Stock A has a beta of 0.77 and volatility of 0.67. Stock B has a beta of 1.43 and volatility of 0.60. You form a portfolio with $20,000 in Stock A and $12,000 in Stock B. What is your portfolio's expected return if the market risk premium is 7.2% and the T-Bill yield is 3.5%? Enter your answer as a decimal showing four decimal places. For example, if your answer is 8.25%, enter .0825.

To calculate the portfolio's expected return, we need to first determine the expected return for each stock using the **Capital Asset Pricing Model (CAPM)**, and then calculate the weighted average of these returns based on the investment amounts in each stock.

### Step 1: Apply the CAPM formula for each stock
The CAPM formula is:

\[
R_{\text{expected}} = R_f + \beta \times (R_m - R_f)
\]

Where:
- $ R_{\text{expected}} $ is the expected return of the stock.
- $ R_f $ is the risk-free rate (T-Bill yield = 3.5% or 0.035).
- $ \beta $ is the stock's beta.
- $ R_m - R_f $ is the market risk premium (7.2% or 0.072).

### For Stock A:
- $ \beta_A = 0.77 $
- $ R_f = 0.035 $
- $ R_m - R_f = 0.072 $

\[
R_{\text{A, expected}} = 0.035 + 0.77 \times 0.072 = 0.035 + 0.05544 = 0.09044
\]

So, the expected return for Stock A is 0.09044 or 9.044%.

### For Stock B:
- $ \beta_B = 1.43 $
- $ R_f = 0.035 $
- $ R_m - R_f = 0.072 $

\[
R_{\text{B, expected}} = 0.035 + 1.43 \times 0.072 = 0.035 + 0.10296 = 0.13796
\]

So, the expected return for Stock B is 0.13796 or 13.796%.

### Step 2: Calculate the portfolio's expected return

Now we calculate the portfolio's expected return by weighting the expected returns of each stock based on their investment amounts.

Total portfolio value = $20,000 (Stock A) + $12,000 (Stock B) = $32,000

Weight of Stock A in the portfolio:

\[
w_A = \frac{20,000}{32,000} = 0.625
\]

Weight of Stock B in the portfolio:

\[
w_B = \frac{12,000}{32,000} = 0.375
\]

Portfolio's expected return:

\[
R_{\text{portfolio}} = w_A \times R_{\text{A, expected}} + w_B \times R_{\text{B, expected}}
\]

\[
R_{\text{portfolio}} = 0.625 \times 0.09044 + 0.375 \times 0.13796
\]

\[
R_{\text{portfolio}} = 0.056525 + 0.051735 = 0.10826
\]

### Final Answer:
The portfolio's expected return is **0.1083** (rounded to four decimal places).

Would you like further details on the calculations, or have any other questions?

### Related Questions:
1. How would the portfolio's expected return change if you adjusted the investment in Stock A to $15,000?
2. What would happen to the portfolio's risk if Stock A had a higher volatility than Stock B?
3. How do you calculate the beta of a portfolio consisting of multiple stocks?
4. How would the expected return change if the market risk premium were 10% instead of 7.2%?
5. What is the relationship between beta and portfolio risk?

**Tip:** The expected return of a portfolio depends not just on the returns of individual assets, but also on their respective weights in the portfolio. Consider this when balancing risk and return in investment decisions.

Stock A has a beta of 0.77 and volatility of 0.67. Stock B has a beta of 1.43 and volatility of 0.60. You form a portfolio with $20,000 in Stock A and $12,000 in Stock B. What is your portfolio's expected return if the market risk premium is 7.2% and the T-Bill yield is 3.5%? Enter your answer as a decimal showing four decimal places.

Discover how to calculate the expected return of a portfolio consisting of Stock A and Stock B using the Capital Asset Pricing Model (CAPM). This problem details the expected returns of stocks with betas of 0.77 and 1.43, investment amounts of $20,000 and $12,000, a market risk premium of 7.2%, and a T-Bill yield of 3.5%.

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