To calculate the portfolio's expected return and risk, we need to use the information provided:

Given Data

1. Expected Returns of assets:

   • ABC: 20% (0.20)
   • DEF: 15% (0.15)

2. Weights in the portfolio:

   • ABC: 60% (0.60)
   • DEF: 40% (0.40)

3. Covariance Matrix:

   • Variance of ABC = 0.0400
   • Variance of DEF = 0.1600
   • Covariance of ABC and DEF = 0.0240

Part A: Expected Portfolio Return

The expected return of a portfolio, $E(R_p)$, is the weighted sum of the expected returns of each asset:

$E(R_p) = w_{ABC} \times E(R_{ABC}) + w_{DEF} \times E(R_{DEF})$

Substituting in the values:

$E(R_p) = (0.60 \times 0.20) + (0.40 \times 0.15)$ $E(R_p) = 0.12 + 0.06 = 0.18 \text{ or } 18\%$

So, the expected return of the portfolio is 18%.

Part B: Portfolio Risk (Standard Deviation)

To calculate the portfolio's risk (standard deviation), we use the formula for the variance of a two-asset portfolio. The portfolio variance, $\sigma_p^2$, is calculated as follows:

$\sigma_p^2 = (w_{ABC}^2 \times \sigma_{ABC}^2) + (w_{DEF}^2 \times \sigma_{DEF}^2) + 2 \times w_{ABC} \times w_{DEF} \times \text{Cov}(ABC, DEF)$

Where:

• $\sigma_{ABC}^2 = 0.0400$ (variance of ABC)
• $\sigma_{DEF}^2 = 0.1600$ (variance of DEF)
• Covariance $\text{Cov}(ABC, DEF) = 0.0240$

1. Calculate each component:

   • $w_{ABC}^2 \times \sigma_{ABC}^2 = (0.60)^2 \times 0.0400 = 0.0144$
   • $w_{DEF}^2 \times \sigma_{DEF}^2 = (0.40)^2 \times 0.1600 = 0.0256$
   • $2 \times w_{ABC} \times w_{DEF} \times \text{Cov}(ABC, DEF) = 2 \times 0.60 \times 0.40 \times 0.0240 = 0.01152$

2. Add these values to find the portfolio variance:

   $\sigma_p^2 = 0.0144 + 0.0256 + 0.01152 = 0.05152$

3. Calculate the portfolio standard deviation (risk) by taking the square root of the variance:

   $\sigma_p = \sqrt{0.05152} \approx 0.2270 \text{ or } 22.70\%$

Summary

• Portfolio Expected Return: 18%
• Portfolio Risk (Standard Deviation): 22.70%

Would you like further details or clarification on any of these steps?

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Here are five related questions for deeper understanding:

1. How would the portfolio's risk change if the weight of ABC increased?
2. What impact does covariance have on portfolio risk?
3. How would we adjust the portfolio if we aimed to reduce its overall risk?
4. What is the Sharpe Ratio, and how is it used to assess portfolio performance?
5. How can diversification be improved by adding more assets?

Tip: Portfolio risk can be minimized by adding assets with low or negative correlations to the portfolio, as they help offset each other's volatility.