# Efficient Frontier..

TGIF Investment Company specializes in quantitative investment management. A pension fund has approached TGIF to achieve a specific portfolio risk, while maximizing return. Currently, the market portfolio has an expected return of 10% with a standard deviation of 15%. The pension fund has asked that its portfolio have a standard deviation of 30% with a return objective of achieving the maximum return available. How should TGIF invest the pension funds assets? a. Buy a riskier portfolio of securities that lies on the efficient frontier with a 30% standard deviation. b. Borrow at the risk-free rate and invest in the market portfolio to achieve a 30% standard deviation. c. Increase the security-specific risk in the market portfolio to achieve a 30% standard deviation. d. Lend at the risk-free rate and invest in the market portfolio to achieve a 30% standard deviation. - Dinesh S

B?

you would think B… but since you posted this question (harder than that)… my guess would be c

chadtap, I though even lower level to what you thought I would have thought [btw, I am a dumb fellow] … I selected ‘A’. But that is not correct… so that leaves with B, C, D … please specify the reasons too? - Dinesh S

nm

the answer is B… draw up your efficient frontier and CML line… at 30% st dev you can either i) invest ON the efficient frontier, the highest returning portfolio for that level of risk (ans a) ii) invest BELOW the efficient frontier, in a portfolio with security-specific risk (ans c) iii) invest on the CML line, by borrowing at Rf and investing in the market portfolio (ans b) the highest return out of these three options is B. (and D is not acheivable)

Market Conditions… E(Rmkt) = 10% STD(mkt) = 15% Investor Needs… E(Ri) = MAXIMIZE this… STD(i) = 30% So visualizing the Efficient Frontier Curve, if I draw a vertical like cutting the X axis at 30% (as STD is plotted on X axis), the place where this vertical line intersects the Efficient frontier would be the MAXIMUM gain available at that level of Risk, right? So why shouldn’t the answer be A? - Dinesh S

Sorry Dinesh… my bad… you post some pretty tough questions sometimes and you seem to get a lot of the others right…

the efficient frontier IS the maximum gain at that level of risk IF ONLY investing in themarket portfolio… once you introduce the risk-free rate, you can leverage your returns by BORROWING at the risk-free rate, and investing those proceeds in the market… THUS when you draw your line you intersect the Capital Market Line (which is the highest return possible)

Bluey 1.8T Wrote: ------------------------------------------------------- > the answer is B… > > draw up your efficient frontier and CML line… > > at 30% st dev you can either > > i) invest ON the efficient frontier, the highest > returning portfolio for that level of risk (ans > a) > ii) invest BELOW the efficient frontier, in a > portfolio with security-specific risk (ans c) > iii) invest on the CML line, by borrowing at Rf > and investing in the market portfolio (ans b) > > the highest return out of these three options is > B. > > (and D is not acheivable) Superb Bluey!!! Thanks so much for your lucid explanation … I could really visualize those options while I was reading your reply… thanks a billion!! guys, the the real answer is B.

So … one more quicky pops up in my mind… sorry for the clutter If the investor is a real risk averse dude and wants to lower his risk to even below the market risk (i.e. say STD = 5%) ---- does that mean he can invest in market portfolio (STD = 15%) and lend at a RFR (lending here is presumable taken as investing in t-bills)?? - Dinesh S

You can go above the efficient frontier only when using leverage…borrowing at the risk free rate and investing in your portfolio of choice. So your maximum expected return would be when you are totally levered up and in the riskiest portfolio on the efficient frontier.

dinesh.sundrani Wrote: ------------------------------------------------------- > So … one more quicky pops up in my mind… > sorry for the clutter > > If the investor is a real risk averse dude and > wants to lower his risk to even below the market > risk (i.e. say STD = 5%) ---- does that mean he > can invest in market portfolio (STD = 15%) and > lend at a RFR (lending here is presumable taken as > investing in t-bills)?? > > - Dinesh S Exactly. That is the whole point. Look up a graph of the CML at any point below the market portfolio.

portfolios on CML are a combination of M market portfolio and RF asset to have the best risk reward ratio you need to be on the CML if market portfolio has a Std of 15% owning 100% of it won’t do it(give you a 30%std) . the only way to achieve more risk is by leveraging- that is borrowing at the RFR and investing in M now i might be wrong but A does not make sense to me.if we believe the theory if you have a riskier portfolio still you wont achieve more than market returns so that would mean that the additional risk taken would not create additional returns ??

thanks dinesh… although, im wondering WHY a pension fund would want such a high level of risk, compared to the market? anyways, good luck everyone!

florinpop Wrote: ------------------------------------------------------- > portfolios on CML are a combination of M market > portfolio and RF asset > to have the best risk reward ratio you need to be > on the CML > if market portfolio has a Std of 15% owning 100% > of it won’t do it(give you a 30%std) . the only > way to achieve more risk is by leveraging- that is > borrowing at the RFR and investing in M > > now i might be wrong but A does not make sense to > me.if we believe the theory if you have a riskier > portfolio still you wont achieve more than market > returns so that would mean that the additional > risk taken would not create additional returns ?? It wouldn’t be optimal. The portfolio described in part A would be dominated (higher return for the same amount of risk) by buying the market and levering up to achieve your 30% SD.

mwvt9 Buy a riskier portfolio of securities that lies on the efficient frontier with a 30% standard deviation. not only that wouldn’t be optimal but a riskier portfolio of securities wouldn’t be situated on the efficient frontier -as answer A states- unless it’s the leveraged market portfolio.Am i right?

true… you could only achieve returns above market [i.e you can only be above the efficient frontier curve] by leveraging and that comes with an inherent risk. - Dinesh S

If you look at the efficient frontier before considering a risk free asset you can be above the market portfolio and still be in an efficient portfolio. This happens by holding risky securities in different weights than the market (or just holding more risky securities). Remember, in theory the Market portfolio is a combination of all risky securities in the world (stocks, bonds, other). That being said, once the risk free asset is introduced I think you are right. If you look at the graph. If you borrowed cash and levered up on a portfolio above the market on the efficient frontier you still wouldn’t get the optimal risk/return tradeoff. In a market in equilibrium (a basis for markowitz theories) the market portfolio has to be optimal. I think I am correct in everything I am saying here, but you may want a second opinion.

i thought that the whole point is that you can not beat the market return in risk adjusted conditions thanks for your opinion