Variance-Covariance Analysis
The variance-covariance matrix is a crucial tool for assessing portfolio diversification, as high indicators of asset dependence suggest that the risks of being left with nothing in the event of a significant market decline are substantial. In this regard, such an analysis can reveal efficiency if the covariance values between stocks are relatively low. For instance, if we evaluate the historical movements of monthly returns for CVS, Apple, and Walmart, their correlation is extremely low, which makes the portfolio diversified and less risky. Calculations for the last year were made using Excel and are presented in Table 1.
Table 1 – Variance-Covariance Portfolio Matrix
Alternative Analysis Methods
Among the alternative methods are the single-index model, constant correlation model, shrinkage method, option method, and implied volatility-based methods. The last two are relevant when an options instrument is used, or data about them is available (Liang et al., 2020). The simplest is the single-index model, which typically compares performance with the S&P or, for example, the FTSE indices (Kelly et al., 2023).
The constant correlation model is not applicable because the portfolio includes shares from various business industries. Finally, shrinkage methods are used in cases of limited data, which require a particular structuring. In this case, the simplest index benchmark is the best way to assess the portfolio’s volatility relative to the market.
Combined Approach
To reduce risks and assess diversification, the following approach is feasible. First, beta can be calculated for each portfolio asset in this way, providing a measure of volatility relative to the required index. Secondly, it is possible to include this indicator in the matrix as index returns and compare it with the covariance ratios of each stock. This method will be the most suitable, as it will provide the investor with additional information to inform their risk management in the portfolio.
References
Kelly, B., Palhares, D., & Pruitt, S. (2023). Modeling corporate bond returns. The Journal of Finance, 78(4), 1967-2008.
Liang, C., Wei, Y., & Zhang, Y. (2020). Is implied volatility more informative for forecasting realized volatility: An international perspective. Journal of Forecasting, 39(8), 1253-1276.