Why is the CAL line bent?

See page 385 of CFAI Derivatives and Portfolio Management.

I didn’t know this was in the curriculum, but purely from UG recollection- I believe it has to do with differing borrowing and lending rates.

The (actually, _ a _) CAL line isn’t bent; nor is the CML.

However, as monkeyCFA points out, if you cannot borrow at the risk-free rate, then your CALs (or CML) will be bent.

I’m confused If there is no risk free rate is the efficient frontier the CAL? I thought CAL only exists if there is a risk free rate.

I’m also confused because on that page in the book, it looks pretty bent.

A CAL is created using a combination of risky and risk-free assets. The efficient frontier only allows for combinations of risky assets.

The point where the CAL is tangent to the efficient frontier is the point on the CAL where your portfolio is fully invested in risky assets (remember: portfolios on the efficient frontier consist of only risky assets). To be able to invest in portfolios on the CAL, beyond the tangency point, you should be able to borrow at the risk-free rate. This way you can invest > 100% weight in the risky asset portfolio. When borrowing at the risk-free rate is not possible, you can not invest in any portfolios on the CAL which are higher than the tangency portfolio. In that case, your investment possibilities switch from being on the CAL to being on the efficient frontier. Hence why the straight line becomes curved beyond the tangency point.

You seem to be confusing a CAL with the CML.

A capital allocation line (CAL) runs from the risk-free asset through a given risky portfolio; every risky portfolio has its own CAL.

The capital market line (CML) is the CAL with the highest Sharpe ratio; it is tangent to the efficient frontier, and the point of tangency is called the market portfolio.

Keep these two straight on Saturday!

I do have a tendency mixing those up. In fact, I have a tendency to mix a lot up. angry

But I won’t forget this anymore, thanks for putting it straight!