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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.  
  9. using namespace std;
  10.  
  11. using Portfolio = vector<int>; // weights in percent, size = 6
  12.  
  13. double percentile15(vector<double>& data) {
  14.     sort(data.begin(), data.end());
  15.     size_t index = static_cast<size_t>(floor(0.15 * data.size()));
  16.     if (index >= data.size()) index = data.size() - 1;
  17.     return data[index];
  18. }
  19.  
  20. double median(vector<double>& data) {
  21.     sort(data.begin(), data.end());
  22.     size_t n = data.size();
  23.     if (n % 2 == 0)
  24.         return (data[n / 2 - 1] + data[n / 2]) / 2.0;
  25.     else
  26.         return data[n / 2];
  27. }
  28.  
  29. double lumpSumCAGR(const vector<double>& returns) {
  30.     double compound = 1.0;
  31.     for (double r : returns) {
  32.         compound *= (1.0 + r);
  33.     }
  34.     return pow(compound, 1.0 / returns.size()) - 1.0;
  35. }
  36.  
  37. double portfolioReturn(const vector<vector<double>>& assets, const Portfolio& weights, int year) {
  38.     double result = 0.0;
  39.     for (int i = 0; i < weights.size(); ++i) {
  40.         result += (weights[i] / 100.0) * assets[i][year];
  41.     }
  42.     return result;
  43. }
  44.  
  45. void generatePortfolios(vector<Portfolio>& portfolios, Portfolio current, int pos, int totalWeight, int maxAssets) {
  46.     if (pos == current.size()) {
  47.         if (totalWeight == 100) {
  48.             int nonZero = count_if(current.begin(), current.end(), [](int w) { return w > 0; });
  49.             if (nonZero <= maxAssets) {
  50.                 portfolios.push_back(current);
  51.             }
  52.         }
  53.         return;
  54.     }
  55.     for (int w = 0; w <= 100 - totalWeight; w += 2) {//const int step = 10;
  56.         current[pos] = w;
  57.         generatePortfolios(portfolios, current, pos + 1, totalWeight + w, maxAssets);
  58.     }
  59. }
  60.  
  61. int main() {
  62.     const int numAssets = 6;
  63.     const int maxAssets = 4;
  64.  
  65.  
  66.     // Asset names
  67.     vector<string> assetNames = {
  68.     	"scv", "lcg", "em", "reit", "gld" , "eu ltb"
  69.         //"scv60Lcg15", "scv95", "vti", "20bal", "33gld", "lcbtiltled"
  70.     };
  71.  
  72.     // Return data
  73.     vector<vector<double>> assets = {
  74.  
  75.     	         {-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,-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,-0.32,0.33,0.23,-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},
  76.  
  77.  
  78.     	{
  79.     -0.09, 0.19, 0.18, -0.28, -0.40, 0.24, 0.08, -0.16, -0.02, 0.01,
  80.     0.16, -0.16, 0.20, 0.14, -0.01, 0.30, 0.14, 0.01, 0.07, 0.32,
  81.     -0.05, 0.37, 0.03, 0.00, 0.01, 0.34, 0.22, 0.32, 0.43, 0.29,
  82.     -0.28, -0.13, -0.24, 0.23, 0.04, 0.02, 0.07, 0.06, -0.39, 0.33,
  83.     0.15, -0.01, 0.15, 0.31, 0.13, 0.03, 0.05, 0.25, -0.04, 0.34,
  84.     0.39, 0.18, -0.35, 0.40, 0.31
  85. },
  86.  
  87. {
  88.     -0.17, 0.28, 0.34, -0.18, -0.28, 0.25, 0.04, 0.01, 0.05, 0.06,
  89.     -0.04, -0.25, -0.31, 0.12, 0.12, 0.23, 0.11, 0.09, 0.34, 0.55,
  90.     -0.16, 0.54, 0.09, 0.68, -0.09, -0.06, 0.03, -0.11, -0.25, 0.59,
  91.     -0.31, -0.03, -0.08, 0.53, 0.22, 0.29, 0.29, 0.32, -0.52, 0.72,
  92.     0.18, -0.20, 0.17, -0.02, -0.02, -0.15, 0.10, 0.34, -0.16, 0.16,
  93.     0.16, -0.07, -0.24, 0.09, 0.05
  94. },
  95.  
