11.5 The actual portfolio risk of a 2-asset portfolio using the analytical and mathematical model and its interpretation
To calculate the actual portfolio risk of a 2-asset portfolio, you need to consider the weights of each asset in the portfolio, the standard deviations of their returns, and the correlation coefficient between the two assets.
The formula to calculate the portfolio risk is:
Portfolio Risk = sqrt[(w1^2 * σ1^2) + (w2^2 * σ2^2) + (2 * w1 * w2 * σ1 * σ2 * ρ)]
Where:
- w1 and w2 are the weights of Asset 1 and Asset 2 in the portfolio, respectively.
- σ1 and σ2 are the standard deviations of the returns of Asset 1 and Asset 2, respectively.
- ρ is the correlation coefficient between the returns of Asset 1 and Asset 2.
Interpretation: The actual portfolio risk measures the volatility or variability of the returns of the portfolio as a whole. It takes into account not only the risk of each individual asset but also the correlation between their returns.
A higher portfolio risk implies a greater degree of variability in the portfolio’s returns, indicating a higher level of risk. On the other hand, a lower portfolio risk suggests a more stable and less volatile investment.
By combining assets with different risk characteristics and correlation coefficients, an investor can potentially reduce the overall portfolio risk through diversification. Diversification helps to mitigate the impact of any one asset’s performance on the overall portfolio, as assets that are negatively correlated or have lower correlation tend to balance out each other’s risk.