Nope.
You can just as easily average a height with a weight as you can one nebulous scale with another nebulous scale.
Which is to say, not at all.
Then, I guess we’re on the same page? You can average them, but it doesn’t mean anything, necessarily.
So, I guess, then, how is it that you agree with the way the CFAI is teaching that portion? Again, I assume they don’t mention that one needs to think about this first in real life. And, as always, I think they can give you whatever crazy assumptions they want for test purposes, that’s fine, so they can test everyone on a topic in a somewhat standardized manner; I just think it’s a touch generous to say “world class education” when there’s quite a lot of material that’s not done even in a generally acceptable manner (most related to stat, in one way or another).
I don’t recall saying that I agree with it.
Possibly because I don’t agree with it.
Could be coincidental, I suppose.
You’re right I didn’t ask if you agreed with it. I ask if you think it’s a logical position on the part of the CFAI. So, let me rephrase: initially, why did you say you think their position is logical? Unless, I misread that?
Evidently the sarcasm didn’t come through. Sorry.
It’s exactly as logical as averaging a height and a weight. Which is to say, not logical at all.
No problem. In the original post you made to my question, the sarcasm went right over my head! 
After that, I just tripped over myself a few times.
Tickersu,
As mskhan91 said above, you are overcomplicating things. You are assuming we are using arithmetic mean on averaging “ability to take risk” and “willingness to take risk”. That is silly.
The rationale of “balancing” those variables is that both are contrary forces and probably highly correlated. For example, if you do know your investment portfolio is small, you will probably have low willingness to take high risk on that small portfolio. So, below average ability to take risk and below average willingness to take risk results in a below average risk tolerance, simply as that. We didn’t need to compute a utility function and make tests on it. However, not every individual is rational enough to think in this way. If psychological issues are present (emotional or cognitive biases), then the willingness to take risk could be also biased or affected. Suppose now that the investor knows he has a small portfolio but is extremely willing to take high risk. An advisor would recommend an average risk asset allocation, good enough the portfolio is not destroyed and the investor to stick to [the portfolio] the long-term. Obviously math is used for a more “certain average”.
As you see, humans have different personalities and depending on stage of life, profession, country, culture, education, wealth, etc, they [humans] will act differently.
Considering quantitative and qualitative variables in analysis to get a simple, parsimonious solution is really worthy in terms of cost and time. Nonetheless, if we want to philosophize how rigorous are definitions and concepts and how good are education organizations around the world, that is a whole different story.
If you are still doubtful about the correctness of the statement “average risk tolerance” lets make a simpler, more mundane example.
If I ask you: “How are you going with your new girlfriend?” and your response is “Good”, then you are unconsciously averaging qualitative and quantitative variables that, at the end, the response “good” doesn’t mean nothing under your personal thinking framework. When my response is “good” on such a question my brain calculates, remember and processes a lot of variables that are not necessarily continue variables, mixes different types of data and apply an “average” methodology.
No, unfortunately, I’m not. I think for the purpose of the exam it’s okay to make assumptions so people can answer exam questions. In the real world, it doesn’t work the way you’re talking about. People do it your way, but there is a ton of theory and research that shows this is flat out incorrect. Indeed, you are treating it as an arithmetic mean with equal weighting (for this case of arbitrarily combining different variables); it’s totally nonsense to “average” two different variables like that. I’m again saying this is an issue with how the curriculum is taught because I’m willing to bet they don’t even note that it’s not generally correct in the real world to do what they’ve done. The OP asked a completely valid and good question about this. See S2000’s comment on this, too; his point is that you can’t average two things like this, which is coincident with mine.
The implicit assumptions are: differences from below to average to above are equal within one variable; these differences and measurements are equal across the two variables; the variables are equally important therefore the “scores” are equally weighted to give some kind of “average.” This is, of course, nonsensical. The rationale, overall, is poor; they may appear contrary, but you can’t show or argue to what degree; I don’t think there’s a strong argument that ability and willingess to take risk are highly correlated (they might be, but saying it doesn’t make it so).
Sure, if you make a ton of assumptions that are pretty darn silly. See above.
Your examples have only made your post long-winded and seem to miss much of the point. Your last example seems to imply you’re equating the CFAI’s approach to an ascientific and nonrigorous “gut feeling”, which is exactly what is done when someone says “ah, variable A is high, and variable B is low, this person is average despite variable A and B representing different things!” It should be self-evident how ridiculous this argument is in itself.
Again, I’m okay with the CFAI stating this as an assumption to test candidates, but it’s totally hogwash in real life. There’s a reason many people don’t consider social sciences to be “science”; the field is plagued with situations like this (not my opinion, but a general opinion by others).
