CAL and borrowing at risk-free rate

hi guys, just revising portfolio management.

Schweser says that if an investor can’t borrow at risk free rate, the CAL ends at the point of tangency and the investor should then switch to the portfolios on the curved bit of the efficient frontier.

I am sure I can remember from level 1, graphs of what happens if an investor can’t borrow at the risk free rate, and they just showed the slope of the upper part getting flatter after the tangency point. (because the investor was paying more to borrow, eating away at the returns). They definitely didn’t show the upper part becoming curved and they didn’t imply that the investor should hold a different optimum portfolio. (Which seems to be the implication from the advice to switch to the curved part of the efficient frontier.)

Does anyone have any thoughts on this?


If you cannot borrow at Rf, then you cannot increase your return beoynd what the EF dictates. The extension of the CAL line beyond the optimal portfolio will not be there, so you can only increase return by taking on additional risk.

Yes, I recall this as well. If borrowing costs more than the risk-free rate, then the CAL will be “kinked” and become flatter after the point of tangency. I don’t remember where I read this - it might have been at uni.

If the investor cannot borrow at all, then the CAL will follow the curve of the EF to the right of the point of tangency - but the investor is essentially investing 100% in riskier portfolios, as Dreary said.

Does anyone else have feedback?

The kinked CAL you recall from level I was for different rates for borrowing and lending. In this scenario (Level II) there is no borrowing at all, so the CAL takes the shape of the efficient frontier beyond the market portfolio.