The Grinch Who Stole Asset Allocation

bwg:

The Dow Jones article is based on an article by William Jahnke. It can be found at:

www.financial-design.com/hoax.html

(We are guerillas in the war on MPT)

:-)

The cited Dow Jones articles are accessible only to paid subscribers (and hackers) who can supply a valid userID and password.

Bylo:

You have to register at the DJ site, but you don't have to pay. I'm vigorously opposed to paying, and I saw the DJ article.

:-)

Thanks thbox. So yer "vigorously opposed to paying" -- does that also apply to books, investment advice, MERs and such-like? :-)

The dates, titles, and authors of the articles are:

Dec. 97, 'The Grinch Who Stole Asset Allocation', by Robert N. Veres

Feb. 98, 'Mad As Hell', by Philip S. Wilson

April 98, 'Grinched Again', by Bill Jahnke

bwg

I read the William Jahnke articles, and they do not come close to "destroying" the asset allocation concept. Janke is quilty of bad (actually really, really bad) reasoning. His intrepretations were than parroted by Morningstar and other sources.

Esentially what Jahnke did was take the data from the original Brinson study, and instead of using variance (as ALL research, in any field, uses) he replaced it with range -- a very weak measure of distribution. This is akin to replacing mean or median with the mode -- very dumb. He than compared the range of the actually data (which was obviously impacted by the extreme outlyer data points, and compared it to the range as predicted by Brinson's least square regression. From this he concluded that asset allocation only accounts for about 13% (if memory serves me correctly) instead of the Brinson study over 90%. Again, this is a VERY DUMB use of statistics.

If anybody doesn't believe that Jahnke is quilty of bad reasoning, do the following simple exercise. If you have a speadsheet program that does some stats (I use Excel), make up 100 pairs of data sets. For 99 of the pairs, establish a pefect positive 1 correlation (eg. 1-3; 2-6; etc.). Then on the last pair come up with an extreme outlyer pair (say 100-1000). Now run a least squares regression and compare the result to what you would obtain if you used Jahnke's logic. You will see that the least square regression captures a good part of a relationshiop you know is strongly related, while Jahnke approach does not even come close.

Good stats NEVER rely on range or mode. They use measures that depend on all data points as compared to just two for the range.

It occurs to me that an easier way to understand how silly is Jahnke's approach is to take a relationship that you know has a reasonably strong positive correlation -- say height vs weight. Lets say you took 1000 men of similiar age (say age 40, because by than some weight variability is likely to have set in) and you correlated their weight and height. If you then conducted a least-square regression you would surely find a resaonably stong, positive relationship between weight and height. When you do this type of regression, you statistically predict a value for weight (the dependent variable) based on each and every height (the independent variable). What Jahnke's approach then does is take the range from the least-square prediction and compare it to the range from the actual data. So, if in the actual data one man is anorexic and another guy is destined to be buried in a piano case these two individuals establish the range of the actual data. Jahnke would than conclude that the predicted range does not account for much of the real range. To repeat myself -- THIS IS VERY DUMB.

Thanks PK, once again you bring sound reasoning and tangible evidence to this forum. Your grasp of statistical methodology is impressive and contributes to a well-informed debate.

PK, The Jahnke position appeals to me on an intuitive level. I always found it hard to accept that it did not matter much which securities you held in a particular class since such a large portion of the return came from the class itself. In the Wilson rebuttal (Dow Jones Investment Advisor, Feb 98) we are told that a broad based portfolio will correlate very closely with the representative index. Well sure, that the same as saying that the average person will have a similar height and weight to the average person in the study you use in your example above. This is only helpful in the world of index funds (and perhaps we should all be investing in index funds). Given that the majority of investors invests in either individual securities or managed funds the position that Wilson takes is not very helpful. Clearly what is held in your portfolio will make a difference to the return that your portfolio will generate, and sometimes a very significant difference indeed. The problem that I have with the asset allocation accounts for 90%+ of return argument is that in the real world it does not help me improve the performance of my portfolio. According to the argument as long as I have 75% of my portfolio in Canadian stocks and 25% of my portfolio in Canadian bonds, then my return should be relatively similar to other portfolios with a 75%/25% mix of Canadian securities. Well in fact it just ain't so. If it were then all Canadian growth funds would deliver roughly the same return, and all Canadian bond funds will do likewise. This is however not the case. MPT is valuable for demonstrating the relationship between risk, reward, and diversification. It is clearly beneficial to spread your risks. However to ignore the reality that not all funds/stocks/bonds are equal. To accept the idea that 90%+ of the return of a portfolio comes from the asset mix alone, and that the maximum range of returns possible beyond that is something less than 10% makes no sense at all to me. Now I admit that maybe I have missed the point entirely. Perhaps it is the case that I have completely misunderstood the point. If that is the case then I would appreciate it if some one can set me straight.

bwg:

I think that you are missing the key aspect of asset allocation. IMHO, what I read seems to infer that asset allocation can reduce the risk required for a given return.

