Holding-Period and Cumulative Return

/**
 * Fintech Math Bootcamp · Lesson 018 of 120
 * Holding-Period and Cumulative Return
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: A two-period performance report with changing bases
 * Rule:     cumulative = Π(1+Rₜ) − 1
 *
 * Try it:   What gain is needed to recover from 96 to 100?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson018() {
  const returns = [0.20, -0.20];
  let wealth = 100;
  const path = [wealth];
  for (const r of returns) {
    if (!(1 + r > 0)) throw new Error("Growth factor must be positive");
    wealth *= 1 + r; path.push(wealth);
  }
  const result = {path, cumulative: wealth / path[0] - 1};
  return result;
}

export const checkedResult = {"path":[100,120,96],"cumulative":-0.040000000000000036};

// Run this file directly: npx tsx lessons/02-financial-arithmetic-time-value-and-returns/018-holding-period-and-cumulative-return.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson018(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 018 of 120
Holding-Period and Cumulative Return
Module 02: Financial Arithmetic, Time Value, and Returns

Scenario: A two-period performance report with changing bases
Rule:     cumulative = Π(1+Rₜ) − 1

Try it:   What gain is needed to recover from 96 to 100?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.

Run it: python main.py
"""

import json


def lesson018() -> dict:
    returns = [0.20, -0.20]
    wealth = 100
    path = [wealth]
    for r in returns:
        if not 1 + r > 0:
            raise ValueError("Growth factor must be positive")
        wealth *= 1 + r
        path.append(wealth)
    result = {"path": path, "cumulative": wealth / path[0] - 1}
    return result


if __name__ == "__main__":
    print(json.dumps(lesson018(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 018 of 120
 * Holding-Period and Cumulative Return
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: A two-period performance report with changing bases
 * Rule:     cumulative = Π(1+Rₜ) − 1
 *
 * Try it:   What gain is needed to recover from 96 to 100?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: javac Main.java && java Main
 */

import java.util.ArrayList;
import java.util.List;

public class Main {
    static final class WealthPath {
        final List<Double> path;
        final double cumulative;

        WealthPath(List<Double> path, double cumulative) {
            this.path = path;
            this.cumulative = cumulative;
        }
    }

    static WealthPath lesson018() {
        double[] returns = {0.20, -0.20};
        double wealth = 100;
        List<Double> path = new ArrayList<Double>();
        path.add(wealth);
        for (double r : returns) {
            if (!(1 + r > 0)) throw new IllegalArgumentException("Growth factor must be positive");
            wealth *= 1 + r;
            path.add(wealth);
        }
        WealthPath result = new WealthPath(path, wealth / path.get(0) - 1);
        return result;
    }

    public static void main(String[] args) {
        WealthPath result = lesson018();
        List<String> path = new ArrayList<String>();
        for (double value : result.path) path.add(num(value));
        System.out.println(object("path", array(path), "cumulative", num(result.cumulative)));
    }

    // Formats a double the way JSON.stringify does: whole numbers without ".0", null for NaN or infinity.
    static String num(double x) {
        if (Double.isNaN(x) || Double.isInfinite(x)) return "null";
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return String.valueOf((long) x);
        return String.valueOf(x);
    }

    static String quote(String text) {
        return "\"" + text.replace("\\", "\\\\").replace("\"", "\\\"") + "\"";
    }

    // Indents an already formatted JSON value by one level.
    static String nested(String json) {
        return json.replace("\n", "\n  ");
    }

    static String object(String... keysAndValues) {
        if (keysAndValues.length == 0) return "{}";
        StringBuilder out = new StringBuilder("{");
        for (int i = 0; i < keysAndValues.length; i += 2) {
            out.append(i == 0 ? "\n  " : ",\n  ")
               .append(quote(keysAndValues[i])).append(": ").append(nested(keysAndValues[i + 1]));
        }
        return out.append("\n}").toString();
    }

    static String array(java.util.List<String> items) {
        if (items.isEmpty()) return "[]";
        StringBuilder out = new StringBuilder("[");
        for (int i = 0; i < items.size(); i++) {
            out.append(i == 0 ? "\n  " : ",\n  ").append(nested(items.get(i)));
        }
        return out.append("\n]").toString();
    }
}

