Which of the following statements about the ‘Portfolio Theory’ section of the lecture material are TRUE: The standard deviation of a portfolio of shares in two different companies will always be less than the weighted average of the standard deviations of the individual shares. A share portfolio that follows a diversified market index is expected to offer a reasonably efficient trade-off between expected return and risk.

Question

BlackTom AI · Accepted Answer

Let's break down each statement and evaluate it against portfolio theory concepts.

Option 1: 'The standard deviation of a portfolio of shares in two different companies will always be less than the weighted average of the standard deviations of the individual shares.'
- This claim asserts a universal inequality that the portfolio’s risk (standard deviation) is always smaller than the simple weighted average of the individual risks. In reality, diversification can reduce risk, but it does not guarantee a strict inequality in every case. If the two assets are highly positively correlated, the portfolio SD can approach the weighted average, and in some configurations it may equal it (e.g., perfectly correlated assets with certain weights). Therefore, the statement 'will always be less' is false because there are scenarios where the portfolio SD is not strictly less than the weighted average.

Option 2: 'A share portfolio that follows a diversified market index is expected to offer a reasonably efficient trade-off between expected return and risk.'
- A diversified market index is designed to capture broad market risk and return characteristics. By spreading investments across many assets, idiosyncratic (company-specific) risks tend to cancel out, leaving exposure primarily to systematic market risk. In mean-variance terms, a well-diversified index sits near the efficient frontier, offering a favorable balance between return and risk relative to concentrated portfolios. This statement is consistent with standard portfolio theory and the idea of market efficiency.

Option 3: 'Neither of the statements are true (both are false)'
- If we accept that the first statement is false and the second is true, this option is incorrect because at least one statement (the second) is true.

Option 4: 'Only statement 1 is true'
- This would require the first statement to be true and the second false, which contradicts our assessment that the first is not always true and the second is true.

Option 5: 'Both statements are true (neither are false)'
- Since we established that the first statement is not universally true, this option is incorrect.

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