# CFAI 2008 exam question 4

Did a search but couldn’t find anything, so… In part B of this question (the one with Thurlow Corporation), they can lend or borrow as the risk free rate and you have to determine the combination of the risk-free asset and the corner portfolio. The answer stated you would invest 106.5% in portfolio 4 and borrow 6.5% of the funds at the risk free rate. Why can’t you invest 84.48% in portfolio 3 and 15.52% in the risk free asset? You get the same return (9.4%). When doing one of these corner portfolio mean-variance analysis questions, and you can borrow/lend, do you always use the corner portfolio with the expected return one notch below the required return? Surely they don’t expect us to calculate it twice: once with borrowing and once with lending and see which one provides the highest Sharpe Ratio? Or maybe they do?

newsuper, i was having trouble with this one as well, i don’t know where they get the 6.5% do you? in terms of why they chose portfolio 4, highest sharpe ratio that meets the minimum requirement (9.4 - 4.5) / 10 = 0.49?

you always use the Rf assets in combination with the portfolio w/the highest Sharpe Ratio if there is not restriction on short selling. if there is a restriction on short selling you use the two corner portfolios as stated above. hope this helps

mingo54 Wrote: ------------------------------------------------------- > you always use the Rf assets in combination with > the portfolio w/the highest Sharpe Ratio if there > is not restriction on short selling. if there is a > restriction on short selling you use the two > corner portfolios as stated above. > > hope this helps Mingo54, do you know where they got the 6.5%? Thanks

The reason to pick the corner portfolio w/highest Sharpe ratio, the combination will have highest sharpe ratio likewise, the highest sharpe ratio means for same target return 9.4%, its sigma is lower than other combination. Thus this is most appropriate strategic assest allocation as the Q asks. the 6.5% weight is from calculation in P15 of answer file. 9.4=9.1*W4+4.5*(1-W4) W(risk free)=1-W4 W(risk free)=-6.5

If the portfolio’s not sign-constrained (i.e. you can borrow, hold a “negative” asset allocation) then you always want to over-allocate to the portfolio with the highest Sharpe Ratio… here, #4. That’s the most efficient portfolio from a risk-return standpoint. You can tell that this portfolio’s slightly better than the one constructed in Part A, i and ii (w/the corner portfolio’s) because you’re achieving the same expected return but with slightly lower expected deviation (see the answer key for the numbers).

annexguy Wrote: ------------------------------------------------------- > The reason to pick the corner portfolio w/highest > Sharpe ratio, > the combination will have highest sharpe ratio > likewise, the highest sharpe ratio means for same > target return 9.4%, its sigma is lower than other > combination. > Thus this is most appropriate strategic assest > allocation as the Q asks. > > the 6.5% weight is from calculation in P15 of > answer file. > 9.4=9.1*W4+4.5*(1-W4) > W(risk free)=1-W4 > W(risk free)=-6.5 thanks a lot, much appreciated.

Another question surrounding # 4…would if be wrong to geometrically link the return object as well as the management fees? 1.087 * 1.007 = 9.461% I did all of the other calculations correctly on this question except my required rate of return was different because they simply added them together: 8.7 + .7 = 9.4 Any help would be appreciated best, TheChad

TheChad Wrote: ------------------------------------------------------- > Another question surrounding # 4…would if be > wrong to geometrically link the return object as > well as the management fees? > > 1.087 * 1.007 = 9.461% > > I did all of the other calculations correctly on > this question except my required rate of return > was different because they simply added them > together: 8.7 + .7 = 9.4 > > Any help would be appreciated > > best, > TheChad I have the same question… Not sure if it’s right to use the geometrically link…