  96. {
  97.     -0.01, 0.10, 0.05, -0.23, -0.30, 0.13, 0.41, 0.14, 0.01, 0.20,
  98.     0.11, -0.02, 0.18, 0.26, 0.16, 0.16, 0.18, -0.08, 0.09, 0.04,
  99.     -0.20, 0.32, 0.12, 0.17, 0.00, 0.13, 0.30, 0.19, -0.18, -0.07,
  100.     0.21, 0.12, 0.01, 0.35, 0.27, 0.08, 0.31, -0.19, -0.37, 0.25,
  101.     0.26, 0.05, 0.16, 0.03, 0.28, 0.02, 0.07, 0.03, -0.07, 0.23,
  102.     -0.09, 0.33, -0.28, 0.10, 0.06
  103. },
  104.  
  105. {
  106. 0.00, 0.13, 0.42, 0.55, 0.44, -0.26, -0.06, 0.15, 0.25, 1.00,
  107. 0.01, -0.36, 0.13, -0.17, -0.21, 0.04, 0.17, 0.18, -0.17, -0.06,
  108. -0.09, -0.09, -0.07, 0.15, -0.05, 0.00, -0.06, -0.20, -0.03, -0.02,
  109. -0.08, 0.00, 0.21, 0.19, 0.02, 0.13, 0.20, 0.25, 0.02, 0.22,
  110. 0.27, 0.05, 0.07, -0.25, 0.00, -0.12, 0.07, 0.10, -0.03, 0.16,
  111. 0.22, -0.09, -0.06, 0.11, 0.21
  112. },
  113.  
  114. // {
  115. //     -0.02, 0.16, 0.04, -0.04, -0.10, 0.08, -0.05, 0.16, 0.15, -0.10,
  116. //     -0.16, -0.16, -0.23, 0.09, -0.02, 0.04, 0.43, 0.48, 0.17, -0.02,
  117. //     -0.02, 0.12, 0.14, -0.02, 0.24, -0.03, 0.24, 0.18, 0.02, 0.22,
  118. //     -0.24, 0.01, 0.00, 0.28, 0.24, 0.19, -0.04, 0.06, 0.03, 0.04,
  119. //     0.05, -0.03, -0.01, 0.17, 0.05, 0.14, -0.08, 0.02, 0.10, -0.04,
  120. //     0.11, 0.20, -0.18, -0.41, 0.11, -0.08
  121. // }
  122.  
  123.  
  124. //         {-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,-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,-0.26,0.31,0.22,-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},
  125. //         {-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,-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,-0.32,0.33,0.23,-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},
  126. //         {-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,-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,-0.37,0.26,0.16,-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},
  127.  {-0.03,0.15,0.18,-0.07,-0.14,0.12,0.18,0.04,0.07,0.28,0.06,-0.13,0.17,0.13,0.01,0.22,0.18,0.02,0.07,0.14,-0.13,0.23,0.06,0.17,-0.02,0.16,0.12,0.12,0.04,0.07,-0.03,0.01,-0.02,0.29,0.13,0.08,0.17,0.03,-0.23,0.27,0.21,0.02,0.13,0.07,0.12,-0.03,0.09,0.13,-0.08,0.22,0.14,0.11,-0.23,0.16,0.13},        
  128. //{-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,-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,-0.21,0.25,0.23,0.00,0.13,0.08,0.09,-0.06,0.13,0.10,-0.08,0.20,0.10,0.11,-0.14,0.11,0.14},
  129. //         {-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,-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,-0.32,0.29,0.17,-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}
  130. //     
  131.  
  132.  
  133.     };
  134.  
  135.     int numYears = assets[0].size();
  136.  
  137.     for (int duration = 2; duration <= 31; duration += 111) {
  138.         cout << "\n========== Duration: " << duration << " years ==========" << endl;
  139.  
  140.         vector<Portfolio> portfolios;
  141.         generatePortfolios(portfolios, Portfolio(numAssets, 0), 0, 0, maxAssets);
  142.  
