ________    __________________    ________________    ____________

       Africa       Primary Energy | Bioenergy     2020       15.502           15.502               15.502            15.502   
       Africa       Primary Energy | Bioenergy     2025       15.302           15.302               15.302            15.302   
       Africa       Primary Energy | Bioenergy     2030       15.221           15.203               15.221            15.292   
       Africa       Primary Energy | Bioenergy     2035       15.072           15.042               15.084            15.218   
       Africa       Primary Energy | Bioenergy     2040       15.016           15.055                15.23            15.631   
       Africa       Primary Energy | Bioenergy     2045       14.249           14.273               14.652            14.993   
       Africa       Primary Energy | Bioenergy     2050       13.591               14               14.645            14.607   
       Africa       Primary Energy | Coal          2020       4.5909           4.5909               4.5909            4.5909   

Select the geography and subsector, and then compute the market share. By default, in this example, a coal project in China is selected.

Geography = "China";
Sector = "Coal";
SectorFullName = "Primary Energy | " + Sector;
BaseSector = "Primary Energy | Total";

Years = (2020:5:2050)';
GeographyData = MarketShareData(MarketShareData.CL_GEOGRAPHY == Geography, :);
MarketShare = GeographyData{GeographyData.CL_VARIABLE == SectorFullName, 4:7} ./ GeographyData{GeographyData.CL_VARIABLE == BaseSector, 4:7} * 100;

Plot the market shares for different climate scenarios. For the coal sector in China, the baseline scenario shows a drop in market share. However, this drop is accelerates in each of the three climate scenarios. The Below 2C Delayed scenario coincides with the baseline up until 2030, after which there is a sudden fall in market share, whereas the other two scenarios (Below 2C Immediate and Net-Zero 2050) lose market share more gradually until 2050.

figure;
msPlot = plot(Years, MarketShare, 'LineWidth',2);
grid on
set(msPlot, {'LineStyle'}, {'-';'--';':';'-.'})
legend("Baseline", "Below 2C Immediate", "Below 2C Delayed", "Net-Zero 2050 (1.5C)", 'Location','best');
xlim([2020 2050])
ylabel('Market Share (%)')
xlabel('Year')
title(Sector + " Market Share in " + Geography)

Compute shocks for all climate scenarios.

Shocks = (MarketShare(:,2:4) - MarketShare(:,1))./MarketShare(:,1)*100;

Plot the shocks for different scenarios. For the default coal sector in China, the Below 2C Immediate and the Net-Zero 2050 scenarios have a gradual negative market share shock over time. However, the Below 2C Delayed scenario shows no market share shock until 2030, and then there is a sudden drop until 2050.

figure;
shp = plot(Years, Shocks, 'LineWidth',2);
grid on
set(shp, {'LineStyle'}, {'--';':';'-.'})
xlabel('Year')
ylabel('Market Share Shocks (%)')
xlim([2020 2050])
legend("Below 2C Immediate", "Below 2C Delayed", "Net-Zero 2050 (1.5C)", 'Location','best');
title(Sector + " Market Share Shocks in " + Geography);

Obtain Loan Portfolio Data

This example uses a second data set (ClimateLoanPortfolioData.mat) for a loan portfolio. This data set contains simulated loan data of two fictitious banks: Bank 1 and Bank 2. The portfolio of loans are from different geographies and sectors. The example uses the face value of the loans to compute the change in reserves that a bank has to allocate when a climate shock occurs.

The distribution of loans for the two banks, by energy sector, is:

Generate histograms to show the distribution of loans, by region and sector, for the two simulated banks.

load ClimateLoanPortfolioData
LoanPortfolioDataBank1 = ClimateLoanPortfolioData(ClimateLoanPortfolioData.Bank=='Bank1',:);
LoanPortfolioDataBank2 = ClimateLoanPortfolioData(ClimateLoanPortfolioData.Bank=='Bank2',:);

[CountsRegion1, BinsRegion1] = histcounts(LoanPortfolioDataBank1.BorrowerRegion);
[CountsSector1, BinsSector1] = histcounts(LoanPortfolioDataBank1.BorrowerSector);
[CountsRegion2, BinsRegion2] = histcounts(LoanPortfolioDataBank2.BorrowerRegion);
[CountsSector2, BinsSector2] = histcounts(LoanPortfolioDataBank2.BorrowerSector);

figure
tiledlayout(2,1)
nexttile
barh(categorical(BinsRegion1), [CountsRegion1; CountsRegion2]);
xlabel('Loans')
ylabel('Regions')
title('Distribution of Regions')
legend({'Bank 1', 'Bank 2'},'Location','best')
nexttile
barh(categorical(BinsSector1), [CountsSector1; CountsSector2]);
xlabel('Loans')
ylabel('Sectors')
title('Distribution of Sectors')
legend({'Bank 1', 'Bank 2'},'Location','best')

Bank 1 is heavily invested in fossil fuel projects (primarily oil) and Bank 2 is invested in green energy projects (primarily hydro). Regarding the distribution of projects across geographies, both banks are similar, with a larger number of projects in developing regions like China, India, and Africa.

