# Calculate Portfolio Volatility with Two Stocks - Information and Explanation

## What is the formula to calculate the volatility of a portfolio with two stocks?

Given the expected return and volatility of two stocks, along with the correlation coefficient between them, how can we determine the portfolio's volatility?

## Explanation: Calculating Portfolio Volatility

The portfolio's volatility is approximately 0.47. The volatility of a portfolio can be calculated using the formula: Portfolio Volatility = √(w₁² * σ₁² + w₂² * σ₂² + 2 * w₁ * w₂ * ρ * σ₁ * σ₂)

When it comes to investing in multiple stocks, understanding the volatility of a portfolio is crucial for risk management and decision-making. The formula for calculating the volatility takes into account the weights, volatilities, and correlation coefficient of the individual stocks in the portfolio.

In this scenario, we have Stock A with an expected return of 0.102 and volatility of 0.3, and Stock B with an expected return of 0.149 and volatility of 0.8. The correlation between Stocks A and B is 0.4. We form a portfolio with $3,000 in Stock A and $3,000 in Stock B.

To calculate the weights of Stock A and Stock B in the portfolio, we divide the individual investment amounts by the total investment in the portfolio, which is $6,000 in this case. Both Stock A and Stock B have a weight of 0.5 in the portfolio.

Substitute the values into the formula: Portfolio Volatility = √(0.5² * 0.3² + 0.5² * 0.8² + 2 * 0.5 * 0.5 * 0.4 * 0.3 * 0.8)

After simplification, we find that the portfolio volatility is approximately 0.47. This calculation considers the volatilities of the individual stocks and their correlation coefficient, providing insight into the overall risk of the portfolio.

Understanding how to calculate the volatility of a portfolio with multiple stocks can help investors make informed decisions and manage their investment risk effectively.