  143.         vector<tuple<Portfolio, double, double, double, double>> results;
  144.  
  145.         for (const Portfolio& p : portfolios) {
  146.             vector<double> cagrList;
  147.             for (int start = 0; start <= numYears - duration; ++start) {
  148.                 vector<double> subReturns;
  149.                 for (int i = 0; i < duration; ++i) {
  150.                     subReturns.push_back(portfolioReturn(assets, p, start + i));
  151.                 }
  152.                 double cagr = lumpSumCAGR(subReturns);
  153.                 cagrList.push_back(cagr);
  154.             }
  155.  
  156.             double p15 = percentile15(cagrList);
  157.             double pmin = *min_element(cagrList.begin(), cagrList.end());
  158.             double pmax = *max_element(cagrList.begin(), cagrList.end());
  159.             double pmed = median(cagrList);
  160.  
  161.             results.emplace_back(p, p15, pmin, pmax, pmed);
  162.         }
  163.  
  164.         sort(results.begin(), results.end(), [](const auto& a, const auto& b) {
  165.             return get<1>(a) > get<1>(b);
  166.         });
  167.  
  168.         cout << fixed << setprecision(2);
  169.  
  170.         // Summary table
  171.         cout << "\nTop 2 Portfolios Summary (Bottom 15th Percentile CAGR):" << endl;
  172.         cout << left << setw(10) << "#" << setw(40) << "Portfolio" << setw(10) << "P15%" << setw(10) << "Min" << setw(10) << "Max" << setw(10) << "Median" << endl;
  173.         cout << string(80, '-') << endl;
  174.  
  175.         for (int i = 0; i < 2 && i < results.size(); ++i) {
  176.             auto [weights, p15, pmin, pmax, pmed] = results[i];
  177.             string portStr;
  178.             for (int j = 0; j < numAssets; ++j) {
  179.                 if (weights[j] > 0) {
  180.                     portStr += assetNames[j] + ":" + to_string(weights[j]) + "% ";
  181.                 }
  182.             }
  183.             cout << left << setw(10) << (i + 1) << setw(40) << portStr << setw(10) << p15 * 100 << setw(10) << pmin * 100 << setw(10) << pmax * 100 << setw(10) << pmed * 100 << endl;
  184.         }
  185.  
  186.         // // Detailed breakdown
  187.         // for (int i = 0; i < 2 && i < results.size(); ++i) {
  188.         //     auto [weights, p15, pmin, pmax, pmed] = results[i];
  189.         //     cout << "\nPortfolio " << (i + 1) << ":\n";
  190.         //     cout << left << setw(15) << "Asset" << setw(10) << "Weight\n";
  191.         //     cout << "-------------------------\n";
  192.         //     for (int j = 0; j < numAssets; ++j) {
  193.         //         if (weights[j] > 0) {
  194.         //             cout << left << setw(15) << assetNames[j] << setw(10) << weights[j] << "\n";
  195.         //         }
  196.         //     }
  197.         //     cout << "-------------------------\n";
  198.         //     cout << "Bottom 15th % CAGR : " << p15 * 100 << "%\n";
  199.         //     cout << "Min CAGR           : " << pmin * 100 << "%\n";
  200.         //     cout << "Max CAGR           : " << pmax * 100 << "%\n";
  201.         //     cout << "Median CAGR        : " << pmed * 100 << "%\n";
  202.         // }
  203.     }
  204.  
  205.     return 0;
  206. }
  207.  
Success #stdin #stdout 3.89s 58908KB
comments (?)
stdin 
Standard input is empty
stdout 
========== Duration: 2 years ==========

Top 2 Portfolios Summary (Bottom 15th Percentile CAGR):
#         Portfolio                               P15%      Min       Max       Median    
--------------------------------------------------------------------------------
1         scv:60% lcg:4% reit:14% gld:22%         1.61      -14.69    27.51     9.16      
2         scv:58% lcg:4% reit:16% gld:22%         1.59      -14.84    27.15     9.06
https://ideone.com/U0zAEj
language:
C++ (gcc 8.3)
created:
9 days ago
visibility:
public

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