Position of Rf on expected return-risk graph

[verma.rahul]

Dear David

In Reading "The Capital Asset Pricing Model and Its Application to Performance Measurement" can you please clarify the footnote 2 as I think that Rf should be positioned below any point on the efficient frontier and not just below the summit point as when we get onto the efficient frontier for risky portfolio, risk starts , the same logic as per footnote 2.

Rahul

 

[David Harper CFA FRM]

Hi Rahul,

Unless I misunderstand, I agree with you and I think what you say is consistent with Amenc. Because the efficient frontier, prior to introducing the RF asset, begins at the minimum variance portfolio (the summit). Therefore, if Rf < min variance, it must also be the case that RF < entire efficient frontier (before the intro of the riskless asset).
(after the introduction of the RF rate, the RF rate becomes part of the efficient frontier; i.e., the efficient frontier is the CML, so I think we have two meaning for the efficient frontier)

David

 

[verma.rahul]

Hi David

First of all sorry that my question was not clear.
I do not know if I have misunderstood the graph of efficient frontier prior to introduction of Rf, but to me it seems that there are lot of points on the frontier left to summit (having lower standard deviation means less risk and hence lower returns) and I feel that Rf should be lower than any of those point. To me summit means maxima of the graph (probably near portfolio M) and I think my confusion is related to summit of hyperbola only .
Also, can you please clarify how can one get a zero beta asset by short selling. As per the definition, a short seller sells an asset that is not owned by him/her but anyhow s/he is looking for its price to fall down which is an effect of market forces/Interest rate volatility i.e. systematic risk.
Also, does risk free asset have a systematic risk ??? otherwise why does merton model take a third portfolio into consideration ???

 

[David Harper CFA FRM]

Hi frm_aspirant,

Sorry for delay, I missed your question. Before the RF asset is introduced, the efficient frontier plots only combinations of risky assets (i.e., by definition, the assets that are not risk free). The minimum variance portfolio is the furthest left (the summit), by definition. The optimal portfolio will be different (it has highest Sharpe ratio).

You are right, the RF asset, also be definition, will be to the left of the minimum variance portfolio. Okay, that's after we add the RF asset, but then the efficient frontier because the CML (various mixes/allocations of the riskfree asset and the market portfolio). So, maybe this helps: the minimum variance portfolio includes risky asset and excludes the riskfee asset.

Also, can you please clarify how can one get a zero beta asset by short selling
The asset will not be risk free; the asset will have a beta.
But the investor can achieve a zero beta portfolio by (i) avoiding risky assets altogether [invest only in riskfree asset] or (ii) by shorting to offset postive beta with negative beta in the portfolio.

Risk free asset has no systematic risk. We can visually confirm by looking at the SML where X = 0 (beta = 0) and expected return = riskfree rate.

Re: therwise why does merton model take a third portfolio into consideration ??? I don't follow, sorry?

David