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  1. #include <iostream>
  2. #include <vector>
  3. #include <cmath>
  4. #include <algorithm>
  5. #include <iomanip>
  6. #include <tuple>
  7. #include <string>
  8. #include <sstream>
  9.  
  10. using namespace std;
  11.  
  12. using Portfolio = vector<int>; // weights in percent, size = 6
  13.  
  14. double percentile15(vector<double>& data) {
  15.     sort(data.begin(), data.end());
  16.     size_t index = static_cast<size_t>(floor(0.15 * data.size()));
  17.     if (index >= data.size()) index = data.size() - 1;
  18.     return data[index];
  19. }
  20.  
  21. double lumpSumCAGR(const vector<double>& returns) {
  22.     double compound = 1.0;
  23.     for (double r : returns) {
  24.         compound *= (1.0 + r);
  25.     }
  26.     return pow(compound, 1.0 / returns.size()) - 1.0;
  27. }
  28.  
  29. double portfolioReturn(const vector<vector<double>>& assets, const Portfolio& weights, int year) {
  30.     double result = 0.0;
  31.     for (int i = 0; i < weights.size(); ++i) {
  32.         result += (weights[i] / 100.0) * assets[i][year];
  33.     }
  34.     return result;
  35. }
  36.  
  37. void generatePortfolios(vector<Portfolio>& portfolios, Portfolio current, int pos, int totalWeight, int maxAssets) {
  38.     if (pos == current.size()) {
  39.         if (totalWeight == 100) {
  40.             int nonZero = count_if(current.begin(), current.end(), [](int w) { return w > 0; });
  41.             if (nonZero <= maxAssets) {
  42.                 portfolios.push_back(current);
  43.             }
  44.         }
  45.         return;
  46.     }
  47.     for (int w = 0; w <= 100 - totalWeight; w += 5) {
  48.         current[pos] = w;
  49.         generatePortfolios(portfolios, current, pos + 1, totalWeight + w, maxAssets);
  50.     }
  51. }
  52.  
  53. int main() {
  54.     const int numAssets = 6;
  55.     const int maxAssets = 3;
  56.     const int step = 5;
  57.  
  58.     vector<string> assetNames = {"scv60Lcg15", "scv95", "vti", "11all", "33gld", "lcbtilted"};
  59.  
  60.     vector<vector<double>> assets = {
  61.         // Asset 1
  62.         {-0.04,0.14,0.15,-0.14,-0.19,0.26,0.28,0.04,0.08,0.28,0.08,-0.06,0.24,0.22,-0.01,0.26,0.14,-0.02,0.14,0.16,
  63.         -0.16,0.29,0.15,0.18,-0.03,0.20,0.13,0.20,0.02,0.08,-0.04,0.04,-0.07,0.33,0.12,0.06,0.15,0.01,-0.26,0.31,
  64.         0.22,-0.03,0.15,0.19,0.08,-0.06,0.16,0.13,-0.11,0.21,0.13,0.12,-0.18,0.15,0.12},
  65.  
  66.         // Asset 2
  67.         {-0.03,0.13,0.06,-0.29,-0.31,0.43,0.46,0.08,0.07,0.21,0.12,0.06,0.31,0.38,0.02,0.31,0.12,-0.08,0.23,0.14,
  68.         -0.22,0.37,0.24,0.19,-0.02,0.24,0.17,0.31,-0.06,0.02,0.04,0.11,-0.13,0.41,0.17,0.04,0.15,-0.09,-0.32,0.33,
  69.         0.23,-0.06,0.18,0.32,0.09,-0.06,0.23,0.09,-0.15,0.20,0.03,0.19,-0.16,0.11,0.08},
  70.  
  71.         // Asset 3
  72.         {-0.02,0.11,0.12,-0.25,-0.36,0.30,0.21,-0.11,-0.01,0.05,0.16,-0.11,0.19,0.19,0.01,0.28,0.15,-0.02,0.12,0.24,
  73.         -0.10,0.29,0.06,0.08,-0.01,0.34,0.19,0.30,0.24,0.19,-0.13,-0.09,-0.25,0.30,0.08,0.02,0.12,0.01,-0.37,0.26,
  74.         0.16,-0.02,0.14,0.31,0.12,0.00,0.11,0.19,-0.07,0.28,0.19,0.18,-0.24,0.22,0.20},
  75.  
  76.         // Asset 4
  77.         {-0.02,0.12,0.14,-0.13,-0.19,0.22,0.26,0.04,0.06,0.19,0.07,-0.07,0.20,0.20,0.03,0.26,0.19,0.00,0.14,0.15,
  78.         -0.16,0.24,0.10,0.20,-0.02,0.19,0.12,0.17,0.01,0.05,0.01,0.02,-0.06,0.32,0.14,0.07,0.17,-0.01,-0.25,0.25,
