So i’ve taken both the 2008 and the 2007 CFA essay sections. One thing I have found to be inconsistant with their answers is the usage of arithmetic and geometic methods for summing required returns with management fees, inflation etc. On the 2008 exam I found they used the arithmentic method while in the 2007 i found they used the geometric on several occations. I thought the CFAI didnt care which method is used, but considering a particular method was used in the “answer sheet”, i am getting confused as to what I should do. What are all of your thoughts on this?
On page 224 in reading 26 in CFA text they state: “The reading on managing institutional investor portfolios notes than an additive formulation of a return objective can serve as a starting point. Because additive formulations provide an intuitive wording of a return objective, such formulations are common in actual investment policy statements. The differences between additive and multiplicative formulations can be essentially negligible for low levels of spending rates and inflation. Nevertheless, portfolio managers should prefer the multiplicative formulation for strategic asset allocation purposes; managers should also observe the distinction between compound and arithmetic mean rates of growth”
As a follow up you’ll notice in the old exams that the guideline answer contains both the arithmetic and geometric
thats what i was looking at, sucha as in the 2007 exam where you are supossed to fgure out the corner portfolio weights. The CFAI answer is completely based off the arithmetic answer, it never mentioned Geo. I know what you guys are saying…i was just confused by the inconsistency in the answer sheet.
i am using geometric methodology solely. i think on the written exam, either is acceptable.
AFJunkie Wrote: ------------------------------------------------------- > thats what i was looking at, sucha as in the 2007 > exam where you are supossed to fgure out the > corner portfolio weights. The CFAI answer is > completely based off the arithmetic answer, it > never mentioned Geo. > > I know what you guys are saying…i was just > confused by the inconsistency in the answer sheet. Junkie, From what I remember (I haven’t look at this in quite awhile) the formula for determining a corner portfolio return is the same formula you use when determining the return FOR a portfolio. It is just a weighted sum of the portfolio asset classes. I also remember that you use the standard deviation formula to figure out the risk, but the convention is to assume there is perfect positive correlation in the last term (so you basically drop the last term). This is kind of a worst case scenario. I think this situation may be different than figuring out the required return for an IPS. Have you seen other inconsistencies besides this example?
going from the answers provided with past cfai exams (eg I have going back to 2003) - they accept both arith and geo. I can even remember one where they paid 3 different answers. So it doesn’t look like you’ll lose marks for either as long as you apply it correctly. That’s the beauty of the essay format (where most/all of the IPS questions come up) - you can show your workings. the cfai texts are just chapters from different text books by different authors - so is not consistent. In IPS, CME, Econ chapters and currencies they prefer geo. But other sections (eg Asset alloc, bonds, ) they sometimes use arith. the key difference is summed up in LOS 26(f) - if the goal is a geo target then the arithmetic return will need to be ABOVE the geo return by half the variance. Eg if the CAGR (geo) return required to reach a goal= 15% pa and the st.dev = 20%, then the av arithmetic return rquired pa = = 15% + 0.5(0.2^2) = 15% + 2% = 17% pa. This is a big difference in returns required to reach the goal. (this is a useful quick approximation calc - but shows the difference is non-trivial) Most people make the mistake of saying that if the CAGR goal is 15%, then if you achieve an average 15% arithmetic return each year you will reach the goal. Well, if you achieved 15% EVERY year consistently then you will reach the goal, but with a st.dev of 20% in returns you will not reach the goal. You will need 17% av arithmetic return to hit the 15% CAGR (geo) goal. Personally I stick to geo. ie always multiply out things like return, inflation, costs to get total return required.
Either one is fine. The difference between the two should be small enough not to make a difference in portfolio/asset allocation selection.
N&N has made a good point. I would think the reason they used the arithmetic return in the corner port example is becauseyou are looking at the average yearly return (it is appropriate in this context). When you are doing an IPS you should really use the geometric because that is what pays the bills. For example, T=0 I have $100 T=1 return is 100% = $200 t=2 return is -50% = $100 Geometric return would capture this while arithmetic would not (as you average return is 25%). BUT if you were estimating next years return arithmetic would be better. So basically in the corner portfolio example the purpose of the return calculations use is different from the IPS.
- also corner portfolio approach is basically MVO - which is based on a single period model - where arith = geo. But any multi-period approach (ie the real world) should use geo.
Agree.
From what i understand either is acceptable for individuals and most institutions. However, I know Schweser noted that for foundations and endowments, the geo average should be used due to the long time horizons and the impact of compounding the minor difference between the arithmatic and geo average over such a long period of time could be quite substantial.