Suppose you operate in a market where there are only two risk-bearing assets, stock A and stock B, and a risk-free investment option. Stock A has an expected return of 23.64% and a standard deviation of 39.19% and stock B has an expected return of 15.98% and a standard deviation of 31.50%. The risk-free rate is 1.04% and shares A and B have a covariance of -407.38.
Whats the market portfolio return? 

To determine the **market portfolio return**, we need to first understand the **Capital Market Line (CML)** and how the assets relate to the market.

In a two-asset model with a risk-free asset, the **market portfolio** is a weighted combination of risky assets (stock A and stock B) that maximizes the Sharpe ratio, i.e., the ratio of expected excess return to the standard deviation of returns.

### Key data given:
- **Stock A:**
  - Expected return (\(E(R_A)\)) = 23.64% = 0.2364
  - Standard deviation (\(\sigma_A\)) = 39.19% = 0.3919
- **Stock B:**
  - Expected return (\(E(R_B)\)) = 15.98% = 0.1598
  - Standard deviation (\(\sigma_B\)) = 31.50% = 0.3150
- **Covariance (A, B):** Cov(A, B) = -407.38 = -0.040738 (in percentage terms)
- **Risk-free rate:** \(r_f = 1.04\%\) = 0.0104

### Step 1: Calculate the portfolio weights
To calculate the optimal weights (\(w_A\) for stock A and \(w_B\) for stock B), we need to use the formula for optimal weights in a portfolio that maximizes the Sharpe ratio:

\[
w_A = \frac{\sigma_B^2 - \text{Cov}(A, B)}{\sigma_A^2 + \sigma_B^2 - 2 \cdot \text{Cov}(A, B)}
\]
\[
w_B = 1 - w_A
\]

Let's compute the weights.

### Step 2: Calculate the expected return of the market portfolio
Once we have the weights \(w_A\) and \(w_B\), we can calculate the **market portfolio return** (\(E(R_m)\)) as:

\[
E(R_m) = w_A \cdot E(R_A) + w_B \cdot E(R_B)
\]

I will calculate these values now.The optimal portfolio weights are:
- \( w_A \) (weight of stock A) = 41.87%
- \( w_B \) (weight of stock B) = 58.13%

The expected return of the **market portfolio** is approximately **19.19%**.

Would you like to explore the process in more detail, or have any other questions?

Here are some related questions:
1. How do the weights change if the covariance between stocks A and B changes?
2. What is the standard deviation of the market portfolio in this case?
3. How does the risk-free rate affect the overall portfolio return?
4. How would the portfolio perform if we only invested in stock A or B?
5. What is the Sharpe ratio of this market portfolio?

**Tip:** Understanding how the covariance between two assets influences portfolio diversification is crucial for effective risk management.

Learn how to calculate the market portfolio return using stocks A and B with given expected returns and standard deviations, along with a risk-free rate. Explore the optimal portfolio weights and expected return calculations step-by-step.

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