  79.         0.20,0.00,0.14,0.15,0.11,-0.04,0.13,0.12,-0.10,0.20,0.07,0.12,-0.19,0.10,0.08},
  80.  
  81.         // Asset 5
  82.         {-0.01,0.11,0.19,0.03,-0.05,0.13,0.23,0.07,0.10,0.44,0.08,-0.13,0.20,0.14,-0.04,0.19,0.16,0.02,0.06,0.08,
  83.         -0.15,0.17,0.08,0.16,-0.03,0.17,0.11,0.12,0.00,0.02,-0.01,0.02,-0.02,0.30,0.11,0.07,0.19,0.03,-0.21,0.25,
  84.         0.23,0.00,0.13,0.08,0.09,-0.06,0.13,0.10,-0.08,0.20,0.10,0.11,-0.14,0.11,0.14},
  85.  
  86.         // Asset 6
  87.         {-0.03,0.13,0.12,-0.22,-0.30,0.25,0.24,-0.02,0.00,0.07,0.08,-0.09,0.14,0.20,0.07,0.26,0.15,-0.02,0.16,0.24,
  88.         -0.13,0.33,0.10,0.21,-0.03,0.22,0.16,0.21,0.05,0.15,-0.05,-0.02,-0.12,0.32,0.14,0.08,0.17,0.02,-0.32,0.29,
  89.         0.17,-0.01,0.14,0.17,0.13,-0.03,0.11,0.16,-0.09,0.23,0.11,0.14,-0.24,0.14,0.11}
  90.     };
  91.  
  92.     for (int duration = 1; duration <= 31; duration += 1) {
  93.         int numYears = assets[0].size();
  94.         vector<Portfolio> portfolios;
  95.         generatePortfolios(portfolios, Portfolio(numAssets, 0), 0, 0, maxAssets);
  96.  
  97.         vector<tuple<Portfolio, double>> portfolioResults;
  98.  
  99.         for (const Portfolio& p : portfolios) {
  100.             vector<double> cagrList;
  101.             for (int start = 0; start <= numYears - duration; ++start) {
  102.                 vector<double> subReturns;
  103.                 for (int i = 0; i < duration; ++i) {
  104.                     double portRet = portfolioReturn(assets, p, start + i);
  105.                     subReturns.push_back(portRet);
  106.                 }
  107.                 double cagr = lumpSumCAGR(subReturns);
  108.                 cagrList.push_back(cagr);
  109.             }
  110.             double bottom15 = percentile15(cagrList);
  111.             portfolioResults.emplace_back(p, bottom15);
  112.         }
  113.  
  114.         sort(portfolioResults.begin(), portfolioResults.end(),
  115.              [](const auto& a, const auto& b) {
  116.                  return get<1>(a) > get<1>(b);
  117.              });
  118.  
  119.         cout << "\n================ Duration: " << duration << " years ================\n";
  120.         cout << left
  121.              << setw(6) << "Rank"
  122.              << setw(10) << "Duration"
  123.              << setw(60) << "Portfolio Weights"
  124.              << "Bottom 15% CAGR\n";
  125.         cout << string(100, '-') << '\n';
  126.  
  127.         for (int i = 0; i < 2 && i < portfolioResults.size(); ++i) {
  128.             auto [weights, cagr] = portfolioResults[i];
  129.             stringstream weightDesc;
  130.             for (int j = 0; j < numAssets; ++j) {
  131.                 if (weights[j] > 0) {
  132.                     weightDesc << assetNames[j] << ": " << weights[j] << "%  ";
  133.                 }
  134.             }
  135.             cout << setw(6) << i + 1
  136.                  << setw(10) << duration
  137.                  << setw(60) << weightDesc.str()
  138.                  << fixed << setprecision(2) << (cagr * 100) << "%\n";
  139.         }
  140.     }
  141.  
  142.     return 0;
  143. }
  144.  
Success #stdin #stdout 3.42s 5280KB
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================ Duration: 1 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     1         11all: 35%  33gld: 65%                                      -2.65%
2     1         vti: 5%  11all: 25%  33gld: 70%                             -2.65%

