We can discard choice (A): portfolio P is efficient because nothing is obviously better; i.e., nothing lies in its upper-left quadrant that could enjoy better return for the same risk, or lower risk for the same returnMy favorite distinction between SML and CML is: CML is only efficient portfolios, but the SML includes any portfolio, including non-efficient portfolio
@David Harper CFA FRMHi @Akriti1 Thanks but um, no, it's a flawed question and perhaps even counterproductive. Why? Because it penalizes a more knowledgeable candidate!
If (b) is false, then (c) must also be false: If we can expect the Portfolio to have a beta of 1.0, then we can also expect it to lie on the SML! More profoundly, as mentioned, we can expect all portfolios to lie on the SML. The best answer to this question is actually (B). But the fundamental problem is that the question is flawed because the writers lack an understanding of mean-variance and CAPM theory.
First, there are no assumptions provided to require that portfolio P is the Market portfolio. The "mean-variance" assumption is only one of the CAPM assumptions. CAPM implies mean-variance but the converse is not true. The curved line that plots return versus volatility is merely a Portfolio Possibilities Curve (PPC). The PPC can be constructed with only two assets, and it often is thusly constructed (!), but that doesn't make P the Market portfolio obviously. Portfolio P is simply the most efficient portfolio on the PPC (i.e., highest Sharpe ratio) conditional on the given riskfree rate (the most efficient portfolio is actually variant to the riskfree rate which you can visualize by shifting up/down the riskfree rate and realizing that the point of tangency moves!). Probably/possibly the question writer intends for the it to be the Market Portfolio but the assumption(s) to justify that should be provided.
Second, because there is no assumption given to justify evaluating Portfolio P as the Market Portfolio, the best choice is (B): among the given set of risky assets, it is highly plausible that Portfolio P has a beta that is not exactly equal to 1.0.
Third, as mentioned, we should understand why (C) is technically wrong: the CML is efficient, but the SML manifests CAPM and plots the expected return of a portfolio/asset (as a function of its systematic risk, beta w.r.t. the Market Portfolio) for any security. We can expected Portfolio P to like on the SML, like we expect any of the less efficient portfolios on the PPC to lie on the SML! If P does not lie on the SML, then an arbitrage is possible (and this in fact a classic FRM type question).
Fourth, here are two possible answers which could replace the problematic choice (C), to the question "Portfolio P is least likely to"
Again, my problem with this question is that it penalizes a more knowledgeable candidate who discards (C), because such a knowledge candidate understands that all of the portfolios lie on the SML (if the CAPM assumptions apply), and selects answers (B) for the good reason of inferring that (P) is "merely" a highly efficient portfolio among the risky portfolios.
- [easy variant] have a Sharpe ratio that is lower than another portfolio on the CML; i.e., easy false statement b/c all portfolios on the CML have the same Sharpe ratio
- [hard variant] have a Sharpe ratio that is invariant to the riskfree rate; i.e., harder to realize false statement but interesting that P (and its Sharpe) is variant to the riskfree rate