Create Valuation Framework for Loan Contracts Subject to Climate Policy Shocks

Using the same notation as in Monsaterolo [5], consider a bank i endowed with a portfolio of investments in a set of projects through loan contracts. Each loan is represented by a distinct value j. The goal is to carry out a valuation of this loan portfolio that accounts for climate policy shocks. The methodology assumes an underlying structural model that is similar to the Merton model (see mertonmodel). The valuation model includes three time steps: ${\mathit{t}}_0,{\mathit{t}}^{*},\mathrm{and}{\mathit{T}}_{\mathit{j}},\mathrm{with}{\mathit{t}}_0<{\mathit{t}}^{*}<{\mathit{T}}_{\mathit{j}}$. Time step ${\mathit{t}}_0$ denotes the time at which the valuation is carried out, ${\mathit{t}}^{*}$denotes the time at which the climate policy shock potentially occurs, and ${\mathit{T}}_{\mathit{j}}$ denotes the maturity of the loan $\mathit{j}$.

The valuation of bank i's loan portfolio is written as

$${\mathrm{A}}_{\mathit{i}}\left({\mathit{t}}_0\right)=\sum _{\mathit{j}}{\mathit{A}}_{\mathit{i},\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}}\right)$$.

Consider an approach based on the expected value of the loan

$${\mathit{A}}_{\mathit{i},\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}}\right)={\mathit{p}}_{\mathit{j}}\left({\mathit{t}}_{0,}{\mathit{T}}_{\mathit{j}}\right){\mathit{r}}_{\mathit{j}}{\mathit{F}}_{\mathit{i},\mathit{j}}+\left(1-{\mathit{p}}_{\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}}\right)\right){\mathit{F}}_{\mathit{i},\mathit{j}}={\mathit{F}}_{\mathit{i},\mathit{j}}-\left({\mathit{F}}_{\mathit{i},\mathit{j}}\left(1-{\mathit{r}}_{\mathit{j}}\right){\mathit{p}}_{\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}}\right)\right)$$,

where ${\mathit{F}}_{\mathit{i},\mathit{j}}$ is the face value of the loan, ${\mathit{r}}_{\mathit{j}}$ is the recovery rate on the loan contract, and ${\mathit{p}}_{\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}}\right)$ is the probability, based on the information available at time ${\mathit{t}}_0$ that the borrower, j, defaults on the loan at maturity ${\mathit{T}}_{\mathit{j}}$.

Therefore, the expected value of the loan is the face value of the loan ${\mathit{F}}_{\mathit{i},\mathit{j}}$ minus the reserves or provisions that need to be set aside by the bank for that loan ${\mathit{F}}_{\mathit{i},\mathit{j}}\left(1-{\mathit{r}}_{\mathit{j}}\right){\mathit{p}}_{\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}}\right)$.

At time t* the occurrence of a climate policy shock implies that the economy switches from a business-as-usual scenario characterized by no climate policy (B) to scenario P, where the market shares of some economic sectors are affected. This change in default probability implies a proportional change in the expected value of the loan

$$\Delta {\mathit{A}}_{\mathit{i},\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}},\mathit{P}\right)=-{\mathit{F}}_{\mathit{i},\mathit{j}}\left(1-{\mathit{r}}_{\mathit{j}}\right)\Delta {\mathit{p}}_{\mathit{j}}\left(\mathit{P}\right)$$,

where $\Delta {\mathit{p}}_{\mathit{j}}\left(\mathit{P}\right)$ denotes the difference of the default probability going from scenario B to P.

This change is the negative of the change in provisions for the loan. That is, if the value goes down, it is due to an increase in provisions driven by the change in probability.

