2 Corner-Portfolios vs CAL


Is my understand of this topic correct ?

  1. If Investor faces restriction on borrowing or lending at Risk-free rate, then his optimal portfolio is determined by the classic 2 Corner Portfolio procedure
  2. If, however, he can borrow or lend at Risk-free rate, then his optimal portfolio is the tangency portfolio which is the highest-Sharpe-ratio portfolio ; the investor’s optimal portfolio is on the CAL, which is further split into 2 cases :
  • If Investor’s Return Objective > Return of tangency portfolio, the investor then borrows at Risk-free rate to leverage the tangency portfolio
  • If Investor’s Return Objective < Return of the tangency portfolio , the investor combines the Risk-free rate (lends) and the Tangency Portfolio

Is this correct ? I think it pretty much is.

Last question : are there cases when lending / borrowing at the Risk-Free rate is allowed, but it is still optimal to not use the tangency portfolio ?

You are correct.

It is always optimal to use the tangency portfolio unless there is some investor constraint that prevents it (i.e. no leverage or is restricted against an asset class that is in the tangency potfolio etc)


the annoying bit it when they ask you for the weights of the borrowed Rf and the investment into the corner portfoio.

Haven’t ran into that in mocks / previous exams yet. How do you establish the negative weight of Rf in this case ?

Calculating the weights is a simple equation, check the books.

Before you default to thinking about checking the corner ports first - realize that if cal suits your needs you invest here, and reduce weighting by rfr to get your target return. With or without constraints this is kosher