To calculate the expected return on the portfolio, we use the formula:

$E(R_p) = w_1 \cdot E(R_1) + w_2 \cdot E(R_2)$

Where:

• $w_1$ and $w_2$ are the portfolio weights for Roll and Ross, respectively.
• $E(R_1)$ and $E(R_2)$ are the expected returns for Roll and Ross.

Step 1: Calculate the Expected Return for Each Security

The expected return for a security is calculated as:

$E(R) = \sum \text{Probability of State} \cdot \text{Return in State}$

Roll:

$E(R_{\text{Roll}}) = (0.40 \cdot -0.10) + (0.60 \cdot 0.28) = -0.04 + 0.168 = 0.128 \, \text{or} \, 12.8\%.$

Ross:

$E(R_{\text{Ross}}) = (0.40 \cdot 0.21) + (0.60 \cdot 0.18) = 0.084 + 0.108 = 0.192 \, \text{or} \, 19.2\%.$

Step 2: Calculate the Portfolio Expected Return

Given weights $w_{\text{Roll}} = 0.55$ and $w_{\text{Ross}} = 0.45$:

$E(R_p) = (0.55 \cdot 0.128) + (0.45 \cdot 0.192)$

$E(R_p) = 0.0704 + 0.0864 = 0.1568 \, \text{or} \, 15.68\%.$

Final Answer:

The expected return on the portfolio is 15.68%.

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Would you like a detailed breakdown of any part of this process?

Related Questions:

1. How do changes in state probabilities affect the expected return?
2. What is the portfolio variance and standard deviation for this setup?
3. How would different weights affect the portfolio's expected return?
4. How are these calculations related to risk assessment in portfolio management?
5. Can we derive the portfolio’s beta using this data?

Tip:

When diversifying portfolios, always check both expected returns and risk metrics to make informed investment decisions.