Assume that the policy shock impacts the borrower's balance sheet, and thus the expected value of the loan. We define a market share shock, ${\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)$, as

$${\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)=\frac{\left({\mathit{m}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)-{\mathit{m}}_{\mathit{S},\mathit{R}}\left(\mathit{B},\mathit{M},{\mathit{t}}^{*}\right)\right)}{{\mathit{m}}_{\mathit{S},\mathit{R}}\left(\mathit{B},\mathit{M},{\mathit{t}}^{*}\right)}$$.

Assume that a relative change in the market share of borrower $\mathit{j}$'s sector $\mathit{S}$ within the geographic region $\mathit{R}$, denoted by ${\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)$, implies a proportional relative change in $\mathit{j}$'s profitability. Also, because the net worth is the integral of profits over one period of time, the relative change in net worth and profit coincide. Therefore, it is equivalent to assume that a relative change in net worth is proportional to the relative shock in market share

$$\frac{\Delta {\mathit{E}}_{\mathit{j}}}{{\mathit{E}}_{\mathit{j}}}=\chi {\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)$$,

where $\chi$ denotes the elasticity of profitability with respect to market share. Monsaterolo [5] assumes a value of $\chi$constant and equal to 1 (typical empirical values range from 0.2 and 0.6).

Another assumption by Monsaterolo [5] is that the probability distribution $\mathit{p}\left({\eta }_{\mathit{j}}\right)$ of the shocks on the borrower's asset side follows a uniform distribution with support $\delta$and mean $\mu$, for a given model $\mathit{M}$, region, and sector. Therefore, the change in default probability is expressed as

$$\Delta \mathit{P}=\frac{{\theta }_{\mathit{j}}\left(\mathit{P}\right)-{\theta }_{\mathit{j}}\left(\mathit{B}\right)}{\delta }=-\frac{{\mathit{E}}_{\mathit{j}}}{\delta }\chi {\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)$$.

The change in expected value of the loan, conditional to a change from scenario B to scenario P becomes:

$$\Delta {\mathit{A}}_{\mathit{i},\mathit{j}}={\mathit{F}}_{\mathit{i},\mathit{j}}\left(1-{\mathit{r}}_{\mathit{j}}\right)\frac{{\mathit{E}}_{\mathit{j}}}{\delta }\chi {\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)$$.

Summing the projects j in the portfolio, you obtain the total change in loan value:

$$\sum _{\mathit{j}}^{}\Delta {\mathit{A}}_{\mathit{i},\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}},\mathit{P}\right)=\sum _{\mathit{j}}^{}{\mathit{F}}_{\mathit{i},\mathit{j}}\left(1-{\mathit{r}}_{\mathit{j}}\right)\frac{{\mathit{E}}_{\mathit{j}}}{\delta }\chi {\mathit{u}}_{\mathit{S},\mathit{R}}\left(\mathit{P},\mathit{M},{\mathit{t}}^{*}\right)$$.

This example computes the change in value for one loan. By default, the 12th row of the data set is selected, which is an oil project in the United States for Bank 1. you can choose another loan by using the Loan slider. You can also select a different ClimateScenario from the three available scenarios. By default, the Below $2°\mathit{C}$ Delayed scenario is selected.

Loan = 12;
ClimateScenario = 2;
Geography = string(ClimateLoanPortfolioData{Loan,'BorrowerRegion'});
Sector = string(ClimateLoanPortfolioData{Loan,'BorrowerSector'});
LoanID = ClimateLoanPortfolioData{Loan,'LoanID'};
FaceValueOfLoan = ClimateLoanPortfolioData{Loan,"FaceValue"};
SectorFullName = "Primary Energy | " + Sector;

Compute the value of the selected Loan.

disp(ClimateLoanPortfolioData(Loan,:));

      LoanID       BorrowerCreditRating    LoanType    Bank     InterestRate    InterestType      BorrowerID      BorrowerRegion    BorrowerSector    OriginationDate    MaturityDate    FaceValue    FairValue 
    ___________    ____________________    ________    _____    ____________    ____________    ______________    ______________    ______________    _______________    ____________    _________    __________

    "786801JSP"             A2               Term      Bank1       0.028           Fixed        "SI14476197XI"    United States          Oil            31-Oct-2019      30-Nov-2031       6e+06      5.7948e+06

You can modify the recovery rate ${\mathit{r}}_{\mathit{j}}$, as well as, $\chi$. By default, ${\mathit{r}}_{\mathit{j}}=0.4$ and $\chi =0.3$. A normal range of $\chi$ is from 0.2 to 0.6.

