Calculate the Rate of Return on a Price-weighted Index

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Price-Weighted Index Return Calculator

Initial Stock Prices

Final Stock Prices

The divisor is used to calculate the actual index value. For a simple average of 3 stocks, use 3.

Results

Initial Index Value 0.00
Final Index Value 0.00
Rate of Return (RoR) 0.00%
function calculatePWI() { var p1i = parseFloat(document.getElementById('p1i').value) || 0; var p2i = parseFloat(document.getElementById('p2i').value) || 0; var p3i = parseFloat(document.getElementById('p3i').value) || 0; var p1f = parseFloat(document.getElementById('p1f').value) || 0; var p2f = parseFloat(document.getElementById('p2f').value) || 0; var p3f = parseFloat(document.getElementById('p3f').value) || 0; var divisor = parseFloat(document.getElementById('divisor').value) || 1; if (divisor <= 0) { alert("Divisor must be greater than zero."); return; } var initialSum = p1i + p2i + p3i; var finalSum = p1f + p2f + p3f; var initialIndex = initialSum / divisor; var finalIndex = finalSum / divisor; var rateOfReturn = ((finalIndex – initialIndex) / initialIndex) * 100; document.getElementById('initial-index-display').innerText = initialIndex.toFixed(2); document.getElementById('final-index-display').innerText = finalIndex.toFixed(2); document.getElementById('ror-display').innerText = rateOfReturn.toFixed(2) + "%"; document.getElementById('pwi-result-box').style.display = 'block'; }

Understanding the Price-Weighted Index Calculation

A price-weighted index is a type of stock market index where each component stock is weighted by its price per share. In this model, stocks with higher prices have a more significant influence on the index's movement and total value than stocks with lower prices, regardless of the company's actual size or market capitalization.

The Formula for Price-Weighted Return

To calculate the rate of return, you must first determine the index value at two different points in time. The basic formula for the index value is:

Index Value = Σ (Prices of Individual Stocks) / Divisor

Once you have the initial and final index values, the Rate of Return (RoR) is calculated as:

RoR = [(Final Index Value – Initial Index Value) / Initial Index Value] × 100

Example Calculation

Imagine an index consisting of three stocks:

  • Stock A: Initial Price $100, Final Price $110
  • Stock B: Initial Price $50, Final Price $40
  • Stock C: Initial Price $10, Final Price $12

If we assume the divisor is 3:

  1. Initial Index: (100 + 50 + 10) / 3 = 160 / 3 = 53.33
  2. Final Index: (110 + 40 + 12) / 3 = 162 / 3 = 54.00
  3. Rate of Return: [(54.00 – 53.33) / 53.33] × 100 = 1.25%

The Role of the Divisor

The divisor is not always equal to the number of stocks in the index. In professional indices like the Dow Jones Industrial Average (DJIA) or the Nikkei 225, the divisor is adjusted to account for stock splits, spin-offs, or changes in the index components. This ensures that such corporate actions do not artificially change the value of the index.

Key Characteristics

  • Price Dominance: A $100 stock moving 1% has a much larger impact than a $10 stock moving 10%.
  • Simplicity: Historically, these were easier to calculate before the era of high-speed computing.
  • Criticism: Many analysts argue that price-weighting is arbitrary because a stock's price (unrelated to market cap) shouldn't dictate its importance in the economy.

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