Coefficient of Variation (Risk per unit of Return):0.00
function calculateRiskAndReturn() {
// Retrieve inputs using var
var p1 = parseFloat(document.getElementById('prob1').value) || 0;
var r1 = parseFloat(document.getElementById('ret1').value) || 0;
var p2 = parseFloat(document.getElementById('prob2').value) || 0;
var r2 = parseFloat(document.getElementById('ret2').value) || 0;
var p3 = parseFloat(document.getElementById('prob3').value) || 0;
var r3 = parseFloat(document.getElementById('ret3').value) || 0;
var p4 = parseFloat(document.getElementById('prob4').value) || 0;
var r4 = parseFloat(document.getElementById('ret4').value) || 0;
// Elements for display
var errorDiv = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('results');
var sumSpan = document.getElementById('currentSum');
// Check Probability Sum
var totalProb = p1 + p2 + p3 + p4;
// Allow small floating point margin of error (e.g., 99.99 – 100.01)
if (totalProb 100.1) {
sumSpan.innerText = totalProb.toFixed(2);
errorDiv.style.display = 'block';
resultsDiv.style.display = 'none';
return;
}
// Hide error if valid
errorDiv.style.display = 'none';
// 1. Calculate Expected Return E(R)
// Formula: Sum of (Probability * Return)
// Convert probability to decimal for calculation (e.g., 20% -> 0.20)
var er1 = (p1 / 100) * r1;
var er2 = (p2 / 100) * r2;
var er3 = (p3 / 100) * r3;
var er4 = (p4 / 100) * r4;
var expectedReturn = er1 + er2 + er3 + er4;
// 2. Calculate Variance
// Formula: Sum of [Probability * (Return – ExpectedReturn)^2]
var v1 = (p1 / 100) * Math.pow((r1 – expectedReturn), 2);
var v2 = (p2 / 100) * Math.pow((r2 – expectedReturn), 2);
var v3 = (p3 / 100) * Math.pow((r3 – expectedReturn), 2);
var v4 = (p4 / 100) * Math.pow((r4 – expectedReturn), 2);
var variance = v1 + v2 + v3 + v4;
// 3. Calculate Standard Deviation (Risk)
// Formula: Square root of Variance
var stdDev = Math.sqrt(variance);
// 4. Calculate Coefficient of Variation (CV)
// Formula: StdDev / Expected Return (absolute measure of dispersion)
// Handle division by zero
var cv = 0;
if (expectedReturn !== 0) {
cv = stdDev / expectedReturn;
}
// Update DOM
resultsDiv.style.display = 'block';
document.getElementById('expectedReturn').innerText = expectedReturn.toFixed(2) + "%";
document.getElementById('varianceResult').innerText = variance.toFixed(4);
document.getElementById('stdDevResult').innerText = stdDev.toFixed(2) + "%";
// CV is a ratio, usually not a percentage
document.getElementById('cvResult').innerText = cv.toFixed(2);
}
Understanding Expected Rate of Return and Risk
In financial modeling and portfolio management, understanding the relationship between the potential reward of an investment and its inherent volatility is crucial. This calculator utilizes a probability-weighted approach to determine two key metrics: the Expected Rate of Return and the Standard Deviation (Risk).
What is Expected Rate of Return?
The Expected Rate of Return (E[R]) is the weighted average of all possible returns that an investment class could generate. It is calculated by multiplying potential outcomes by the chances (probability) of them occurring and summing the results. It attempts to answer the question: "Given the various economic scenarios (Boom, Recession, Stagnation), what is the average return I should anticipate over the long run?"
Formula: E[R] = ∑ (Pi × Ri)
Where Pi is the probability of a specific scenario and Ri is the projected return in that scenario.
What is Investment Risk (Standard Deviation)?
While the expected return gives you an average, it doesn't tell you how "bumpy" the ride will be. In finance, risk is often quantified as Standard Deviation (σ). This metric measures how dispersed the actual returns are likely to be around the expected average.
Low Standard Deviation: Returns are clustered tightly around the average (Low Risk).
High Standard Deviation: Returns are spread out over a large range (High Risk).
How to Use This Calculator
This tool is designed for scenario analysis. Instead of inputting dollar amounts, you input percentages regarding probabilities and returns.
Identify Scenarios: Think of different market conditions (e.g., Bull Market, Flat Market, Bear Market).
Assign Probabilities: Estimate the likelihood of each scenario occurring. Note: The total probability must equal 100%.
Estimate Returns: For each scenario, estimate the percentage return (gain or loss) of the asset.
Calculate: Click the button to see the weighted average return and the volatility (risk) associated with those probabilities.
Example Calculation
Imagine a stock with the following projections:
30% Chance of a Boom Economy with a 20% Return.
40% Chance of a Normal Economy with a 10% Return.
30% Chance of a Recession with a -5% Return.
Using the calculator, you would input these values to find that the Expected Return is 8.5% and the Standard Deviation indicates the volatility around that average.