I realize that to achieve the absolute maximum return, one would have to be invested in the single investment vehicle that achieved the maximum return. Unfortunately this is an unrealistic expectation. More reasonable is to design a portfolio that minimizes your risk.

All the back tested methods (that I have seen) indicate that a mix of domestic, foreign, stocks and equities give the best risk/return over any lengthy time period.

The key is to consider your time period in question. Holding Asian funds over the last 3 years would not have made for much of a return, no matter how well they did in the previous 20 years (or whatever the appropriate time span is). Similarly the North American markets haven't always outperformed all the other world wide markets. One more reason for diversification.

BL (not sure where this discussion is going to or coming from)

Hi bwg -

I think the primary problem you are having is that you believe the asset allocation studies state that 90%+ of returns (in absolute terms) are accounted for by mix. This is NOT what they state. They state that 90%+ of THE VARIABILITY OF RETURNS is accounted for by mix. Variance is a specifically determined statistic. To arrive at variance, you first have to determine the mean of your sample. Then, using the mean you subtract each and every data point. Each of these differentials is then squared, and then they are all summed to arrive at the variance. It is this property that asset mix accounts for.

Variance is a robust measure of dispersion. Another measure of dispersion is range. Range is a far weaker measure of dispersion because it only uses two data points -- the minimum and the maximum. All points in between are ignored. It is very dangerous to draw conclusions from the range, as Jahnke does, because most of the data is ignored.

To illustrate why this is so, I find it useful to go outside the investment world and think about research in other fields. To accomplish this lets think about heart disease. A factor that contributes to heart disease is smoking. So lets establish smoking as the independent variable and lets hypothesis that heart disease is dependent on how much you smoke. Since smoking can be continuosly quantified (ie. you could smoke 0 cigarettes or you could smoke 500 cigarettes a day, or anywhere in between) lets define heart disease in a similar, continuous way. One way you could do this is by determing what percentage of your arteries are blocked to blood flow. Some people can have 0% blockage, while others could have their artieries (or some of them) 100% blocked. By defining the variables in this way you can now correlate two, continous variables.

In the above scenario, lets say you run the regression and you find that smoking accounts for 50% of the variability of artery blockage (BTW, I'm making this numbers up for illustrative purposes only). This is a reasonably strong relationship and gives you alot of information. It allows you to conclude that smoking should be avoided and also tells you that the more you smoke the greater is your likelyhood of having your arteries blocked. Does it tell you that all people who smoke will get heart disease? NO. Does it tell you that if you don't smoke you won't get heart disease? NO. What it does tell you is that going forward, smoking is a reasonably good predictor of heart disease.

If you now use Jahnke's logic, you could very easily come to faulty conclusions. Let's say your sample has one individual who doesn't smoke but has their arteries severely blocked. As well, lets say in your study you have another individual who smokes 500 cigarettes a day and has zero blockage. If you use range, as Janke does, you would conclude that smoking does not account for any of the incidence of heart disease. It arrives at this faulty conclusion because range is a very weak measure of dispersion.

So, in the above hypothetical, you do not conclude that everybody who smokes, say 100 cigarettes a day, will have the same amount of artery blockage. A number of individuals who smoke the same amount will have a distribution of blockage. The same is true of investments. Portfolios with similar asset mix will also have varying returns. But, in both cases, the variables that accounts for the most variance can be used as your best guess as to future outcomes.

I hope this was not to confusing!

