totalAttribution

Compute total performance attribution by Brinson model

Since R2022b

Syntax

[AggregateTotalAttribution,PeriodicTotalAttribution] = totalAttribution(brinsonAttributionObj)

Description

[AggregateTotalAttribution,PeriodicTotalAttribution] = totalAttribution(brinsonAttributionObj) computes the total performance attribution of the portfolio, summed up for all categories, using the Brinson model.

Examples

Compute Total Performance Attribution Using brinsonAttribution Object

This example shows how to create a brinsonAttribution object and then use totalAttribution to compute the total performance attribution of the portfolio summed up for all categories (sectors).

Prepare Data

Create a table for the monthly prices for four assets.

 GM =[17.82;22.68;19.37;20.28];
 HD = [39.79;39.12;40.67;40.96];
 KO = [38.98;39.44;40.00;40.20];
 PG = [56.38;57.08;57.76;55.54];
 MonthlyPrices  = table(GM,HD,KO,PG);

Use tick2ret to define the monthly returns.

MonthlyReturns = tick2ret(MonthlyPrices.Variables)';
  [NumAssets,NumPeriods] = size(MonthlyReturns); 

Define the periods.

Period = ones(NumAssets*NumPeriods,1);
  for k = 1:NumPeriods
      Period(k*NumAssets+1:end,1) = Period(k*NumAssets,1) + 1;
  end

Define the categories for the four assets.

Name = repmat(string(MonthlyPrices.Properties.VariableNames(:)),NumPeriods,1);
  Categories = repmat(categorical([ ...
      "Consumer Discretionary"; ...
      "Consumer Discretionary"; ...
      "Consumer Staples"; ...
      "Consumer Staples"]),NumPeriods,1);

Define benchmark and portfolio weights.

BenchmarkWeight = repmat(1./NumAssets.*ones(NumAssets, 1),NumPeriods,1);
  PortfolioWeight = repmat([1;0;1;1]./3,NumPeriods,1);

Create AssetTable Input

Create AssetTable as the input for the brinsonAttribution object.

  AssetTable = table(Period, Name, ...
      MonthlyReturns(:), Categories, PortfolioWeight, BenchmarkWeight, ...
      VariableNames=["Period","Name","Return","Category","PortfolioWeight","BenchmarkWeight"])

AssetTable=12×6 table
    Period    Name     Return             Category           PortfolioWeight    BenchmarkWeight
    ______    ____    _________    ______________________    _______________    _______________

      1       "GM"      0.27273    Consumer Discretionary        0.33333             0.25      
      1       "HD"    -0.016838    Consumer Discretionary              0             0.25      
      1       "KO"     0.011801    Consumer Staples              0.33333             0.25      
      1       "PG"     0.012416    Consumer Staples              0.33333             0.25      
      2       "GM"     -0.14594    Consumer Discretionary        0.33333             0.25      
      2       "HD"     0.039622    Consumer Discretionary              0             0.25      
      2       "KO"     0.014199    Consumer Staples              0.33333             0.25      
      2       "PG"     0.011913    Consumer Staples              0.33333             0.25      
      3       "GM"      0.04698    Consumer Discretionary        0.33333             0.25      
      3       "HD"    0.0071306    Consumer Discretionary              0             0.25      
      3       "KO"        0.005    Consumer Staples              0.33333             0.25      
      3       "PG"    -0.038435    Consumer Staples              0.33333             0.25      

Create brinsonAttribution Object

Use brinsonAttribution to create the brinsonAttribution object.

  BrinsonPAobj = brinsonAttribution(AssetTable)

BrinsonPAobj = 
  brinsonAttribution with properties:

                  NumAssets: 4
         NumPortfolioAssets: 3
         NumBenchmarkAssets: 4
                 NumPeriods: 3
              NumCategories: 2
                  AssetName: [4x1 string]
                AssetReturn: [4x3 double]
              AssetCategory: [4x3 categorical]
       PortfolioAssetWeight: [4x3 double]
       BenchmarkAssetWeight: [4x3 double]
    PortfolioCategoryReturn: [2x3 double]
    BenchmarkCategoryReturn: [2x3 double]
    PortfolioCategoryWeight: [2x3 double]
    BenchmarkCategoryWeight: [2x3 double]
            PortfolioReturn: 0.0598
            BenchmarkReturn: 0.0540
               ActiveReturn: 0.0059

Compute Total Performance Attribution

Use the brinsonAttribution object with totalAttribution to compute the total performance attribution of the portfolio summed up for all categories.

[AggregateTotalAttribution, PeriodicTotalAttribution] = totalAttribution(BrinsonPAobj)

AggregateTotalAttribution=1×4 table
    Allocation    Selection    Interaction    ActiveReturn
    __________    _________    ___________    ____________

    -0.014353     0.030316      -0.010105      0.0058578  

PeriodicTotalAttribution=3×6 table
    Period    LinkingCoefficient    Allocation    Selection    Interaction    ActiveReturn
    ______    __________________    __________    _________    ___________    ____________

      1            0.97032           -0.019306     0.072391      -0.02413        0.028955 
      2             1.0838            0.011036    -0.046391      0.015464       -0.019891 
      3             1.0391          -0.0072954    0.0099623    -0.0033208     -0.00065389 

Input Arguments

brinsonAttributionObj — Brinson attribution model

object

Brinson attribution model, specified as a brinsonAttribution object.

Data Types: object

Output Arguments

AggregateTotalAttribution — Total attribution aggregated over all periods

table

Total attribution aggregated over all periods, returned as a table with the following columns:

• Allocation — Category allocation effect for the category

• Selection — Effect of selecting individual assets within the category

• Interaction — Allocation-selection interaction effect

• ActiveReturn — Active return compared with benchmark

PeriodicTotalAttribution — Total attribution for each period

table

Total attribution for each period, returned as a table with the following columns:

• Period — Time period numbers (1 for the first period, 2 for the second period, and so on)

• LinkingCoefficient — Linking coefficients used to aggregate the attribution results over all time periods

• Allocation — Category allocation effect for the category

• Selection — Effect of selecting individual assets within the category

• Interaction — Allocation-selection interaction effect

• ActiveReturn — Active return compared with benchmark

References

[1] Brinson, G. P. and Fachler, N. “Measuring Non-US Equity Portfolio Performance.” Journal of Portfolio Management. Spring 1985: 73–76.

[2] Brinson, G. P., Hood, L. R., and Beebower, G. L. “Determinants of Portfolio Performance.” Financial Analysts Journal. Vol. 42, No. 4, 1986: 39–44.

[3] Menchero, J. “Multiperiod Arithmetic Attribution.” Financial Analysts Journal. Vol. 60, No. 4, 2004: 76–91.

[4] Tuttle, D. L., Pinto, J. E., and McLeavey, D. W. Managing Investment Portfolios: A Dynamic Process. Third Edition. CFA Institute, 2007.

Version History

Introduced in R2022b