Awkward sharpe ratio question possible, question, correct, produce, general

mfleming1983

When compared to all other possible portfolios, the portfolio that has the smallest variance would have a Sharpe ratio that:
A) could not be the highest of all possible portfolios.
B) may or may not be the highest of all possible portfolios; there is no general rule.
C) is the highest of all possible portfolios.
Your answer: B was incorrect. The correct answer was A) could not be the highest of all possible portfolios.
Minimizing the variance does not produce the portfolio with the highest Sharpe ratio. A point along the efficient frontier above the minimum variance portfolio will have both a higher return and standard deviation, but it will have a higher Sharpe ratio. (Study Session 18, LOS 66.b)
so i put B because the formula is [E(r) - rfr)]/stddev and just because a portfolio has a small variance (and small stddev) does not necessarily mean it has the higehst sharpe ratio, since the numerator matters too. first off, theire choice A is awkwardly worded: does it mean “it CANNOT be the highest” or “it could be possible that it is not the highest”? if the latter, choice a and b are the same. also, i read their explanation three times and dont get what theyre saying.

iteracom

Answer A)
cr*p quesiton.
smallest variance = 100% in RF.
So there is at least one portfolio that benefits over the RF portfolio.

stalkey

I would imagine a tagency portfolio to min. variance frontier to have a maximum sharpe ratio.
More often than not, the line from Rf to Globally Min Var portfolio will have lesser slope than tangency portfolio. (risk reward ratio).
I’m not sure if it is mathematically possible to prove that this holds 100% of the time.
They should say globally minimum varience in the question, for answer A to be correct, I think.