When we form an equally weighted portfolio of stocks and keep increasing the number of stocks in the portfolio

When we form an equally weighted portfolio of stocks and keep increasing the number of stocks in the portfolio, the volatility of the portfolio also increases.

options: True False

The correct answer and explanation is:

Answer: False

Explanation:

When you form an equally weighted portfolio of stocks and keep increasing the number of stocks in the portfolio, the volatility of the portfolio generally decreases, not increases.

Here’s why:

1. Diversification Effect:
   Volatility (or risk) of an individual stock comes from two parts:
   • Systematic risk: Market-wide risk that affects all stocks (like economic recessions, interest rate changes).
   • Unsystematic risk: Company-specific risk (like management changes, product failures).
   When you combine multiple stocks in a portfolio, the unsystematic risks tend to cancel out because they are generally uncorrelated. If one stock has a bad event, it may be offset by another stock doing well.
2. Reduction of Unsystematic Risk:
   As you increase the number of stocks, the unsystematic risk diminishes because it diversifies away. This means the portfolio becomes less volatile due to company-specific shocks.
3. Volatility of the Portfolio:
   The overall volatility of the portfolio depends on:
   • The individual volatilities of stocks
   • The correlations among the stocks
   • The number of stocks
   The formula for portfolio variance shows that as the number of stocks increases, and assuming the correlations are not perfectly 1, the portfolio variance decreases.
4. Limiting Volatility:
   While volatility decreases with diversification, it does not reduce to zero because systematic risk remains. Systematic risk is the market risk that affects all stocks and cannot be diversified away.
5. Why Volatility Does Not Increase:
   Adding more stocks spreads the investment over more assets, smoothing out the idiosyncratic swings. Hence, portfolio volatility tends to decrease or stabilize, not increase.

Summary:

• Increasing the number of stocks in an equally weighted portfolio reduces unsystematic risk, lowering total portfolio volatility.
• Systematic risk remains and sets a lower bound on portfolio volatility.
• Therefore, the statement “the volatility of the portfolio increases as the number of stocks increases” is False.