PK, Thank you for taking the time to respond in such a clear and detailed manner. I do follow what you are saying, but I have frequently seen the position stated that asset allocation is responsible for 90%+ of the return in a portfolio. It is exactly this postulate (and not variance as you argue), (at least as far as I can see) that Jahnke is arguing against. By way of illustration I will quote from the article in the 'Dow Jones Investment Advisor', Dec. 97; "…is it really true that you can create an asset class and then delegate the stock selection process to anybody---and still get substantially the same results? The Steadman portfolios and Magellan Fund were both invested in U.S. equities during the 1980s; one soared while the other floundered. Isn't that more than a 2% difference in the medicines effectiveness?" This certainly sounds as if the subject under discussion is the range of returns and not the variance between returns. The article continues, "How, Jahnke wondered, did the planning profession ever get to the point where we blindly accepted---and repeated to each other at industry meetings--- such an obviously flawed argument?" A few lines later the issue under discussion is spelled out as follows, "At issue: Just exactly how important is the asset allocation mix in determining (or predicting) the return of an investment portfolio?" Again we see that the issue is one of how much influence the asset mix has in determining (or predicting) the portfolios actual return. If as is generally held it accounts for 90%+, then we should be able to predict a portfolios return with a fairly high degree of accuracy. This however is not the case. If at this point there is any doubt left as to what Jahnke is having difficulty with it is made clear in the following quote, " The Brinson, Hood, Beebower article,…offered, in their conclusions, a number so astonishing that it immediately caught the attention of a shell-shocked planning profession. Fully 93.6% of a portfolio's return, they said, could be explained solely by its asset mix. Only about 2% more, the article went on to say, could be explained if you add market timing activities to the equation, and about 4% more if you added security selection. The study modestly concluded, after some qualifiers, that "the normal asset class weights and the passive asset classes themselves…provide the bulk of returns to a portfolio."" At a minimum the planning community accepted this scholarly document without out adequate critical examination. I have heard this position (the one Jahnke is arguing against) so many times and from so many respected individuals that I wondered how come it seemed so wrong to me. Thus when I first read 'The Grinch Who Stole Asset Allocation' I felt vindicated. In truth I have not read the original Brinson,Hood, Beebower article. Perhaps (and I strongly suspect) that the article was put to use in a manner never intended by its authors. I doubt that the math in the original article would be meaningful to me, but I have no doubt that the conclusions drawn from the Brinson, Hood, Beebower article are seriously flawed. PK, if you still feel that I am missing the point I will grant that the statistics are beyond me, if you feel that Jahnke is looking at the statistics in an incorrect manner, I can accept that (your illustrations made perfect sense to me). This however does not negate the value of Jahnkes article. At a minimum it serves to show clearly that it takes more than simply determining the asset mix of a portfolio to achieve success. Thanks again, bwg PS: the Dow article is hot linked above, if for some reason you can not access it, I will be happy to fax a copy to you.

Hi bwg -

Just a couple of quick things. In your original post you quoted the following, "Indeed even the authors of the original study from which the idea sprang forth agree that the conclusions drawn from the original study have been misused."

I would guess that they are referring to exactly what I tryed to illustrate in my posts -- namely, it is the variance of returns asset mix accounts for. It is hardly the original authors fault that some financial planners don't understand what they are talking about. I have no doubt that they have contributed to misunderstanding and confusion.

Despite the above, Jahnke has added nothing of value to the debate. We are left with the fact that portfolio returns vary, just as we are left with the fact that some people get heart disease even if they don't smoke.

I would argue that the variability in returns is based on chance. If you come from this perspective (which has the overwhelming weight of evidence behind it) your best guess as to future relative performance is based primarily on asset mix. To illustrate, using only stocks (forget asset allocation for a moment), my best guess as to how any active manager will do going forward will be the index he/she is trying to beat (less MER, of course). If you believe in active management, your best guess is that the manager will beat the index by some amount (otherwise why would you invest with him/her?).

The only thing that Jahnke does is describe that returns vary. I say big deal -- who doesn't know that? The real question is how do you make decisions going forward. Because asset mix accounts for much of the variability of returns, and because I believe active management is only by chance likely to outperform (or underperform), your best predictor of relative performance is achieved by focusing on asset mix.

Just one more thing. I re-visited Jahnke's article the other day and found that he believes only 14.6% of returns are accounted for by asset mix. How realistic do you think that statement is? If I invest half my money in Canadian stocks and half in Canadian equities, is Jahnke trying to tell me that 85.4% of my returns are going to be based on shrewd security selection and timing decisions? I think not. Both my bond and equity components are going to be largely driven by the overall performance of the markets.

