Satish Joshi

Mathism” – A word I coined to represent the tendency of forcibly converting everything into and justifying everything by, a mathematical equation, just to lend respectability to an argument or a proposition, even when the math is forced, dubious or based on unrealistic assumptions. And having done that, holding that math as the primary goal or the primary representation of reality – while (conveniently) ignoring the gulf between reality and math.

Why did I start talking about it? Well, I will come to that shortly. Until then just hold that thought!

The single biggest fear that every investor has is that he/she is at the mercy of the market over which he/she has no control. The markets decide whether his/her assets multiply or whether they are destroyed, and he/she can do nothing to influence the market to behave in ways that are beneficial to him/her.

While that is true – in the sense that an ordinary investor has no control over how the market may behave. However, there are ways to mitigate the risk that market volatility creates for the investor and a competent and honest professional advisor is usually able to guide an investor to navigate those ways successfully.

While our rational brain understands that, the emotional part of our brain which usually dominates the decision making of even the most rational person, cannot rid itself of this primal fear.

Clever advertisers know that. Most advertising of financial products and services therefore often single-mindedly targets this primal fear. At the same time, they also know that most investors are generally in awe of mathematics and mathematician – just the words create an impression of infallibility.

And of course, that is true too. The rigor in the field of mathematics guarantees that any assertion that has been proved by using rigorous rules of logic, is true for all time to come. What we often fail to grasp is that the words “True” or “False” mean something completely different WITHIN the world of mathematics. To quote the immortal words of Bertrand Russel (I think ALL education of Mathematics in ALL centers of learning, should start with this sentence)

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. […] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

In other words, something that has mathematical validity may not be valid in real life, and in fact most often it will not have even the remotest connection with real life. Talking of its Real-life validity or significance itself will then be meaningless!

And once again the emotional part of our brain often refuses to digest this!

All this played in my mind recently because I saw an advertisement of some fund that claimed that it uses a “Mathematical model which automatically balances its portfolio in response to market ups and downs to deliver optimum performance”. The message that was not stated but implied was “And therefore you do not have to be afraid of being at the mercy of the markets AND because its Mathematical, it cannot fail to perform!”

You will find a lot of mutual funds whose promotional material often contains very similar claims. What is not clear to me when I read such statements is – there are many words in it (highlighted in bold letters above) which are very vague and unless they are defined precisely, you cannot determine whether the claim is true or not. I am not rejecting these claims outright but nor can I accept them because of the lack of precision in describing what exactly they are promising to deliver.  In the absence of such precision, you cannot find evidence to either support or reject the claim!

So, let’s talk about the three imprecisely defined words.

Mathematical Model:

What exactly does it mean in the context of a mutual fund? How closely does it resemble or behave like the real system or phenomenon it is supposed to be a model of? What assumptions must hold for the model to actually mimic reality with sufficient fidelity to be of any practical use? As analogy consider a model of a building to be built (architects often create such models). Let’s assume that is an exact scaled down version of the building to be built, constructed using exactly the same materials that the building will use. Such a model will give you a high-fidelity experience of how the building will feel like from the outside. Will you be able to experience the view that you will have from the living room of your to be constructed flat in the to be constructed the building? No! Then what if for you the key deciding factor to purchase a flat in this building is not the exterior view but what you will see from your living room? Then, how-so-ever well-constructed, this model is of no use to you! No model of any kind can ever capture reality with 100% fidelity (if it did, it will not be a “model” it will be reality itself). Most models will leave out attributes of reality which the designer of the model considers not relevant for the purpose. We do not know whether the mathematical models which supposedly drive these funds in fact capture all the attributes of the reality that are important to US (not to the designer of the product)!

That brings us to the next two words in bold in the description above, because my interpretation of the description is that the model is designed to achieve what these two words represent and therefore attributes of the real world which can influence what these two words represent, have been captured in the model:


My interpretation of the description above is that the model “Automatically” achieves the “right balance”. By definition “Balance” should mean achieving an optimum trade-off between two conflicting factors or attributes of reality. Usually in the context of investments this phrase is used to indicate a trade-off between Risk and Returns!

Assuming this is what they mean, it still does not quite answer my questions – which are:

1. There are celebrated, Nobel price winning “mathematical” models (Like Markovitz’s) for doing exactly that. What is the reason for creating yet another one and it is really “improving” on all of those in some manner? If yes, why not explain what the improvements are, that will only lend more respectability to the claims!

2. The term “Returns” is unambiguous enough. But what is this “Risk” that is being balanced? Risk of what and to whom? Again, most often in the context of investments and financial markets, the word “Risk” stands for historical fluctuations in the value of the asset in question and is usually quantified (which is necessary because the mathematical model cannot account for risk unless it is quantified in some manner) by some statistical measure like standard deviation.

The point however is, the word “Risk” to me as an investor, means the possibility that I will not meet my financial goals! I couldn’t care less about the standard deviation or anything else if my financial goals are met. The “Balance” therefore should be between My risks and My rewards and not “Market Risks and Market Returns.” But the fund cannot do that without even attempting to capture my reality (and not market reality) in its mathematical model!

And that brings us to the last word which I had highlighted.


Optimum” with respect to what? Like “Balance” the word “Optimum” is meaningless without a context. Like “Balance” It too implies a trade-off between conflicting requirements and an “Optimum” solution is one which the best one can do, given the negative and positive forces which countermine each other in a given situation.

Does its usage here then mean that the mathematical model finds the best solution given my financial needs and my financial constraints?

How can it, given that my needs and my constraints are not factors in the mathematical model that is finding the “Optimum”?

The point is – These funds may actually be a good investment for you. But not because they are driven by a mathematical model because clearly that model has no knowledge of what you need and what your constraints are. To determine if indeed one should invest in them, one must look beyond the hype. And ask questions such as – Do you need to invest in the type of asset it represents or are you more likely to meet your goals by investing in other types of assets instead? If yes, then is it the best example of its type? Or talk to an honest and competent advisor who may be in a better position to give you the answers to such questions.