Enter up to 5 economic scenarios. Probabilities must sum to 100%.
Scenario 1 (e.g., Boom)
Scenario 2 (e.g., Growth)
Scenario 3 (e.g., Normal)
Scenario 4 (e.g., Recession)
Scenario 5 (e.g., Crash)
Portfolio Risk Metrics
Total Probability Sum:0%
Expected Rate of Return (E[R]):0.00%
Variance (σ²):0.00
Standard Deviation (σ):0.00%
Coefficient of Variation (CV):0.00
function calculateStats() {
var errorDiv = document.getElementById('error-msg');
var resultsDiv = document.getElementById('results');
// Reset
errorDiv.style.display = 'none';
resultsDiv.style.display = 'none';
errorDiv.innerHTML = ";
// Arrays to hold inputs
var probs = [];
var rets = [];
var totalProb = 0;
// Loop through 5 possible inputs
for (var i = 1; i <= 5; i++) {
var pVal = document.getElementById('prob' + i).value;
var rVal = document.getElementById('ret' + i).value;
if (pVal !== "" && rVal !== "") {
var p = parseFloat(pVal);
var r = parseFloat(rVal);
if (isNaN(p) || isNaN(r)) {
errorDiv.innerHTML = "Please ensure all filled fields contain valid numbers.";
errorDiv.style.display = 'block';
return;
}
if (p 0.1) {
errorDiv.innerHTML = "Total probability must equal 100%. Current sum: " + totalProb.toFixed(2) + "%";
errorDiv.style.display = 'block';
// We do not return here if we want to allow users to see calc even if not 100%,
// but for a strict math calculator, stopping is better.
// However, to be helpful, let's stop.
return;
}
// 1. Calculate Expected Return E(R)
// E(R) = Sum(P * R)
var expectedReturn = 0;
for (var j = 0; j 0.20)
var pDecimal = probs[j] / 100;
expectedReturn += (pDecimal * rets[j]);
}
// 2. Calculate Variance
// Var = Sum(P * (R – E(R))^2)
var variance = 0;
for (var k = 0; k < probs.length; k++) {
var pDecimal = probs[k] / 100;
var diff = rets[k] – expectedReturn;
variance += (pDecimal * Math.pow(diff, 2));
}
// 3. Calculate Standard Deviation
// SD = Sqrt(Variance)
var stdDev = Math.sqrt(variance);
// 4. Coefficient of Variation
// CV = SD / E(R)
var cv = 0;
if (expectedReturn !== 0) {
cv = stdDev / expectedReturn;
} else {
cv = 0; // Avoid divide by zero
}
// Display Results
document.getElementById('prob-sum').innerHTML = totalProb.toFixed(1) + "%";
document.getElementById('expected-return').innerHTML = expectedReturn.toFixed(2) + "%";
document.getElementById('variance').innerHTML = variance.toFixed(4); // Variance is usually unit squared
document.getElementById('std-dev').innerHTML = stdDev.toFixed(2) + "%";
document.getElementById('coef-var').innerHTML = cv.toFixed(4);
resultsDiv.style.display = 'block';
}
Understanding the Expected Rate of Return and Risk
In financial modeling and portfolio management, understanding the relationship between potential rewards and associated risks is paramount. The Expected Rate of Return represents the weighted average of potential returns based on the probability of various market scenarios occurring. It is not a guaranteed return, but rather a statistical mean that helps investors forecast performance over time.
How to Calculate Expected Return
To calculate the expected rate of return ($E[R]$), you must identify different economic scenarios (also known as "states of nature"), estimate the probability of each scenario occurring, and determine the return of the investment in that specific scenario. The formula is:
E[R] = (P₁ × R₁) + (P₂ × R₂) + … + (Pₙ × Rₙ)
Where P is the probability of a scenario (expressed as a decimal) and R is the return in that scenario.
Measuring Risk: Variance and Standard Deviation
While the expected return tells you the average outcome, it does not tell you how volatile the investment is. This is where Standard Deviation ($\sigma$) comes in. It measures the dispersion of the returns around the expected mean.
A higher standard deviation indicates that the returns are spread out over a wider range, implying higher volatility and risk. A lower standard deviation suggests that returns are clustered closely around the expected value, indicating stability.
Step 1: Calculate the Variance ($\sigma^2$) by summing the product of each scenario's probability and the squared difference between that scenario's return and the expected return.
Step 2: Take the square root of the Variance to find the Standard Deviation.
The Coefficient of Variation (CV)
The calculator also provides the Coefficient of Variation. This metric allows you to compare the risk-to-reward ratio of different investments. It is calculated by dividing the Standard Deviation by the Expected Return ($CV = \sigma / E[R]$). A lower CV is generally preferred, as it indicates less risk for every unit of return.