Following the Monsaterolo [5] discussion in appendix I, set $\frac{{\mathit{E}}_{\mathit{j}}}{\delta }=1$ to correspond to the assumption that the magnitude of the initial net worth and width of the distribution of the idiosyncratic shocks are comparable. You can adjust the EjDeltaRatio value using the slider.

RecoveryRate =0.4;
Chi =0.3;
EjDeltaRatio = 1;
TargetYear = 4;

GeographyData = MarketShareData(MarketShareData.CL_GEOGRAPHY == Geography, :);
MarketShare = GeographyData{GeographyData.CL_VARIABLE == SectorFullName, 4:7} ./ GeographyData{GeographyData.CL_VARIABLE == BaseSector, 4:7} * 100;
Shocks = (MarketShare(:,2:4) - MarketShare(:,1))./MarketShare(:,1)*100;

ChangeInDefaultProbability = -EjDeltaRatio.*Chi.*(Shocks(:,ClimateScenario)/100);
ChangeInValue = -FaceValueOfLoan.*(1-RecoveryRate).*ChangeInDefaultProbability;

The change in value of a loan is directly translated into a change in the reserves that need to be allocated by the bank for that particular loan.

disp("The change in value of the loan in the selected climate scenario and target year = $" + num2str(ChangeInValue(TargetYear)));

The change in value of the loan in the selected climate scenario and target year = $-155161.6488

% Plot change in value of loan over time superimposed over corresponding
% shock.
f = figure;
ax = axes(f);
yyaxis(ax, 'left')
plot(Years, ChangeInValue, 'LineWidth', 2)
xlabel('Years');
ylabel('US Dollars ($)')
yyaxis(ax, 'right')
plot(Years, Shocks(:, ClimateScenario), 'LineWidth', 2);
ylabel('Market Share Shocks (%)');
title('Change in Loan Value');
grid on

Compute Change in Value of Entire Portfolio of Loans

For each of the two banks, Bank 1 and Bank 2, compute the total change in loan value of the entire portfolio of loans for each climate scenario. You can do this by summing up the changes in values of each individual loan.

% For each of the region and sector pairs, compute the market shocks for
% all scenarios and store these values.
MarketShocks = struct();

Bank1Combos = unique(table(LoanPortfolioDataBank1.BorrowerRegion, LoanPortfolioDataBank1.BorrowerSector,'VariableNames',{'Region','Sector'}),'rows');
Bank2Combos = unique(table(LoanPortfolioDataBank2.BorrowerRegion, LoanPortfolioDataBank2.BorrowerSector,'VariableNames',{'Region','Sector'}),'rows');
TotalCombos = union(Bank1Combos, Bank2Combos);

for i = 1:height(TotalCombos)
    Region = string(TotalCombos.Region(i));
    Sector = string(TotalCombos.Sector(i));
    SectorFullName = "Primary Energy | " + Sector;
    GeographyData = MarketShareData(MarketShareData.CL_GEOGRAPHY == Region, :);
    MarketShare = GeographyData{GeographyData.CL_VARIABLE == SectorFullName, 4:7} ./ GeographyData{GeographyData.CL_VARIABLE == BaseSector, 4:7} * 100;
    Shocks = (MarketShare(:,2:4) - MarketShare(:,1))./MarketShare(:,1)*100;
    if Sector == "Renewables (wind&solar)"
        SectorSplit = strsplit(Sector);
        Sector = SectorSplit(1);
    end
    MarketShocks.(strrep(Region,' ','')).(strrep(Sector,' ','')) = Shocks;
end

Create a table containing the values of each loan, for each bank, for each climate scenario, and for each target year. Use the same model parameter values for simplicity. However, you can change these parameters for different issuers.

RecoveryRate =0.46;
Chi =0.3;
EjDeltaRatio = 1;

LoanValues = ClimateLoanPortfolioData;
LoanValues = removevars(LoanValues,{'LoanType','BorrowerCreditRating','InterestRate','InterestType','BorrowerID','OriginationDate','MaturityDate','FairValue'});
LoanValues = repelem(LoanValues, 7, 1);
LoanValues.Year = repmat([2020; 2025; 2030; 2035; 2040; 2045; 2050], 1000, 1);
LoanValues.Below2CImmediate = zeros(7000, 1);
LoanValues.Below2CDelayed = zeros(7000, 1);
LoanValues.NetZero2050 = zeros(7000, 1);

for i = 1:7:height(LoanValues)
    Region = string(LoanValues.BorrowerRegion(i));
    Sector = string(LoanValues.BorrowerSector(i));
    if Sector == "Renewables (wind&solar)"
        SectorSplit = strsplit(Sector);
        Sector = SectorSplit(1);
    end
    Value = LoanValues.FaceValue(i);
    ChangeInValue = Value.*(1-RecoveryRate).*EjDeltaRatio.*Chi.*(MarketShocks.(strrep(Region,' ','')).(strrep(Sector,' ',''))/100);
    LoanValues{i:i+6, {'Below2CImmediate','Below2CDelayed','NetZero2050'}} = ChangeInValue;
end

