Open-ended Capital allocation line question

[BaseballRedhawks]

So in the real world… most firms use an efficient frontier.
In the AA section, and in all levels, we learn about adding a risk-free asset, which will create a Capital Allocation Line, between the risk-free asset and a single point on the Efficient Forntier. The 1 portfolio on the EF is called the Tangent portfolio and that portoflio is also the one with the higest sharpe ratio. All other portfolios on the CAL are superior to all othr portfolios on the EF.
So they are saying that adding a risk-free asset, increases expected return for all points, but keeps the same risk, since risk-free asset has no risk (standard deviation) - Correct?
Ok, so the next question…. There is no real risk-free asset in this world. So what is the point of all of this?
Kind of open ended, but its a sunday night quesiton after a weekend of studying….
Thanks!

 

[Miamia]

Below is what I understand. It’s good to review it with the graph of CML and EF. Please check my understanding!
What I understand is that portfolios on CML are more superior to those on EF because of better risk-adjusted return.
If you meant ‘risk’ = Sharpe ratio rather than SD then its right when you said ‘keeps the same risk’.
Second note is the return comparison benchmark of E(R) of new portfolio, ie portfolio composed of Rf and Tangency. Also because we start our selection process by choosing Tangency portfolio rather than any portfolio on EF. (What you observe is you compare E(R) for given SD between CML and EF, and certainly it’s higher, what I see is we need to ref Tangency portfolio).
Lending Rf to a Tangency portfolio actually lower E(R) of the new portfolio compared to Return of Tangency portfolio alone (from Rf*(1-w)). Risk, however, is also reduced. SD(new portfolio)=w*SD(Tangency). Sharpe is maintained [across CML reflected by the straighline CML starting at Rf]. In this case, it minimizes risk without lowering Sharpe.
In summary, lower SD, same Sharpe ratio (lower E(R) ). Risk (SD) is weighted but Sharpe ratio is the same along CML.
You can do the same for Borrowing Rf. Weight of Tangency >1 => E(R) > R of Tangency. Risk is higher.
Your 2nd question: if you expect to outperform the best guy out there (Tangency), you gotta take more risk by borrowing, or else be conservative and keep cash and earn less. but by sitting doing nothing, you may do as good considering risk-adjusted return. J/k.