Question

The table below gives statistics relating to a hypothetical 10-year record of two portfolios.

	Mean Annual Return (%)	Standard Deviation of Return (%)	Skewness
Portfolio A	10.25	23.4	-3.4
Portfolio B	10.25	19.5	4.5

Based only on the information in the above table, perform the following:

1. Contrast the distributions of returns of Portfolios A and B.
2. Evaluate the relative attractiveness of Portfolios A and B.

Answer 1

A) Portfolios A and B have the same Mean Return, though the higher standard deviation of returns of A suggests it is riskier than B. Hence, while A and B have the distribution centered at the same point (mean return of 10.25%), the returns are more scattered around the mean for portfolio A (23.4%) compared to that for portfolio B (19.5%).

Despite having the same mean returns, portfolio A has a negative skewness of -3.4, which means it has an asymmetric tail extending towards the left, means more negative outlier values on the lower side of returns. Portfolio B, on the other hand, while having the same return and lower risk (std deviation), also has a positive skew of 4.5, which means more probability of positive outlier returns.

B) Both portfolios A and B have the same level of mean annual return (10.25%). However, portfolio B is less riskier compared to A, given B's lower standard deviation of returns. Additionally, the high positive skew of portfolio B compared to high negative skew of portfolio A suggests that positive higher return scenarios are more probable for portfolio B, while negative lower return (or loss) scenarios are more probable for portfolio A.

Naturally, portfolio B is more attractive for investors.