Compare the change in portfolio values of the two banks, for each climate scenario, and for all target years.

TPVBank1 = zeros(length(Years),3);
TPVBank2 = zeros(length(Years),3);
for i = 1:length(Years)
    TBank1 = LoanValues((LoanValues.Bank == "Bank1") & (LoanValues.Year == Years(i)), :);
    TBank2 = LoanValues((LoanValues.Bank == "Bank2") & (LoanValues.Year == Years(i)), :);
    TPVBank1(i,:) = sum(TBank1{:,7:9});
    TPVBank2(i,:) = sum(TBank2{:,7:9});
end

figure;
t = tiledlayout(3,1);
nexttile
plot(Years, [TPVBank1(:,1),TPVBank2(:,1)], 'LineWidth', 2)
xlabel('Year');
ylabel('US Dollar ($)')
title('Below 2C Immediate')
grid on
nexttile
plot(Years, [TPVBank1(:,2),TPVBank2(:,2)], 'LineWidth', 2)
xlabel('Year');
ylabel('US Dollar ($)')
title('Below 2C Delayed')
grid on
nexttile
plot(Years, [TPVBank1(:,3),TPVBank2(:,3)], 'LineWidth', 2)
xlabel('Year');
ylabel('US Dollar ($)')
title('Net-Zero 2050')
leg = legend({'Bank1','Bank2'});
leg.Layout.Tile = 'south';
grid on
title(t,'Change in Portfolio Value');

Considering that Bank 1 is weighted towards fossil fuels and Bank 2 is weighted toward green energy, the portfolio value of Bank 1 decreases over time, while the portfolio value of Bank 2 increases over time for each climate scenario.

From a reserves standpoint, the provisions of Bank 2 steadily increase over time and those of Bank 1 decrease over time.

Compute Distribution of Changes in Loan Portfolio Values

The Compute Change in Value of Entire Portfolio of Loans section illustrated the aggregate changes to the portfolio value. This section focuses on the entire distribution of value changes for particular climate scenarios.

Select the bank, climate scenario, and target year to compute the quartiles of the change in portfolio values.

Bank = "Bank1";
ClimateScenario = 2;
TargetYear = "2050";

NewTable = LoanValues((LoanValues.Bank == Bank) & (LoanValues.Year == str2double(TargetYear)), :);

Plot the histogram of the change in loan values for the selected bank and climate scenario. Based on the default selection of Bank 1 under the Below 2C Delayed climate scenario for the target year 2050, you see that the distribution of the change in loan values has a long right tail and most of the frequency is below zero. This change occurs because Bank 1 has more projects focusing on fossil fuels, which lose market share, and thus value over time under the Below 2C Delayed climate scenario.

f = figure;
h = histogram(NewTable{:,6+ClimateScenario});
h.Parent.XLabel.String = 'Change in Loan Value';
h.Parent.YLabel.String = 'Counts';
h.Parent.Title.String = 'Histogram of Change in Loan Values';

Compute and plot the quartiles of the changes in portfolio values over time for the selected bank.

PLV = zeros(length(Years),3);
for i = 1:length(Years)
    t = LoanValues((LoanValues.Bank == Bank) & (LoanValues.Year == Years(i)), :);
    PLV(i,1) = prctile(t{:,6+ClimateScenario}, 25);
    PLV(i,2) = prctile(t{:,6+ClimateScenario}, 50);
    PLV(i,3) = prctile(t{:,6+ClimateScenario}, 75);
end

figure;
plot(Years, PLV, 'LineWidth', 2)
xlabel('Years');
ylabel('Change in Portfolio Value ($)')
title('Quartiles of Change in Portfolio Value')
legend({'c = 25%','c = 50%','c = 75%'})
grid on

To compute some standard metrics of risk such as the Value-at-Risk (VaR) of the portfolio, you need to know the joint probaility distribution of the idiosyncratic shocks and the probability of occurrence of climate policy shocks. In the absence of these estimations, Monsaterolo [5] defines a project-level climate VaR as the value such that, conditional to the same climate policy shock for all n loans, the fraction of loans leading to losses higher than the VaR equals the confidence level c

$$|\left\{\mathit{j}|\Delta {\mathit{A}}_{\mathit{i},\mathit{j}}\left({\mathit{t}}_0,{\mathit{T}}_{\mathit{j}},\mathit{P},\mathit{B}\right)\ge \mathrm{VaR}\right\}|/\mathit{n}=\mathit{c}$$.

