The Efficient Frontier: A Note on the Curious Difference between Variance and Standard Deviation

The Markowitz frontier of optimal portfolios is valid in both mean–variance space and in mean–standard deviation space. There are, however, some curious differences because lines in one space become curves in the other. This article explores and explains the curiosity. Key Findings ▪ The capital allocation line is a curve in mean–variance space. ▪ There is a line in mean–variance space that connects the riskless rate with the tangency portfolio, but it is not a capital allocation line. ▪ Volatility can be either standard deviation or variance, but their efficient frontier geometry is curiously different.