Question

Explain the following statement: “As asset held as part of a portfolio is generally less risky than the same asset held in isolation.”

Answer 1

The riskiness of a portfolio is measured by the portfolio variance or standard deviation of the portfolio. The formula to calculate the variance of a portfolio consisting of two assets A and B is given by below formula:

σ_p² = w₁* σ_p² + w₂* σ₂² + 2*w₁*w₂*ρ*σ₁* σ₂

where ρ is the correlation between the return of the assets A and B. From the above equation we can see that the variance of the portfolio is reduced if the Correlation between the returns of assets A and B is negative or we can say that the pair of stocks of negatively correlated. Hence if the portfolio is well diversified, the variance of the portfolio will be less than the variance of one asset in isolation. Diversification helps in reducing the diversifiable risk or the unsystematic risk, while market risk will be present even in a well-diversified portfolio. Hence, increasing the number of stocks reduces the overall variance (by reducing the diversifiable risk) of the portfolio. Hence, we can say that “As asset held as part of a portfolio is generally less risky than the same asset held in isolation”.