// Fintech Math Bootcamp · Lesson 018 of 120
// Holding-Period and Cumulative Return
// Module 02: Financial Arithmetic, Time Value, and Returns
//
// Scenario: A two-period performance report with changing bases
// Rule:     cumulative = Π(1+Rₜ) − 1
//
// Try it:   What gain is needed to recover from 96 to 100?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run it: go run main.go

package main

import (
	"encoding/json"
	"errors"
	"fmt"
	"os"
)

type WealthPath struct {
	Path       []float64 `json:"path"`
	Cumulative float64   `json:"cumulative"`
}

func lesson018() (WealthPath, error) {
	returns := []float64{0.20, -0.20}
	wealth := 100.0
	path := []float64{wealth}
	for _, r := range returns {
		if !(1+r > 0) {
			return WealthPath{}, errors.New("Growth factor must be positive")
		}
		wealth *= 1 + r
		path = append(path, wealth)
	}
	result := WealthPath{Path: path, Cumulative: wealth/path[0] - 1}
	return result, nil
}

func main() {
	result, err := lesson018()
	if err != nil {
		fmt.Fprintln(os.Stderr, "Error:", err)
		os.Exit(1)
	}
	printJSON(result)
}

// printJSON prints a value as JSON indented with two spaces, like JSON.stringify(value, null, 2).
func printJSON(value any) {
	out, err := json.MarshalIndent(value, "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 018 of 120
 * Holding-Period and Cumulative Return
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: A two-period performance report with changing bases
 * Rule:     cumulative = Π(1+Rₜ) − 1
 *
 * Try it:   What gain is needed to recover from 96 to 100?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: g++ -std=c++17 -o main main.cpp && ./main
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <stdexcept>
#include <string>
#include <utility>
#include <vector>

// Formats a double the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
std::string num(double x) {
    if (!std::isfinite(x)) return "null";
    char buffer[32];
    auto [end, error] = std::to_chars(buffer, buffer + sizeof buffer, x);
    (void)error;
    return std::string(buffer, end);
}

std::string quote(const std::string& text) {
    std::string out = "\"";
    for (char c : text) {
        if (c == '"' || c == '\\') out += '\\';
        out += c;
    }
    return out + "\"";
}

// Indents an already formatted JSON value by one level.
std::string nested(const std::string& json) {
    std::string out;
    for (char c : json) {
        out += c;
        if (c == '\n') out += "  ";
    }
    return out;
}

std::string object(const std::vector<std::pair<std::string, std::string>>& fields) {
    if (fields.empty()) return "{}";
    std::string out = "{";
    for (std::size_t i = 0; i < fields.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += quote(fields[i].first) + ": " + nested(fields[i].second);
    }
    return out + "\n}";
}

std::string array(const std::vector<std::string>& items) {
    if (items.empty()) return "[]";
    std::string out = "[";
    for (std::size_t i = 0; i < items.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += nested(items[i]);
    }
    return out + "\n]";
}

std::string numbers(const std::vector<double>& values) {
    std::vector<std::string> items;
    for (double value : values) items.push_back(num(value));
    return array(items);
}

struct WealthPath {
    std::vector<double> path;
    double cumulative;
};

WealthPath lesson018() {
    const std::vector<double> returns{0.20, -0.20};
    double wealth = 100;
    std::vector<double> path{wealth};
    for (double r : returns) {
        if (!(1 + r > 0)) throw std::invalid_argument("Growth factor must be positive");
        wealth *= 1 + r;
        path.push_back(wealth);
    }
    const WealthPath result{path, wealth / path[0] - 1};
    return result;
}

int main() {
    const WealthPath result = lesson018();
    std::cout << object({{"path", numbers(result.path)}, {"cumulative", num(result.cumulative)}}) << "\n";
}

