The portfolio's beta is the weighted average of the individual stock betas, based on the proportion of the total investment in each stock. Here's how to calculate it:

1. Total investment in the portfolio: $\text{Total investment} = 50,000 + 75,000 = 125,000$

2. Proportion of the investment in each stock:

   • For the stock with a beta of 0.5: $\text{Proportion} = \frac{50,000}{125,000} = 0.4$
   • For the stock with a beta of 1.6: $\text{Proportion} = \frac{75,000}{125,000} = 0.6$

3. Calculate the portfolio beta by multiplying each stock's beta by its respective proportion and summing the results: $\text{Portfolio beta} = (0.4 \times 0.5) + (0.6 \times 1.6)$

Let's calculate this step-by-step.

$0.4 \times 0.5 = 0.2$ $0.6 \times 1.6 = 0.96$

4. Sum the contributions: $\text{Portfolio beta} = 0.2 + 0.96 = 1.16$

Thus, the portfolio's beta is 1.16.

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Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

1. How does the portfolio beta affect expected returns compared to the market?
2. What is the significance of a beta less than 1, equal to 1, or greater than 1?
3. How would adding a risk-free asset to the portfolio affect its beta?
4. What is the relationship between portfolio beta and market risk?
5. How does diversification impact portfolio beta?

Tip: A portfolio beta of 1 means the portfolio is expected to move with the market. A beta greater than 1 implies more volatility than the market, while a beta less than 1 implies less volatility.