Efficient Frontier..

florinpop Wrote: ------------------------------------------------------- > i thought that the whole point is that you can not > beat the market return in risk adjusted > conditions > thanks for your opinion That is what I am saying. In order to obtain higher than market rates of return. You must hold more risky assets than the market as a whole. For instance more high beta stocks (in a CAPM framework). How else would you explain the efficient frontier above the market portfolio?

ok I guess the differences come from the fact that I believe there is only one efficient frontier and you believe there are more than one I’ll restate my previous statement . I thought that you can not constantly beat the market (market timing or stock selection) and that is why the market portfolio &risk free asset combinations give you the best risk adjusted returns and that’s why they are on the cml sorry don’t mean to be a pain in the butt

I think is B. Since you introduce risk free asset in to portfolio. the efficient frontier change from a curve into the CML.a straight line though the RFR and Market Portfolio. You can either lend or borrow at RFT and invest in market portfolio the gain maximum return given certain risk level.

You are not being a pain, this is what the board is all about! There is only one efficient frontier. We are on the same page. My point is that IF you couldn’t borrow at the risk free rate (which you can’t in the real world) and you wanted a rate of return higher than market rates you would have to have an assest mix that was riskier than the market portfolio. If you look at the graph what are the points above M that are still on the efficient frontier? They have to be asset mixes that are riskier than the market. The same as points below M are less risky (more bonds than market as a whole). When the risk free asset is introduced the most optimal portfolio will be the one that lies at the point of the frontier that is tangenital (word?) to the risk free asset. This is the market portfolio. Any combination of the risk free and M form the CML. Now that you have this risk free asset there is no reason to invest in any portfolio below M because you can invest in a combination of M and the risk free to get a better return. Also there is no point in investing above the M because you could just borrow and invest more in M. I wrote this earlier “So your maximum expected return would be when you are totally levered up and in the riskiest portfolio on the efficient frontier.” This is wrong. The more I thought about it, there is no way to have a better return than to be totally levered up on the CML. The tangential point on the curve with respect to the risk free should produce the highest returns. I had to draw a picutre to see it.

I think I know what you are trying to say a. Buy a riskier portfolio of securities that lies on the efficient frontier with a 30% standard deviation. so I guess you could have a riskier portfolio with returns greater that the market but it wouldn’t be optimal because the optimal would be attained by leveraging the market portfolio BUT A says that riskier portfolio would be on the efficient frontier and I cant see that happen cause it would have to be under that frontier,

florinpop Wrote: ------------------------------------------------------- > I think I know what you are trying to say > > a. Buy a riskier portfolio of securities that lies > on the efficient frontier with a 30% standard > deviation. > > so I guess you could have a riskier portfolio with > returns greater that the market but it wouldn’t be > optimal because the optimal would be attained by > leveraging the market portfolio Exactly. > BUT A says that riskier portfolio would be on the > efficient frontier and I cant see that happen > cause it would have to be under that frontier, It would be under the CML, but on the efficient frontier. I think you are confusing being on the efficient frontier with being on the CML. The efficient frontier has nothing to do with the risk free asset (only risky assets). The CML is seperate. It shows you your risk/return characteristics when you add a risk free asset to the frontier, but it doesn’t change the frontier itself. When you lever up by borrowing money and investing in M you are no longer on the efficeint frontier you are above it on the CML. In reality, even when levered up you are still on the efficient frontier in portfolio M (your only investment is the M portfolio) you just are using somebody elses money to be there. That moves you risk and return characteristics outside of the efficient frontier. Does that make sense?

yes you are right major Flaw thanks

Does D make sense? On the CML line, the point after the intersect of CML and EF is referred to the lending period, which i have a hard time grasping why would anyone do that. Does it mean that u put 100% of ur capital in porfolio M and also lend out money to others?

ancientmtk Wrote: ------------------------------------------------------- On the CML line, the point > after the intersect of CML and EF is referred to > the lending period the point after intersection of EFC with the CML at “M” are all the borrowing positions

just to confirm, the answer is B, right?

yancey Wrote: ------------------------------------------------------- > just to confirm, the answer is B, right? yep

Answer is b and mwvt is really onto something about the picture. As far as not being able to borrow money at the risk-free rate - if the market portfolio is the S&P 500, then the implied interest rate in the futures contract is pretty close to anything I would call a risk-free rate. Since you can buy an S&P futures contract at 10% margin or less, that’s some pretty easy leverage at low cost.

He’s back!^

My point was that the CML isn’t really a line as it is in the theory. At a minimum it is kinked because there is a cost to borrowing. JoeyDVivre Wrote: ------------------------------------------------------- > Answer is b and mwvt is really onto something > about the picture. As far as not being able to > borrow money at the risk-free rate - if the market > portfolio is the S&P 500, then the implied > interest rate in the futures contract is pretty > close to anything I would call a risk-free rate. > Since you can buy an S&P futures contract at 10% > margin or less, that’s some pretty easy leverage > at low cost. Can you explain that a little more? You lost me.

mwvt9 Wrote: ------------------------------------------------------- > He’s back!^ And the big riddle that is solvable is where was he…

mwvt9 Wrote: ------------------------------------------------------- > My point was that the CML isn’t really a line as > it is in the theory. At a minimum it is kinked > because there is a cost to borrowing. > > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > Answer is b and mwvt is really onto something > > about the picture. As far as not being able to > > borrow money at the risk-free rate - if the > market > > portfolio is the S&P 500, then the implied > > interest rate in the futures contract is pretty > > close to anything I would call a risk-free rate. > > > Since you can buy an S&P futures contract at > 10% > > margin or less, that’s some pretty easy > leverage > > at low cost. > > Can you explain that a little more? You lost me. The market portfolio really isn’t the S&P 500 but for some equity universe it sorta is. So if the market portfolio is the S&P 500, you need to look at ways of levering up an investment in it. The machines that do index arb are always pricing the futures contract relative to the underlier with some cost of funds to do the arb. That gives the futures contract an implied risk-free rate. That rate is easily computed (if you know dividend yields which is a lot of work since they aren’t uniform) and is typically very low, i.e., something like repo rate or Fed funds or something.

JoeyDVivre Wrote: ------------------------------------------------------- > mwvt9 Wrote: > -------------------------------------------------- > ----- > > He’s back!^ > > > And the big riddle that is solvable is where was > he… Honeymoon?

JoeyDVivre Wrote: ------------------------------------------------------- > mwvt9 Wrote: > -------------------------------------------------- > ----- > > He’s back!^ > > > And the big riddle that is solvable is where was > he… Where to Joey? With just 14 more days to go, we needed super-humans around - Dinesh S

mwvt9 Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > mwvt9 Wrote: > > > -------------------------------------------------- > > > ----- > > > He’s back!^ > > > > > > And the big riddle that is solvable is where > was > > he… > > > Honeymoon? Might be onto something there…l

mwvt9 Wrote: ------------------------------------------------------- > When the risk free asset is introduced the most > optimal portfolio will be the one that lies at the > point of the frontier that is tangenital (word?) > to the risk free asset. Tangenital? I presume that’s what happens at a nude beach. Tangential is probably the spelling you were looking for :slight_smile: [Sorry to be so off topic, it’s 2:30 AM, and in studying FSA on a Friday night, making silly jokes is one way to try to preserve sanity]