This project-level climate VaR metric is a percentile of the distribution of value changes for the portfolio.

ConfidenceLevel = 1;
ProjVaR = -prctile(NewTable{:,6+ClimateScenario}, ConfidenceLevel);
disp("The project-level climate VaR at the " + ConfidenceLevel + "% confidence level = $" + num2str(ProjVaR));

The project-level climate VaR at the 1% confidence level = $1453621.915

Plot a graph of distributions of changes in loan values for each target year and for a given scenario and bank. Use the kernel smoothing function estimate for univariate data. The estimate is based on a normal kernel function and is evaluated at equally spaced points that cover the range of the data.

[F1Bank1, Xi1Bank1] = ksdensity(TBank1.Below2CImmediate);
[F1Bank2, Xi1Bank2] = ksdensity(TBank2.Below2CImmediate);

[F2Bank1, Xi2Bank1] = ksdensity(TBank1.Below2CDelayed);
[F2Bank2, Xi2Bank2] = ksdensity(TBank2.Below2CDelayed);

[F3Bank1, Xi3Bank1] = ksdensity(TBank1.NetZero2050);
[F3Bank2, Xi3Bank2] = ksdensity(TBank2.NetZero2050);

figure;
t = tiledlayout(3,1);
ax1 = nexttile;
plot(Xi1Bank1, F1Bank1, 'LineWidth', 1.5)
hold on
plot(Xi1Bank2, F1Bank2, 'LineWidth', 1.5)
ax1.Title.String = "Below 2C Immediate";
xlabel('US Dollar ($)')
ylabel('pdf')
grid on
ax2 = nexttile;
plot(Xi2Bank1, F2Bank1, 'LineWidth', 1.5)
hold on
plot(Xi2Bank2, F2Bank2, 'LineWidth', 1.5)
ax2.Title.String = "Below 2C Delayed";
xlabel('US Dollar ($)')
ylabel('pdf')
grid on
ax3 = nexttile;
plot(Xi3Bank1, F3Bank1, 'LineWidth', 1.5)
hold on
plot(Xi3Bank2, F3Bank2, 'LineWidth', 1.5)
leg = legend("Bank 1","Bank 2");
leg.Layout.Tile = 'south';
ax3.Title.String = "Net-Zero 2050";
xlabel('US Dollar ($)')
ylabel('pdf')
grid on
title(t,'Distribution of Changes in Loan Values');

Conclusion

Following the work Monsaterolo [5], this example demonstrates how the market shares of different energy sectors in different geographies change under specific climate scenarios. The market share changes are converted into market share shocks and you can use these shocks to compute the change in value of a portfolio of loans. Using this approach, you can model additional climate scenarios and then apply the Monsaterolo [5] methodology. In addition, you can use this approach to value a portfolio of other assets such as bonds.

References

[1] Bank of Canada Climate Transition Scenario Data and pilot project available at https://www.bankofcanada.ca/2022/01/climate-transition-scenario-data/ and https://www.bankofcanada.ca/wp-content/uploads/2021/11/BoC-OSFI-Using-Scenario-Analysis-to-Assess-Climate-Transition-Risk.pdf.

[2] Climate IAM Explorer available at https://github.com/bat365/Climate-IAM-Explorer.

[3] EPPA Model Structure available at https://globalchange.mit.edu/research/research-tools/eppa and https://globalchange.mit.edu/research/research-tools/human-system-model.

[4] LIMITS information available at https://tntcat.iiasa.ac.at/LIMITSDB/dsd?Action=htmlpage&page=about.

[5] Monasterolo, I., Zheng, Jiani I., and S. Battiston. "Climate Transition Risk and Development Finance: An Assessment of China's Overseas Energy Investments Portfolio." China and the World Economy. 26, 6(116–142), 2018. Available at https://doi.org/10.1111/cwe.12264.