categoryWeights

Compute average and periodic category weights

Syntax

[AverageCategoryWeights,PeriodicCategoryWeights] = categoryWeights(brinsonAttributionObj)

Description

[AverageCategoryWeights,PeriodicCategoryWeights] = categoryWeights(brinsonAttributionObj) computes the average and periodic category weights for the portfolio and the benchmark as well as the corresponding active weights.

Examples

Compute Category Weights Using brinsonAttribution Object

This example shows how to create a brinsonAttribution object and then use categoryWeights to compute average and periodic category (sector) weights.

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 Category Weights

Use categoryWeights to compute the average and periodic category weights for the portfolio and the benchmark, as well as, the corresponding active weights.

[AverageCategoryWeights,PeriodicCategoryWeights] = categoryWeights(BrinsonPAobj)

AverageCategoryWeights=2×4 table
           Category           AveragePortfolioWeight    AverageBenchmarkWeight    AverageActiveWeight
    ______________________    ______________________    ______________________    ___________________

    Consumer Discretionary           0.33333                     0.5                   -0.16667      
    Consumer Staples                 0.66667                     0.5                    0.16667      

PeriodicCategoryWeights=6×5 table
    Period           Category           PortfolioWeight    BenchmarkWeight    ActiveWeight
    ______    ______________________    _______________    _______________    ____________

      1       Consumer Discretionary        0.33333              0.5            -0.16667  
      1       Consumer Staples              0.66667              0.5             0.16667  
      2       Consumer Discretionary        0.33333              0.5            -0.16667  
      2       Consumer Staples              0.66667              0.5             0.16667  
      3       Consumer Discretionary        0.33333              0.5            -0.16667  
      3       Consumer Staples              0.66667              0.5             0.16667  

Input Arguments

brinsonAttributionObj — Brinson attribution model

object

Brinson attribution model, specified as a brinsonAttribution object.

Data Types: object

Output Arguments

AverageCategoryWeights — Category weights averaged over all periods

table

Category weights averaged over all periods, returned as a table with the following columns:

• Category — Asset category

• AveragePortfolioWeight — Average portfolio weights

• AverageBenchmarkWeight — Average benchmark weights

• AverageActiveWeight — Average active weights

PeriodicCategoryWeights — Category weights for each period

table

Category weights 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)

• Category — Asset category

• PortfolioWeight — Portfolio weights

• BenchmarkWeight — Benchmark weights

• ActiveWeight — Active weights

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