Volatility of a portfolio can be achieved that would be lower than the volatility of each of the portfolio’s constituentsKlausimas 1AtsakymasFalseTrue

Analyzing the Question

1. Break Down the Problem
   The question is asking whether the volatility of a portfolio can be lower than the volatility of each individual asset within that portfolio. The relationship between the assets' volatilities and the overall volatility of the portfolio is the key concept to examine.

2. Relevant Concepts

   • Volatility: A measure of the variation in the price of a financial instrument over time, typically represented as standard deviation.
   • Portfolio Theory: According to Modern Portfolio Theory, combining assets that are not perfectly correlated can reduce overall portfolio risk (volatility).

3. Analysis and Detail
   When constructing a portfolio consisting of multiple assets, the overall volatility of that portfolio can indeed be lower than the individual volatilities of the constituent assets, provided that these assets have low or negative correlations with each other. This occurs because the effects of the fluctuations of the individual assets can offset each other, leading to a lower overall risk for the portfolio.

4. Verify and Summarize
   Portfolio volatility is calculated as:

   $\sigma_P = \sqrt{\sum_{i=1}^{n} w_i^2 \sigma_i^2 + \sum_{i=1}^{n}\sum_{j \neq i} w_i w_j \sigma_i \sigma_j \rho_{i,j}}$

   where $w_i$ is the weight of the asset, $\sigma_i$ is the volatility of the asset, and $\rho_{i,j}$ is the correlation between the assets. If combinations of assets have low or negative correlations, the resulting portfolio volatility $\sigma_P$ can indeed be lower than the individual $\sigma_i$.

Final Answer

True. The volatility of a portfolio can be lower than the volatility of each of its constituents due to the benefits of diversification.