================ Duration: 2 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     2         scv95: 30%  vti: 10%  33gld: 60%                            1.09%
2     2         scv60Lcg15: 30%  scv95: 25%  33gld: 45%                     1.08%

================ Duration: 3 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     3         scv95: 20%  vti: 35%  33gld: 45%                            2.71%
2     3         scv95: 15%  vti: 35%  33gld: 50%                            2.67%

================ Duration: 4 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     4         scv60Lcg15: 20%  33gld: 80%                                 4.50%
2     4         scv60Lcg15: 15%  11all: 5%  33gld: 80%                      4.47%

================ Duration: 5 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     5         scv60Lcg15: 55%  33gld: 45%                                 4.39%
2     5         scv60Lcg15: 40%  33gld: 50%  lcbtilted: 10%                 4.37%

================ Duration: 6 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     6         scv60Lcg15: 45%  33gld: 50%  lcbtilted: 5%                  5.59%
2     6         scv60Lcg15: 50%  33gld: 50%                                 5.56%

================ Duration: 7 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     7         scv60Lcg15: 15%  scv95: 35%  33gld: 50%                     6.15%
2     7         scv60Lcg15: 25%  scv95: 30%  33gld: 45%                     6.15%

================ Duration: 8 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     8         scv60Lcg15: 50%  vti: 5%  33gld: 45%                        6.34%
2     8         scv60Lcg15: 45%  scv95: 10%  33gld: 45%                     6.34%

================ Duration: 9 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     9         scv60Lcg15: 10%  scv95: 30%  33gld: 60%                     7.01%
2     9         scv95: 35%  33gld: 65%                                      7.00%

================ Duration: 10 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     10        scv60Lcg15: 95%  scv95: 5%                                  6.45%
2     10        scv60Lcg15: 100%                                            6.44%

================ Duration: 11 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     11        scv60Lcg15: 20%  scv95: 65%  33gld: 15%                     6.75%
2     11        scv60Lcg15: 25%  scv95: 60%  33gld: 15%                     6.74%

================ Duration: 12 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     12        scv60Lcg15: 75%  33gld: 25%                                 6.84%
2     12        scv60Lcg15: 70%  scv95: 5%  33gld: 25%                      6.83%

================ Duration: 13 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     13        scv60Lcg15: 80%  vti: 15%  33gld: 5%                        6.59%
2     13        scv60Lcg15: 15%  scv95: 70%  33gld: 15%                     6.58%

================ Duration: 14 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     14        scv60Lcg15: 85%  scv95: 10%  vti: 5%                        7.07%
2     14        scv60Lcg15: 90%  scv95: 5%  vti: 5%                         7.06%

================ Duration: 15 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     15        scv60Lcg15: 90%  scv95: 10%                                 7.21%
2     15        scv60Lcg15: 85%  scv95: 5%  33gld: 10%                      7.20%

================ Duration: 16 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     16        scv60Lcg15: 100%                                            6.98%
2     16        scv60Lcg15: 95%  scv95: 5%                                  6.98%

================ Duration: 17 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     17        scv60Lcg15: 85%  scv95: 5%  33gld: 10%                      7.03%
2     17        scv60Lcg15: 80%  scv95: 5%  33gld: 15%                      7.02%

================ Duration: 18 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     18        scv60Lcg15: 65%  scv95: 35%                                 7.05%
2     18        scv60Lcg15: 60%  scv95: 40%                                 7.05%

================ Duration: 19 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     19        scv60Lcg15: 15%  scv95: 85%                                 6.90%
2     19        scv60Lcg15: 10%  scv95: 90%                                 6.90%

================ Duration: 20 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     20        scv95: 90%  33gld: 10%                                      7.33%
2     20        scv95: 85%  33gld: 15%                                      7.33%

================ Duration: 21 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     21        scv60Lcg15: 20%  scv95: 75%  lcbtilted: 5%                  7.70%
2     21        scv60Lcg15: 20%  scv95: 70%  lcbtilted: 10%                 7.70%

================ Duration: 22 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     22        scv60Lcg15: 100%                                            7.26%
2     22        scv60Lcg15: 95%  scv95: 5%                                  7.25%

================ Duration: 23 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     23        scv95: 90%  lcbtilted: 10%                                  7.28%
2     23        scv95: 95%  lcbtilted: 5%                                   7.27%

================ Duration: 24 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     24        scv60Lcg15: 95%  scv95: 5%                                  7.53%
2     24        scv60Lcg15: 90%  scv95: 5%  vti: 5%                         7.53%

================ Duration: 25 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     25        scv95: 45%  vti: 20%  lcbtilted: 35%                        7.74%
2     25        scv95: 50%  vti: 25%  lcbtilted: 25%                        7.74%

================ Duration: 26 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     26        scv95: 85%  vti: 15%                                        8.01%
2     26        scv95: 80%  vti: 15%  lcbtilted: 5%                         8.00%

================ Duration: 27 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     27        scv95: 100%                                                 8.36%
2     27        scv95: 95%  lcbtilted: 5%                                   8.36%

================ Duration: 28 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     28        scv95: 65%  vti: 30%  lcbtilted: 5%                         8.37%
2     28        scv95: 70%  vti: 30%                                        8.36%

================ Duration: 29 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     29        scv95: 80%  vti: 5%  lcbtilted: 15%                         8.56%
2     29        scv95: 75%  vti: 5%  lcbtilted: 20%                         8.56%

================ Duration: 30 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     30        scv95: 75%  lcbtilted: 25%                                  8.34%
2     30        scv95: 70%  lcbtilted: 30%                                  8.34%

================ Duration: 31 years ================
Rank  Duration  Portfolio Weights                                           Bottom 15% CAGR
----------------------------------------------------------------------------------------------------
1     31        scv95: 70%  vti: 20%  lcbtilted: 10%                        8.37%
2     31        scv95: 70%  vti: 15%  lcbtilted: 15%                        8.37%
https://ideone.com/YjJMw4
language:
C++ (gcc 8.3)
created:
10 days ago
visibility:
public

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