使用布林森模型分析业绩归因
此示例演示了如何准备数据，创建 brinsonAttribution 对象，然后分析与类别（行业）权重和收益相关的业绩归因。在此示例中，您会使用到 categoryAttribution、categoryReturns、categoryWeights、totalAttribution 和 summary 函数进行分析。此外，您还可以使用 categoryReturnsChart、categoryWeightsChart 和 attributionsChart 为结果生成绘图。
准备数据
将股票价格数据加载到表格中。
T = readtable('dowPortfolio.xlsx');
MonthIdx = [1;20;39;62;81;103;125;145;168;188;210;231;251];
MonthlyPrices = T(MonthIdx,3:end);使用 tick2ret 计算月收益。
MonthlyReturns = tick2ret(MonthlyPrices.Variables)'; [NumAssets,NumPeriods] = size(MonthlyReturns);
使用 categorical 定义资产类别（行业）。
Category = categorical(["Materials";"Financials";"Financials"; ... "Industrials";"Financials";"Industrials";"Materials"; ... "Communication Services";"Industrials";"Consumer Discretionary"; ... "Consumer Discretionary";"Industrials";"Information Technology"; ... "Information Technology";"Information Technology";"Health Care"; ... "Financials";"Consumer Staples";"Consumer Discretionary"; ... "Industrials";"Consumer Staples";"Health Care"; ... "Information Technology";"Health Care";"Consumer Staples"; ... "Communication Services";"Industrials";"Communication Services"; ... "Consumer Staples";"Energy"]); Category = repmat(Category,1,NumPeriods);
定义基准与投资组合权重
按季度为每只股票资产定义基准权重和投资组合权重。
BenchmarkWeight = 1./length(MonthlyReturns).*ones(NumAssets, NumPeriods); PortfolioWeightQ1 = [0;0;0.022;0.033;0;0.044;0.022;0.011;0.065;0.033; ... 0.055;0.072;0;0.04;0;0.05;0.08;0.042;0.03;0.043;0.055;0.036;0.111; ... 0.036;0;0.03;0;0.05;0;0.04]*ones(1,3); PortfolioWeightQ2 = [0;0;0.022;0.033;0;0.044;0.022;0.011;0.049;0.033; ... 0.055;0.074;0;0.04;0;0.05;0.08;0.042;0.03;0.02;0.055;0.036;0.148; ... 0.036;0;0.03;0;0.05;0;0.04]*ones(1,3); PortfolioWeightQ3 = [0;0;0.022;0.033;0;0.042;0.022;0.01;0.049;0.033; ... 0.05;0.07;0;0.04;0;0.05;0.08;0.042;0.03;0.02;0.055;0.036;0.16; ... 0.036;0;0.03;0;0.05;0;0.04]*ones(1,3); PortfolioWeightQ4 = [0;0;0.022;0.033;0;0.042;0.02;0.01;0.039;0.033; ... 0.05;0.07;0;0.04;0;0.05;0.08;0.042;0.03;0.02;0.055;0.036;0.198; ... 0.036;0;0.03;0;0.03;0;0.034]*ones(1,3); PortfolioWeight = [PortfolioWeightQ1 PortfolioWeightQ2 ... PortfolioWeightQ3 PortfolioWeightQ4]; Period = (1:NumPeriods).*ones(NumAssets,1); Name = repmat(string(MonthlyPrices.Properties.VariableNames(:)),1,NumPeriods);
创建 AssetTable 输入。
使用 table 创建一个 AssetTable 输入以在创建 brinsonAttribution 对象时使用。
AssetTable = table(Period(:), Name(:), ... MonthlyReturns(:), Category(:), ... PortfolioWeight(:), BenchmarkWeight(:), ... VariableNames=["Period", "Name","Return","Category",... "PortfolioWeight","BenchmarkWeight"])
AssetTable=360×6 table
Period Name Return Category PortfolioWeight BenchmarkWeight
______ ______ ___________ ______________________ _______________ _______________
1 "AA" 0.053621 Materials 0 0.033333
1 "AIG" -0.05964 Financials 0 0.033333
1 "AXP" -0.00019406 Financials 0.022 0.033333
1 "BA" -0.030162 Industrials 0.033 0.033333
1 "C" -0.055015 Financials 0 0.033333
1 "CAT" 0.17956 Industrials 0.044 0.033333
1 "DD" -0.090708 Materials 0.022 0.033333
1 "DIS" 0.037221 Communication Services 0.011 0.033333
1 "GE" -0.07381 Industrials 0.065 0.033333
1 "GM" 0.27273 Consumer Discretionary 0.033 0.033333
1 "HD" -0.016838 Consumer Discretionary 0.055 0.033333
1 "HON" 0.025457 Industrials 0.072 0.033333
1 "HPQ" 0.083598 Information Technology 0 0.033333
1 "IBM" -0.009235 Information Technology 0.04 0.033333
1 "INTC" -0.1685 Information Technology 0 0.033333
1 "JNJ" -0.066351 Health Care 0.05 0.033333
⋮
创建 brinsonAttribution 对象
使用 brinsonAttribution 创建一个 brinsonAttribution 对象。
BrinsonPAobj = brinsonAttribution(AssetTable)
BrinsonPAobj =
brinsonAttribution with properties:
NumAssets: 30
NumPortfolioAssets: 22