PK, I want to thank you for your input. While I am still uneasy with the idea that I can buy any fund in the various asset classes, rebalance the portfolio periodically, and be assured of achieving more or less the same return over 10 years that I would have had I selected a completely different set of funds, I do see your point. This does not mean that I am prepared to give up monitoring my manager's performance. I have selected each to fulfill a specific function within the portfolio. This was done in much the same way, and for the same reason that I select funds in various asset classes and sub-classes, that is to fulfill a specific function within the asset mix. When the market is rewarding a certain investment class and investment style, I am prepared to over-weight that class and style. If the market is punishing a class or style I will under-weight that class or style. I see no point in saying that my original asset mix called for a certain mix (i.e. 5% in Japan) so I am going to maintain that weighting no matter what happens. Actually I did in fact start out more-or-less like that, I bought Japan quite some time ago, achieved very nice returns, and then sat and watched them dwindle to nothing. I finally gave up on Japan (for the time being) in the 3rd 1/4 of 94. If the long-term outlook for a sector is sufficiently glum I see no point in leaving resources tied up in it. Have you read 'Investment Policy', by Charles D. Ellis? He says that the reason that money managers have such a hard time beating the market is because they are the market. I found his writing to be very interesting; one of my favorite Ellis gems is "Does the client matter? Indeed he should. But the client will only matter if he asserts his authority and fulfills his responsibility: deciding investment objectives, developing sound investment policies, and holding portfolio managers accountable for implementing long-term investment policy in daily portfolio operations." ('Investment Policy', Charles D. Ellis, Irwin Professional Publishing, 1993, page 4). Thanks again, Bwg PS: I will give your comments some more thought, and I will delve more deeply into the literature surrounding this issue. If I come up with anything I will post it here, or in a new thread. All the best.

Webster's New World Dictionary defines "paragraph" as: 1. a distinct section or subdivision of a chapter, letter, etc. usually dealing with a particular point: it is begun on a new line,. . . . :-)

Yes I know, and I apologize. I used Word to type up my comments, paragraphs and all, I then copied the document and pasted into the message box, & hit submit. I only realized that the paragraphs disappeared afterwards. I guess I must leave a space between paragraphs in Word and not simply jump to the next line.

By the way, no need to be shy, you can include you HANDLE, no need to hide, your point is well taken. Thanks,

bwg

Yes, thats better.

Drat,

I just realized that :-) is your HANDLE. Sorry again. I think it might be a frown, is that correct?

bwg

A lot of people run into problems when they copy and paste passages from a word pro to a forum or newsgroup. Usually line feeds show up in newsgroups as =20 and paragraphs don't come through at all in either one.

Some word pros will allow you to save the text as html. That might do the trick, together with setting margins so you get about 5" of text. a "template" set up especially for newsgroup/online forum replies would be ideal.

Actually, :-) is a smiley, not my real handle. There were several threads a while back about doing html on the forum. Careful, though, the fund-meisters are not thrilled about our using html - specially for anything other than bold or italics or underline.

Jahnke's and Brinson's measures of the fraction of fund returns explained by asset allocation differs in two way. The first difference is the Jahnke uses a funky ratio of ranges, which PK has correctly pointed out, is subject of error from outliers. The second, more important, way it differs is that Jahnke measures the correlation in 5 years returns while Brinson effectively measures correlation in quarterly returns.

Brinson measure is the R-square of a regression of quarterly returns. The R-square measure indicates how closely changes up and down for each observation of the independent variable is matched by ups and downs in the dependent variable. Since each observation in Brinson's regression is a quarterly return, the R-square really measures correlations of quarterly returns for the funds with the index.

Suppose that you had 3 series of numbers like those list below. The first series is the index, the second is Fund A, and the 3rd is fund B.

index: 3,5,4,7,4,6,9

Fund A: 3,6,3,7,5,7,9

Fund B: 3,7,5,9,7,9,12

Running a regression with the index as the independent variable and Fund A as the dependent variable gives an R-square of .88. Running a regression with Fund B as the dependent variable gives an R-square of .93. Fund B more closely matches the zig-zag pattern of the index. HOWEVER, fund B final return varies more from the index than Fund A.

This is a cooked up example but I think that it fairly describe the real world. That is, funds that did very well or very badly in the past 5 years don't differ so much in the way it's zig-zag pattern matches the market. It differs because the good fund tends to have slightly greater ups when the market goes up and slightly lower downs when the market goes down, the good funds don't go up when the market goes down.

So I think Jahnke is correct in using the final returns since that can provides the answer to how much of the return after 5 years is due to asset allocation. Brinson number are accurate only if you plan to invest for a single quarter.

