To calculate the standard deviation of a two-asset portfolio, we use the following formula:

$\sigma_p = \sqrt{w_X^2 \sigma_X^2 + w_Y^2 \sigma_Y^2 + 2 w_X w_Y \rho \sigma_X \sigma_Y}$

Where:

• $\sigma_p$ = Portfolio standard deviation (what we are solving for)
• $w_X = 0.60$ (Weight of Stock X)
• $w_Y = 0.40$ (Weight of Stock Y)
• $\sigma_X = 30\% = 0.30$ (Standard deviation of Stock X)
• $\sigma_Y = 20\% = 0.20$ (Standard deviation of Stock Y)
• $\rho = 0.69$ (Correlation coefficient between the two stocks)

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Step-by-Step Calculation:

1. Calculate the terms:

   • $w_X^2 \sigma_X^2 = (0.60)^2 \times (0.30)^2 = 0.36 \times 0.09 = 0.0324$

   • $w_Y^2 \sigma_Y^2 = (0.40)^2 \times (0.20)^2 = 0.16 \times 0.04 = 0.0064$

   • $2 w_X w_Y \rho \sigma_X \sigma_Y = 2 \times 0.60 \times 0.40 \times 0.69 \times 0.30 \times 0.20$

     $= 2 \times 0.60 \times 0.40 \times 0.69 \times 0.06$ $= 0.3312 \times 0.06 = 0.019872$

2. Sum all terms inside the square root: $0.0324 + 0.0064 + 0.019872 = 0.058672$

3. Take the square root: $\sqrt{0.058672} = 0.2423$

4. Convert to a percentage: $0.2423 \times 100 = 24.23\%$

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Final Answer:

The standard deviation of the portfolio is 24.23%.

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Would you like further details or have any other questions?

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Here are some related questions to explore:

1. How does correlation affect portfolio risk?
2. What happens to portfolio risk if the weights change to 50-50?
3. How is portfolio variance different from portfolio standard deviation?
4. How would the portfolio standard deviation change if the correlation were -1?
5. What are the benefits of diversification based on this example?

Tip: Lower correlation between assets reduces overall portfolio risk, even if individual assets are volatile.