Rethinking the Efficient Frontier - Part 1
Why the textbook plot may obscure the intuition
The efficient frontier is probably the most reproduced chart in portfolio theory. Since Markowitz (1952), it has been drawn the same way by most (if not all):
โธ volatility on the x-axis,
โธ return on the y-axis.
But this convention comes with baggage.
๐๐ก๐ ๐๐ฌ๐ฌ๐ฎ๐ฆ๐ฉ๐ญ๐ข๐จ๐ง๐ฌ ๐จ๐๐ญ๐๐ง ๐จ๐ฏ๐๐ซ๐ฅ๐จ๐จ๐ค๐๐
The textbook frontier quietly relies on constraints that donโt necessarily reflect how institutional investors actually operate:
โธ Long-only - no shorting allowed
โธ Fully invested - no cash, no leverage
โธ Two assets only - just stocks and bonds
In practice, institutional portfolios can go:
โธlong and short
โธhold cash or take leverage
โธallocate well beyond two asset classes
The frontier we study is really a one-dimensional slice of a much richer surface.
๐ ๐ฌ๐ข๐ฆ๐ฉ๐ฅ๐ ๐๐ฑ๐ข๐ฌ ๐ฌ๐ฐ๐๐ฉ
In this set of slides, I keep those assumptions in place (for now) - but I make one small change: I swap the axes.
Return on the x-axis, volatility on the y-axis.
The math doesnโt change. But the curve now reads as: โHow much volatility must I pay for each extra unit of return?โ
That framing - diminishing returns to risk-taking - is arguably closer to how practitioners actually think about the trade-off.
๐๐ก๐๐ญโ๐ฌ ๐ข๐ง๐ฌ๐ข๐๐
โธ The often-taken-for-granted assumptions behind the textbook plot
โธ A decomposition of return, volatility, and Sharpe ratio by portfolio weight
โธ The standard frontier vs. the swapped version, side by side
โธ Why the swapped orientation may be more intuitive
๐๐๐ค๐ง๐จ๐ฐ๐ฅ๐๐๐ ๐๐ฆ๐๐ง๐ญ๐ฌ
The ideas in this presentation were stimulated by enlightening conversations with Thomas Dionysopoulos, CFA dating back to 2014, first as my employer at Advenis Finance in Paris (under visionary boutique Eonos Investment Technologies), then as my client at Brevan Howard Asset Management in London.
This is the first instalment - next, we remove the constraints one by one.
Feedback welcome.