However, Jahnke uses that funky range measure. He should have ran a regression of 5 year fund returns against 5 year index returns with each fund contributing one observation to the regression. The r-square measure from that regression is the proportion of final returns explained by the index. Jahnke's measure can be either higher or lower than the correct R-square measure. If there is an outlier, his measure will understate the effectiveness of asset allocation. My guess is that he understates the effectiveness of asset allocation but it's just a guess.

As PK also points out, this whole debate is only half of the story. To paraphrase what he said, a low r-square on the above regression means that there are large potential benefits to selecting managed funds but not whether it is likely to be realized. In fact, I believe most evidence suggest that predicting future performance only works in the short term, if it works at all. So your best bet may be to select managed funds for the short term even though short-term returns are mostly due to asset allocation. That's better than selecting managed funds for the long term where doing better than the index is due to chance (and you are unlikely to find comfort in knowing that a smaller proportion of the return is due to asset allocation). It is as important to know how likely you can select an above average fund as it is to know the upper limit of returns from selecting the fund.

Dexter,

Thank you very much for the above, it goes a long way to helping me understand the more esoteric aspects of the argument. In addition I particularly appreciate the fact that you have taken an objective position in the discussion, pointing out the weakness and strengths of both camps. It seems to me from both an intuitive understanding, a careful read of the arguments (hot linked above), and in no small part your discussion above, that the "truth" is somewhere between the two poles. I also found particularly interesting your comment about past performance being a better predictor of near term performance as opposed to longer-term performance. Gordon Garmaise has made the same point and my own research supports this as well.

Thanks again, All the best, bwg

Dexter: very impressive analysis-- am in awe of your statistical skills and agree fully with your investment approach.

bwg and Keith, Thanks for the kind words.

I was looking at the financial design site that is hot linked above by Bylo and found more details about the regressions that Jahnke had done. The R-square of the regression of 10-year (not 5-year as I incorrectly wrote above) final returns on 10 year asset policy (index) returns is 3.2%.

Jahnke does not directly state that the R-square is 3.2%. The actual number he gives is a variation of the R-square. In Volume 1 Number 2 of the Financial Designs white papers, he states in endnote 4 that "in terms of standard deviations .... policy returns explain 15.38 percent of actual returns". What he means by expressing explanatory power in term of standard deviations is sqrt(sum of square regression) / ( sqrt( sum of square regression) + sqrt( sum of squares error) ). This makes a lot of sense to me since it is more intuitive to think in terms of standard deviation. Jahnke provides a justification for it in endnote 6. The 15.38 percent based on this more comprehensive measure is very close to the 14.60% he gets using the range measure.

The 15.38 percent explanatory power of asset allocation returns seems low to me. I think the reason for the low number is that there may be little variation in asset allocation. The sample consists on 91 large pension plan which probably have similar asset allocations. A sample consisting of mutual funds might have larger variations and may provide a higher R-square.

The most interesting point in the paper is Jahnke assertion that we should change asset allocations as expectations of future returns from different assets change. Obviously, we should change allocation if our expectations are anyway reliable. He claims that they can be reliable and offers as evidence the performance of Wells Fargo asset allocation program. Does anyone have more information on this program?

The following information is from the AGF site. PDF files about these funds are there as well as the FL.

Barclays Global Investors (BGI) Barclays Global Investors (BGI) is recognized around the world for its distinctive quantitative value investment style. BGI's tactical asset allocation expertise is available in Canada exclusively through the AGF Group of Funds.

BGI - founded in 1996 with the merger of Wells Fargo Nikko and BZW Asset Management - has its Canadian office in Toronto, and global headquarters in San Francisco, California. The firm currently manages more than $68 billion for Canadian clients, and in excess of $450 billion worldwide. for pension plans, foundations, endowments, and other institutional accounts. Funds advised: Kathy Taylor is the Managing Director AGF American Tactical of Barclays Global Investors (BGI) Asset Allocation Fund Canada. Kathy holds a CFA designation and is a registered senior portfolio AGF Canadian Tactical manager and registered commodities Asset Allocation Fund trading manager. Kathy is an expert on the unique quantitative value AGF RSP International investment model which is the Equity Allocation Fund hallmark of the BGI asset allocation management style. Kathy is also a member of the Investment Committee overseeing the management of all Canadian equity strategies.

Style: The Tactical Asset Allocation strategy is a quantitative value investment style which allocates the Fund's assets among equities, bonds and cash according to a computer-assisted model.