Final note: If this is “so simple”, tell me, then, the “average” of above average willingness to take risk and average ability to take risk.
In my personal opinion, you are overreacting. There should be literature about the incorrectness of averaging different variables, but just stay alert what are the relationship of those variables and what type they are. If you try to average level of happiness with number of accidents in highways, then you are stupid af. However, talking about the ability and willingness to do something sounds pretty reasonable. Would you try to jump having just 1 leg? I think the “ability” and the “willing” have similar weights for most people, except extraordinary cases.
Again, if we want to be extremely rigorous with everything and forget about the balance of cost-benefit in real life, then we should even reinvent the simplest of things. As I said in my first response, this “average” of different variables is just a preliminary, pathfinder outcome that leads us to a way. I’m pretty sure (intuitively speaking) the correlation between the outcome of a professional or mathematical analysis of the true ability and willingness to take risk for a common individual is [the correlation] very high with the outcome of this average. After this preliminary hint, we can continue to make the formal calculations of return, risk and analysis of investment constraints (which are more important than pointing out if my “silly” average was incorrect or not from a theoretical stand point of view).
I see you just refuse to surrender to your own intuition about the relationship between “ability to take risk” and “willingness to take risk” because you can’t mathematically prove the true relationship of both or their functional shape. In Economics we say: “Ok, I know I’m making a lot of assumptions, but there out exist stupid assumptions and reasonable assumptions”.
In my personal opinion, we are making a reasonable assumption at “averaging” those both variables. Note that both look to be exhaustive at explaining risk tolerance and it is reasonable to think both variables have similar weights in the equation for the vast majority of people. I’m pretty sure my ability to take risk doesn’t extremely outweigh my willingness to take risk, they look to be equally important to me at investment decision making.
You are overcomplicating yourself. I think you may have more important things to do.
In this case, variables A and B are not bananas and bricks. They are the other way around, a good explanators of risk tolerance, so your rigorous (absurd instead) thesis just collapses itself. I know we have to make some assumptions to this to work, but remember they are reasonable assumptions (see above).
Social sciences have a hard work trying to explain the unexplainable, however they are sciences at the end. Just search for the definition of “science” in any book or internet. A question for you: Is quantum physics a science?
A risk tolerance between average and above average.
Just don’t overcomplicate yourself.
That depends on who you believe has defined science; most books or internet sources are written by people without a background in it. The scientific method is founded on the idea that you have well defined and falsifiable hypothesis that can be tested. This is the generally accepted definition by Western standards and probably in most other developed nations, but I don’t have any data to look into that. This is the reason many people argue social sciences aren’t “science” because their research often lacks one or more of those elements. Again, I’m not saying what my view is, but this is the way the argument is posed. So, I would say for the common definition of science (not the Facebook or media definition of science), that quantum physics is a scientific subdiscipline of the larger discipline of Physics. Sure.
Right, which gets to the main point and problem of whether the overall tolerance is closer to average and above average? (Again, assuming those variables even have comparable measurements scales! Which they don’t!) I would look at the different kinds of measurement levels for nominal, ordinal, interval, and ratio scaled measurements for variables. The distinction of what is logical and valid as you move from each category should be apparent; I think you’ll then recognize how silly it is to use a gut feeling to eyeball them, which is what CFAI and you are suggesting.
Since you were attempting to get at examples: Take a random sample of independent investors (ones who choose their own investment product) and look at their investment portfolios. For each look at measures of risk (some kind of dependent variable) for the overall portfolio. Ahead of time you should administer some of these “validated” risk assessment questionnaires that can help describe each person’s ability to take risk, and helps assess their willingness to take risk (both independent variables). Making a composite investment risk score with this might be a better approach to reducing the dimensions from N-measures of risk tolerance to a single number; on that single composite score, then find out what the “typical” composite score looks like since you will see how those two variables actually play into some measure of composite risk taking ability (if we’re assuming it’s manifested in the actual decisions)…
Even this situation would seem to benefit from a factor analysis to look for this hidden construct of “overall risk tolerance” (I’m assuming you remember factor analysis with factor loadings and all that from APT)…by the way, FA is a really popular methodology in the social sciences, for what it’s worth… so they would very likely disagree with the CFAI “simple average” approach…
all of this might be “complicated” but seems a litttttle better to look for structure in the data than arbitrarily slapping our finger on the map and claiming we found the country we were in search of…
You can lead a horse to water but you can’t make him drink…
At this stage, I think that everyone’s pretty much clarified their positions, and further discussion is likely to provide little added value.
Translation: locked.