//! Fintech Math Bootcamp · Lesson 018 of 120
//! Holding-Period and Cumulative Return
//! Module 02: Financial Arithmetic, Time Value, and Returns
//!
//! Scenario: A two-period performance report with changing bases
//! Rule:     cumulative = Π(1+Rₜ) − 1
//!
//! Try it:   What gain is needed to recover from 96 to 100?
//!
//! Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
//! Free course:    https://courses.thefintechbuilder.com
//! Synthetic teaching example, not financial advice or a production library.
//!
//! Run it: rustc main.rs && ./main

struct WealthPath {
    path: Vec<f64>,
    cumulative: f64,
}

fn lesson018() -> Result<WealthPath, String> {
    let returns = [0.20, -0.20];
    let mut wealth: f64 = 100.0;
    let mut path = vec![wealth];
    for &r in returns.iter() {
        if !(1.0 + r > 0.0) {
            return Err("Growth factor must be positive".to_string());
        }
        wealth *= 1.0 + r;
        path.push(wealth);
    }
    let cumulative = wealth / path[0] - 1.0;
    let result = WealthPath { path, cumulative };
    Ok(result)
}

fn main() {
    match lesson018() {
        Ok(result) => println!("{}", object(&[
            ("path", numbers(&result.path)),
            ("cumulative", num(result.cumulative)),
        ])),
        Err(message) => {
            eprintln!("Error: {}", message);
            std::process::exit(1);
        }
    }
}

/// Formats a number the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
fn num(x: f64) -> String {
    if x.is_finite() {
        format!("{}", x)
    } else {
        "null".to_string()
    }
}

fn quote(text: &str) -> String {
    format!("\"{}\"", text.replace('\\', "\\\\").replace('"', "\\\""))
}

/// Indents an already formatted JSON value by one level.
fn nested(json: &str) -> String {
    json.replace('\n', "\n  ")
}

fn object(fields: &[(&str, String)]) -> String {
    if fields.is_empty() {
        return "{}".to_string();
    }
    let lines: Vec<String> = fields
        .iter()
        .map(|(key, value)| format!("  {}: {}", quote(key), nested(value)))
        .collect();
    format!("{{\n{}\n}}", lines.join(",\n"))
}

fn array(items: &[String]) -> String {
    if items.is_empty() {
        return "[]".to_string();
    }
    let lines: Vec<String> = items.iter().map(|item| format!("  {}", nested(item))).collect();
    format!("[\n{}\n]", lines.join(",\n"))
}

fn numbers(values: &[f64]) -> String {
    let items: Vec<String> = values.iter().map(|&value| num(value)).collect();
    array(&items)
}

/**
 * Fintech Math Bootcamp · Lesson 018 of 120
 * Holding-Period and Cumulative Return
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: A two-period performance report with changing bases
 * Rule:     cumulative = Π(1+Rₜ) − 1
 *
 * Try it:   What gain is needed to recover from 96 to 100?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/holding-period-return/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: dotnet run  (inside a console project that holds this Program.cs)
 */

using System.Text.Json;

var jsonOptions = new JsonSerializerOptions { WriteIndented = true, PropertyNamingPolicy = JsonNamingPolicy.CamelCase };
Console.WriteLine(JsonSerializer.Serialize(Lesson018(), jsonOptions));

static WealthPath Lesson018()
{
    double[] returns = { 0.20, -0.20 };
    double wealth = 100;
    var path = new List<double> { wealth };
    foreach (var r in returns)
    {
        if (!(1 + r > 0)) throw new ArgumentException("Growth factor must be positive");
        wealth *= 1 + r;
        path.Add(wealth);
    }
    var result = new WealthPath(path, wealth / path[0] - 1);
    return result;
}

record WealthPath(List<double> Path, double Cumulative);