NumBenchmarkAssets: 30
NumPeriods: 12
NumCategories: 9
AssetName: [30×1 string]
AssetReturn: [30×12 double]
AssetCategory: [30×12 categorical]
PortfolioAssetWeight: [30×12 double]
BenchmarkAssetWeight: [30×12 double]
PortfolioCategoryReturn: [9×12 double]
BenchmarkCategoryReturn: [9×12 double]
PortfolioCategoryWeight: [9×12 double]
BenchmarkCategoryWeight: [9×12 double]
PortfolioReturn: 0.2234
BenchmarkReturn: 0.2046
ActiveReturn: 0.0188
计算类别权重
使用 brinsonAttribution 对象和 categoryWeights 计算投资组合和基准的平均及周期性类别权重，以及相应的主动权重。
[AverageCategoryWeights,PeriodicCategoryWeights] = categoryWeights(BrinsonPAobj)
AverageCategoryWeights=9×4 table
Category AveragePortfolioWeight AverageBenchmarkWeight AverageActiveWeight
______________________ ______________________ ______________________ ___________________
Communication Services 0.0855 0.1 -0.0145
Consumer Discretionary 0.1155 0.1 0.0155
Consumer Staples 0.097 0.13333 -0.036333
Energy 0.0385 0.033333 0.0051667
Financials 0.102 0.13333 -0.031333
Health Care 0.122 0.1 0.022
Industrials 0.22375 0.2 0.02375
Information Technology 0.19425 0.13333 0.060917
Materials 0.0215 0.066667 -0.045167
PeriodicCategoryWeights=108×5 table
Period Category PortfolioWeight BenchmarkWeight ActiveWeight
______ ______________________ _______________ _______________ ____________
1 Communication Services 0.091 0.1 -0.009
1 Consumer Discretionary 0.118 0.1 0.018
1 Consumer Staples 0.097 0.13333 -0.036333
1 Energy 0.04 0.033333 0.0066667
1 Financials 0.102 0.13333 -0.031333
1 Health Care 0.122 0.1 0.022
1 Industrials 0.257 0.2 0.057
1 Information Technology 0.151 0.13333 0.017667
1 Materials 0.022 0.066667 -0.044667
2 Communication Services 0.091 0.1 -0.009
2 Consumer Discretionary 0.118 0.1 0.018
2 Consumer Staples 0.097 0.13333 -0.036333
2 Energy 0.04 0.033333 0.0066667
2 Financials 0.102 0.13333 -0.031333
2 Health Care 0.122 0.1 0.022
2 Industrials 0.257 0.2 0.057
⋮
计算类别收益
使用 brinsonAttribution 对象和 categoryReturns 计算投资组合和基准的聚合及周期性类别（行业）收益。
[AggregateCategoryReturns,PeriodicCategoryReturns] = categoryReturns(BrinsonPAobj)
AggregateCategoryReturns=9×3 table
Category AggregatePortfolioReturn AggregateBenchmarkReturn
______________________ ________________________ ________________________
Communication Services 0.41756 0.42797
Consumer Discretionary 0.27772 0.34718
Consumer Staples 0.20572 0.14112
Energy 0.33598 0.33598
Financials 0.22678 0.15838
Health Care 0.19451 0.20679
Industrials 0.14132 0.14253
Information Technology 0.14339 0.13485
Materials 0.17109 0.10402
PeriodicCategoryReturns=108×4 table
Period Category PortfolioReturn BenchmarkReturn
______ ______________________ _______________ _______________
1 Communication Services 0.056262 0.052385
1 Consumer Discretionary 0.079767 0.10017
1 Consumer Staples -0.01485 -0.0033588
1 Energy 0.073093 0.073093
1 Financials -0.0021179 -0.029374
1 Health Care 0.012124 0.022297
1 Industrials 0.0018686 0.0088589
1 Information Technology 0.033481 -0.011315
1 Materials -0.090708 -0.018543
2 Communication Services 0.069253 0.078033
2 Consumer Discretionary -0.023091 -0.036416
2 Consumer Staples 0.0027749 0.00096619
2 Energy -0.0487 -0.0487
2 Financials 0.033379 0.02054
2 Health Care 0.014975 0.015929
2 Industrials 0.047732 0.041906
⋮
计算类别归因
使用 brinsonAttribution 对象和 categoryAttribution 计算投资组合在每个类别（行业）中的业绩归因。
[AggregateCategoryAttribution,PeriodicCategoryAttribution] = categoryAttribution(BrinsonPAobj)
AggregateCategoryAttribution=9×5 table
Category Allocation Selection Interaction ActiveReturn
______________________ __________ ___________ ___________ ____________
Communication Services -0.0025318 -0.00071062 0.0002061 -0.0030363
