Which of the following statements is FALSE?

Question

BlackTom AI · Accepted Answer

First, let's restate what each option is saying and set the context about portfolio weights and returns.
Option 1: 'Without trading, the portfolio weights will decrease for the stocks in the portfolio whose returns are above the overall portfolio return.' This claim is misleading because when a stock outperforms the portfolio, its value tends to rise relative to the others, causing its weight (the fraction of total investment allocated to it) to increase, not decrease, assuming no trading occurs. In other words, high-performing components typically gain share of the total value as markets move, so the weight would rise rather than fall. The statement asserts the opposite, making it incorrect.
Option 2: 'The expected return of a portfolio is simply the weighted average of the expected returns of the investments within the portfolio.' This is a standard and correct property from portfolio theory: the portfolio's expected return is the sum of each asset's expected return multiplied by its portfolio weight.
Option 3: 'Portfolio weights add up to 1 so that they represent the way we have divided our money between the different individual investments in the portfolio.' This is true by definition; weights are fractions of the total investment, and their sum equals 1.
Option 4: 'A portfolio weight is the fraction of the total investment in the portfolio held in an individual investment in the portfolio.' This is also true, describing exactly how weights are interpreted in a portfolio context.
To identify the false statement, compare each option against fundamental concepts: weights drift due to price changes, but the intuitive direction described in Option 1 contradicts how weights respond to relative performance when no rebalancing occurs. The rest align with standard definitions and properties of portfolio weights and expected returns.

BU.232.725.81.SP25 M2 Comprehension Check

Which of the following statements is FALSE?

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