A portfolio manager is examining the risk and return characteristics of two investment portfolios, P1 and P2. The following graph displays the expected annual return and the standard deviation (risk) for each portfolio. [Imagine a scatter plot where x-axis is Standard Deviation (Risk) and y-axis is Expected Return.] **Portfolio P1:** Expected Return = 10%, Standard Deviation = 5% **Portfolio P2:** Expected Return = 12%, Standard Deviation = 8% Consider the following two statements: Statement 1: Portfolio P1 offers a better risk-adjusted return than Portfolio P2. Statement 2: An investor who prioritizes absolute return over risk would prefer Portfolio P2. Which of the statements alone is sufficient to determine that an investor focused solely on maximizing return for a given level of risk would choose P1?
- AStatement 1 alone is sufficient, but Statement 2 alone is not sufficient.
- BNeither statement alone nor both statements together are sufficient.
- CBoth statements together are sufficient, but neither statement alone is sufficient.
- DStatement 2 alone is sufficient, but Statement 1 alone is not sufficient.
Show answer & explanationAnswer & explanation
Correct answer: A. Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.
The question asks to determine if an investor focused solely on maximizing return for a given level of risk would choose P1. This is the definition of better risk-adjusted return. Let's calculate the risk-adjusted return (Return/Risk ratio) for each portfolio: P1: 10% / 5% = 2.0 P2: 12% / 8% = 1.5 So, P1 indeed has a better risk-adjusted return (2.0 > 1.5). Statement 1: 'Portfolio P1 offers a better risk-adjusted return than Portfolio P2.' This statement directly answers the implicit question of which portfolio maximizes return for a given level of risk (which is what 'better risk-adjusted return' means). Therefore, Statement 1 alone is sufficient. Statement 2: 'An investor who prioritizes absolute return over risk would prefer Portfolio P2.' This statement tells us about the preference of an investor focused on absolute return, not an investor focused on maximizing return for a *given level of risk*. While P2 does have a higher absolute return (12% vs 10%), this doesn't tell us about its risk-adjusted performance. An investor maximizing return for a given level of risk might still prefer P1 due to its lower risk relative to its return. So, Statement 2 alone is not sufficient.
Why the other options are wrong
- B. Statement 1 alone is sufficient, making this option incorrect.
- C. Statement 1 alone is sufficient, making this option incorrect.
- D. Statement 2 is insufficient as it describes a different investor preference and doesn't address risk-adjusted return.
Risk-Adjusted Return (GMAT DS)
In Data Sufficiency, a statement about 'better risk-adjusted return' directly implies a higher ratio of return to risk. This metric is crucial for investors aiming to maximize returns while controlling for risk.
- Often represented by the Sharpe Ratio or similar metrics.
- Higher values indicate more return per unit of risk.
- A direct comparison of this metric is sufficient to answer questions about 'maximizing return for a given risk'.
Memory trick: Risk-adjusted return is key, for balanced prosperity.