Tangency Portfolio (CML)

Might be in the weeds here, however I figure I’d shoot.

So, I understand that you always select the port with the highest Sharpe for the tangency port. However, if there’s a constraint against leverage - what if this port does not meet your required rate of return. Do you go to the 2nd highest Sharpe and so-forth until you find the right one?

Perhaps this isn’t a feasible question. However, in the back of my mind it seems like a possibility. Thanks in advance!

Wouldn’t you just find the appropriate portfolio by taking a weighted average of the nearest 2 corner portfolios that meet your return requirement?


if there’s constraint against leverage, you just combin the 2 corner portfolio that surrounds your requirement.

if you can leverage, combine tangency portfolio with risk-free to meet requirement

Yeah, you just get your desired portfolio on the efficient frontier. That’s the whole point of the questions where we are given a return and then asked to find the weight of the portfolio’s asset class B by solving for the weight of two corners.

if question states you can’t leverage, does that also mean you can’t borrow at risk free rate?

this is what confuses me.

Say you have a return requirement that is less than return of tangency portfolio. In that case, if I combine tangency with risk free, I can still meet the required return with lower standard deviation compared to combining 2 corner portfolios. Since both tangency portfolio and risk free asset will have positive weight, I’m violating the leverage/short selling constraint, right?

On the other hand, if leverage is allowed and tangency portfolio return is less than required return, than it makes sense to short risk free and overweight tangency to meet required return.

My interpretation is that if your return requirement is lower than the lowest portfolio on the efficient frontier then only invest part of your money in the efficient portfolio equal to your required expected return. Done. Doesn’t matter if you can leverage or not. You aren’t going to see this on the exam

Your second situation is referring to the CML/CAL, which is what happens when you can leverage. I don’t see a question here.

Tangency port is not synonymous with using the two corner ports that provide your return (after solving for the weights)

So you can always leverage up/down on the CML/CAL?! Much appreciated.

This makes sense. Thank you.

Yes, and if you can’t leverage you are stuck with portfolios on the efficient frontier, hence us finding the corner portfolios for our clients on the exam, because it’s unlikely that they’ll take their money and lend it/consistently borrow due to 2 reasons: 1) practicality of lending and borrowing for individual investors and 2) the risk free asset is not risk free over multiple periods

Thanks bro

If the tangency portfolio meets your return requirements, you can combine it with the risk-free asset (invest in, not borrow at). The effect of this combination maintains return objective and reduces standard deviation without comprimising the sharpe ratio. This is optimal compared to combining the tangency portfolio with an adjacent (lower return) corner portfolio.