Answer: greater than the annualized standard deviation of Investment 2.

## Explanation Investment 1 involves holding a single randomly chosen asset from the index, which is replaced monthly with another random asset. This strategy has **no diversification** - it's essentially holding a single stock portfolio each month. Investment 2 equally weights all 100 assets in the index, providing **full diversification** across the entire index. ### Key Concepts: 1. **Diversification Effect**: A well-diversified portfolio (Investment 2) will have lower volatility than individual assets because unsystematic risk (idiosyncratic risk) is diversified away. 2. **Single Asset Volatility**: Individual assets typically have higher volatility than a diversified portfolio because they bear both systematic (market) risk and unsystematic (firm-specific) risk. 3. **Random Selection**: Even though Investment 1 changes assets monthly, each month it holds a single asset with high idiosyncratic risk. ### Mathematical Reasoning: - For Investment 1: Standard deviation ≈ σ_individual (high) - For Investment 2: Standard deviation ≈ σ_market (lower due to diversification) Since Investment 1 lacks diversification while Investment 2 is fully diversified, Investment 1 will have **greater annualized standard deviation** (higher volatility) than Investment 2. **Correct Answer: C** - greater than the annualized standard deviation of Investment 2.

Author: LeetQuiz .