Consumer Discretionary 0.0024505 -0.00678 -0.0011609 -0.0054903
Consumer Staples 0.0023692 0.0093618 -0.0025511 0.00918
Energy 0.00038824 1.3872e-19 2.7745e-20 0.00038824
Financials 0.0013464 0.0097268 -0.0022858 0.0087874
Health Care 0.00011567 -0.0013031 -0.00028667 -0.0014741
Industrials 0.0016701 -0.00035051 -5.7623e-05 0.001262
Information Technology 0.0015686 0.0017812 0.00016898 0.0035187
Materials 0.0040725 0.0050687 -0.0034678 0.0056734
PeriodicCategoryAttribution=108×7 table
Period LinkingCoefficient Category Allocation Selection Interaction ActiveReturn
______ __________________ ______________________ ___________ ___________ ___________ ____________
1 1.1901 Communication Services -0.00034021 0.00038766 -3.489e-05 1.2564e-05
1 1.1901 Consumer Discretionary 0.0015405 -0.0020403 -0.00036725 -0.00086699
1 1.1901 Consumer Staples 0.00065192 -0.0015322 0.00041752 -0.00046274
1 1.1901 Energy 0.00039006 0 0 0.00039006
1 1.1901 Financials 0.0013774 0.0036342 -0.00085403 0.0041575
1 1.1901 Health Care 0.00016968 -0.0010173 -0.0002238 -0.0010714
1 1.1901 Industrials -0.00032634 -0.0013981 -0.00039845 -0.0021229
1 1.1901 Information Technology -0.00045756 0.0059728 0.0007914 0.0063066
1 1.1901 Materials 0.0014797 -0.004811 0.0032234 -0.00010793
2 1.1935 Communication Services -0.00058016 -0.000878 7.902e-05 -0.0013791
2 1.1935 Consumer Discretionary -0.00089975 0.0013325 0.00023985 0.00067261
2 1.1935 Consumer Staples 0.00045794 0.00024116 -6.5715e-05 0.00063338
2 1.1935 Energy -0.00041514 0 0 -0.00041514
2 1.1935 Financials -0.00021838 0.0017119 -0.0004023 0.0010912
2 1.1935 Health Care 5.19e-05 -9.5418e-05 -2.0992e-05 -6.451e-05
2 1.1935 Industrials 0.0016152 0.0011651 0.00033205 0.0031123
⋮
计算总归因
使用 brinsonAttribution 对象和 totalAttribution 计算投资组合在所有类别（行业）中汇总的总业绩归因。
[AggregateTotalAttribution,PeriodicTotalAttribution] = totalAttribution(BrinsonPAobj)
AggregateTotalAttribution=1×4 table
Allocation Selection Interaction ActiveReturn
__________ _________ ___________ ____________
0.011449 0.016794 -0.0094348 0.018809
PeriodicTotalAttribution=12×6 table
Period LinkingCoefficient Allocation Selection Interaction ActiveReturn
______ __________________ ___________ ___________ ___________ ____________
1 1.1901 0.0044852 -0.00080413 0.0025538 0.0062349
2 1.1935 0.00087285 0.0032617 -0.0025973 0.0015372
3 1.1904 -6.9025e-05 0.0052394 0.00069386 0.0058643
4 1.208 -0.004707 -0.0095748 -0.0046622 -0.018944
5 1.1995 -0.00030704 -0.006091 -0.00061525 -0.0070132
6 1.1935 0.0012025 -0.00026724 0.00058932 0.0015246
7 1.1813 0.0032236 0.017541 -0.0021062 0.018658
8 1.196 0.004629 -0.004929 -0.0018038 -0.0021038
9 1.1927 0.0013046 0.00036681 0.00099195 0.0026634
10 1.1923 0.0032172 0.0023077 -0.0023663 0.0031586
11 1.194 -0.001881 0.00044958 0.0022018 0.00077039
12 1.1918 -0.0022819 0.0069324 -0.0007375 0.003913
生成业绩归因汇总
使用 brinsonAttribution 对象和 summary 生成一个表格，该表格汇总使用布林森模型进行的业绩归因的最终结果（涵盖所有时间段和类别）。
SummaryTable = summary(BrinsonPAobj)
SummaryTable=11×1 table
Brinson Attribution Summary
___________________________
Total Number of Assets 30
Number of Assets in Portfolio 22
Number of Assets in Benchmark 30
Number of Periods 12
Number of Categories 9
Portfolio Return 0.22345
Benchmark Return 0.20464
Active Return 0.018809
Allocation Effect 0.011449
Selection Effect 0.016794
Interaction Effect -0.0094348
生成收益、权重和业绩归因的水平条形图
使用 brinsonAttribution 对象以及 categoryReturnsChart、categoryWeightsChart 和 attributionsChart 生成水平条形图。
categoryReturnsChart(BrinsonPAobj)
categoryWeightsChart(BrinsonPAobj)
attributionsChart(BrinsonPAobj, Style="stacked")
另请参阅
brinsonAttribution | categoryAttribution | categoryReturns | categoryWeights | totalAttribution | summary
