Final answer:
The statement that a portfolio converges to a minimum variance portfolio as the number of stocks decreases is false. A portfolio generally reduces its risk and approaches minimum variance through diversification, which is achieved by increasing, not decreasing, the number of stocks.
Step-by-step explanation:
True or False: As the number of stocks in a portfolio decreases, the portfolio converges to a minimum variance portfolio. The statement is False. When constructing a portfolio, the goal is often to minimize risk while maximizing return. Diversification is a key strategy in achieving this goal. It involves spreading investments across a variety of assets to reduce exposure to any single asset or risk. As the number of stocks in a portfolio increases, the portfolio becomes more diversified, not less. The concept of a minimum variance portfolio comes from Modern Portfolio Theory (MPT), which posits that for a given level of expected return, there is a portfolio with the lowest variance (or risk). The central limit theorem mentioned is more relevant to statistics and probability, regarding the distribution of sample means and its approach to a normal distribution as the sample size increases. It isn't directly applicable to the construction of stock portfolios and their variances. As you decrease the number of stocks in a portfolio, you actually move away from the principle of diversification and increase the risk, as the portfolio is more exposed to the volatility of individual stocks. Therefore, reducing the number of stocks in a portfolio does not necessarily converge it to a minimum variance portfolio. The minimum variance portfolio is typically found by optimizing the mix of investments to achieve the lowest possible risk for a given rate of return.