From Reading 13 of the CFA curriculum, “The slope of the efficient frontier is greatest at the far left of the efficient frontier, at the point representing the global minimum variance portfolio.”
Isn’t the slope of the efficient frontier greatest where the efficient frontier is tangent to the CAL, representing the portfolio with the highest Sharpe ratio?
You’re thinking of the slope of the CAL, not the slope of the efficient frontier.
Ah, yes.
I should know this, but I’m having a hard time wrapping my head around it all.
Are these statements all correct?
The efficient frontier represents portfolios with the highest return for a given level of risk.
The CAL represents the tradeoff between risk and return.
The tangency portfolio is the point at which an investor maximizes return for a given level of risk.
One of the things I’m struggling with is if the slope of the CAL (Sharpe ratio) is the same at all levels of risk, why do we care about the efficient frontier? There has to be something I’m missing.
Now you’re good.
Once you include the risk-free asset, yes.
No: all portfolios on the efficient frontier maximize the return for a given level of risk. (See your first statement.)
The tangency portfolio is the portfolio with the highest Sharpe ratio, so the highest excess return per unit of risk.
Thanks @S2000magician . That’s helpful. Is the tangency portfolio made up of the optimal combination of the risk free asset and the risky portfolio?
The tangency portfolio is the optimal (in the sense of having the highest Sharpe ratio) combination of risky assets; it doesn’t have the risk-free asset in it.
The CML comprises all of the combinations of the risk-free asset and the tangency portfolio.
So the tangency portfolio is the optimal risky portfolio, and an investor’s positioning on the CML is based on how they allocate between the tangency portfolio and the risk-free asset?
Bingo!
Thank you so much!
My pleasure.