Value at risk (VAR): Would you buy a car with a faulty airbag!

Value At Risk (VAR) is a risk measure used to determine the probability of a certain percentage loss (or gain!) in the value of a security based on historical data.  Although widely used by risk managers to determine worst case scenarios and handle the risk a firm can take (in a bid to earn more!), it is deeply flawed.

Not because it uses historical data to calculate future risk, but because it assumes that the historical returns (daily. monthly etc.) fall under a normal distribution or bell curve - the one used to fix employee appraisals (another flawed application!).

It is widely documented that VAR models is one of the reasons for why, and the manner in which the 2008 crash  occurred. Watch the movie margin call for a non-technical account or get hold of the book, Alchemists of Loss: How Modern Finance and Government Intervention crashed the financial system!

The title of this post (written by a student of the subject) is a reference to US hedge fund manager, David Einhorn's quote that VAR is "an airbag that works all the time, except when you have a car accident."

Technically, it does not work at any time.

I do not wish to get into the details of the VAR model only to later show that it is flawed. Instead, using a simple measure called the SKEW, will demonstrate why using the VAR is incorrect. Alternatives to the VAR are not intuitive but that is no excuse for using a faulty model.

This is a how a textbook handles this issue:

"The most questionable assumption, however, is that of normality because evidence shows that most securities prices are not normally distributed. Despite this, the assumption that continuously compounded returns are normally distributed is, in fact, a standard assumption in finance".

Terrific! The 'standards'were set by the alchemists of loss!

Let us start with how the normal distribution looks.

Standard deviation diagram.svg
By Mwtoews - Own work, based (in concept) on figure by Jeremy Kemp, on 2005-02-09, CC BY 2.5. The Normal distribution Here μ refers to the average and σ to the standard deviation. "Each band has 1 standard deviation, and the labels indicate the approximate proportion of area".

 

The x-axis will be monthly or daily stock returns and the y-axis the corresponding probability of occurrence.  So VAR can be used to calculate the probability associated with a range of returns.

(1) The peak corresponds to the average return. Notice that the data is distributed symmetrically on either side of the peak. That is the SKEW of a normal distribution is zero

(2) Also, notice how smoothly and rapidly the probability falls off from the peak. Extreme events are extremely rare! Meaning, a Harshad Mehta scam which saw the Sensex shoot up by 270% or the 2008 crash would have such a low probability of occurring that you can safely discount them. Yet as B Mandelbrot writes in his book - the misbehaviour of markets - such events are common enough.

These two are the hallmarks of a normal distribution.  Stock price returns look nothing like this!

Mandelbrot showed the even over a period of several decades, price movements do not follow a bell curve. That his contributions were largely ignored and he was sidelined by the proponents of the modern financial theory*  is another story!

(*) also depends on the normal distribution which makes mutual fund star ratings questionable!

Here is the skew observed in the daily and monthly returns of a few stocks (15 year history).  For an ideal normal distribution, the value should be zero. Even small departures from zero can result in bad predictions.

Stock-returns-skew

It would be foolhardy to bet that these distributions can be approximated as normal and use the VAR model.

Have a look at the monthly returns distribution of Manali Petro Chem.

Stock-returns-distributionNotice that asymmetry (non-zero skew) and the so-called 'fat tail' regions, marked by arrows.

Normal distributions do not behave like that!

As Ramesh Mangal once told me, why choose a model that is exactly wrong? In order to assess volatility, we need to use models that do not depend on the normal distribution assumption.

The upside/downside calculator and geometric information ratio calculator for mutual funds are some of my baby steps in that direction.

What do you think? Would you buy a car with a faulty airbag because it looks elegant?

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5 thoughts on “Value at risk (VAR): Would you buy a car with a faulty airbag!

  1. Shan Rajasekaran

    Excellent article Pattu Sir.

    As George E. P. Box said "Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." Various probability distributions - like random, normal, exponential - all have their use. But when people use it without understanding their predictive abilities and limitations, they cause much damage. In that sense the normal distribution must be one of the most abused mechanised models of thinking.

    Thanks for writing about this and bringing a scientific perspective to a practical problem!

    Reply
  2. kalyan05

    Some times we over analyze. All these models work on stationary processes and we know that market moves are non stationary. That is the reason I believe except alpha nothing matters for mutual funds (in an ideal world even that shouldn't matter). The only principle is that markets most probably do well in the long term so stay invested. If indian indices are proper and there are good index funds that is the best way.
    Infact if you randomly select 1 diversified equity fund every year you will not be far off from the best funds performance (after eliminating bad funds due to external factors, e.g., LIC funds ofcourse). Yes some funds do so bad that they don't recover but they are like that black swan events which other funds also may encounter.
    For stock picking any way it is company analysis and statistics may not matter much. As I don't invest in direct equity can't comment much on that.

    Reply
  3. Abhishek Bhattacharya

    Hi,
    The graph images are no longer visible. Can you please update them? I am checking this on Chrome on iPad.

    Reply

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