Sunday, February 21, 2010

The Ultimate Risk Analysis

 Playing the Expectations Game !

What are your expectations from the trading business? It is a business where extraordinary profits are possible. (That is why we are in it.)  But the question is why extraordinary  profits are possible in trading. It is because it is a business where extraordinary losses are also possible.

After all, the business of trading, especially the derivative trading is a zero sum game! A trader's profits are another one's losses. If you are to consider the considerable costs of trading, which adds up to substantial sums over a period, it is actually a negative expectations game!. It is always better to have a realistic understanding of the  eventualities one may encounter in the business to avoid the risk of ruin. Therefore, here are some of the  pieces of advice or rules I have picked up over a period,  even  though  the sources and the contexts have been forgotten.

You  can  pick  any  one  of  these rules or all  of  them!  They  are  all different  but  they are  all  saying  the one thing !!

  • Expect the unexpected !
  • If anything can go wrong, it will  !!
  • Hope for the best, but prepare for the worst !!!

All in a day's Trade
We are all normal people. As we are normal, we expect a normal trading day, OK! The Nifty may trade higher, lower or do both and close higher, lower or end near the yesterday's close. As normal people our memory spans are also short. We have a tendency to forget the times on which the liquidity dried up completely on the one side of the trade and the index moved one way beyond all expectations.  Therefore, let us refresh our memory or load it afresh with some real history. Here comes the Nifty history which explains why the above high sounding cliches are applicable to trading.

S&P CNX Nifty - Daily Returns in Per cent
( On a daily close to close basis )

Chart 1

The above is the graph of daily returns obtained by the S&P CNX Nifty index calculated as a percentage change over the previous days close. Here are some observations about the chart.
  •  Volatility increases and decreases in clusters.
  •  Large negative returns are accompanied by large positive returns in the cluster and vice versa.
  •  Most of the daily returns are confined to a +/- 5 % range.
  •  There are significant numbers of  extraordinary returns in the data.  That is, Nifty is capable of making extraordinary movements in a day's time. 
  • Some of these extreme movements were the result of one-off events like the general election results in 2004 and 2009.
The three extreme data points of both, the positive as well as the negative returns during the period are shown in the following chart.

S&P CNX Nifty - Highest Three Positive and Negative  Daily Returns

Table 1

 S&P CNX Nifty Daily Returns ( + / - Signs Removed )

Now let us see the above data from another angle by removing the positive and negative signs from the data to get an even better view of the daily movements on a close to close basis.

Chart 2

The above chart reiterates our earlier observations. So far we have examined the Nifty on a daily close to close to basis. However, such an analysis is more suitable for investors than the traders.  It is seen that the close to close to analysis eliminates the intraday extremes of the index and those extremes are more pertinent to traders, especially to those who have to manage their intraday risk and use stop losses. Therefore, let us use a technical analysis tool called the True Range ( TR ).

According to the Wikipedia the True Range is a technical analysis tool developed by J. Welles Wilder. and the following is a copy of it's description from the Wikipedia.

"The range of a day's trading is simply high − low. The true range extends it to yesterday's closing price if it was outside of today's range.

Or, in plain English, true range is the largest of the
  • most recent period's high less the most recent period's low
  • absolute value of (the most recent period's high less the previous close) or
  • absolute value of (the most recent period's low less the previous close)."
S&P CNX Nifty Daily True Range ( TR ) 

The following chart shows the daily true ranges of the Nifty index for the same period.

Chart 3

Here are some basic observations made after a comparison of the daily returns chart (without the + / - signs) and the true range chart :
  • There are more extreme data points in the TR chart than in the daily returns chart.
  • There are eight TR values which are higher than 10% in the TR chart whereas there are only three similar values in the daily returns chart.
  • The TR data points are significantly higher than the daily returns chart and therefore a Nifty futures trader is susceptible to significantly higher risks.
The three extreme data points of TR both the highest as well as the  lowest during the period are shown in the following chart.

S&P CNX Nifty - Highest and Lowest True Range Values

Table 2

Now, how much is the margin for the Nifty futures? On an average it is around ten percent. It doesn't require much extrapolation to find that on all days the index has returned a TR of ten percent or more , at least one side of the traders would have lost their entire margins. The brokers would start their margin calls and by the time the trader either remits the margin or the broker squares off the position the losses might have become even higher. I have seen people becoming frozen or paralyzed and incapable of taking  any decisions on such days. Thankfully the broker  takes the decision and squares off the positions but mostly at the worst possible prices.

As we have seen the worst let us see what is the normal or 'the new normal ' values of daily returns and the true range. The following table shows the average, median and the geometric mean of both the daily returns and the true range for the sample period.

S&P CNX Nifty - Average, Median and Geometric Mean of Daily Returns and TR

 Chart 3

It is observed that the geometric mean of the daily returns and the average, median and geometric mean of TR are nearly identical at around 2.6 % of the previous day's closing value.

What are the key takeaways from the above statistics? They are very simple.

  • Don't take big leveraged positions in the market. Even small positions can lead to extraordinary  losses in trading.
  • It is better to avoid market turmoil due to the expected event risks like election results, union budgets etc by keeping no positions or only positions of long options.   
  • Trading is a business in which any skills or advantages of a trader is used by him to build substantial profits over a period and not a wham bam game.
  • Even if a trader is using all the risk control methods described in the page named Position Limits, the trader may be susceptible to significantly higher risks due to totally unanticipated events or any other reasons. Therefore, keeping a part of the trading capital as a reserve is a prudent option.
The Tail Piece

Is it mandatory to have tail piece towards the end  of any discussion?  Even if it is not mandatory or  if it is totally unnecessary, I am having an inclination to add  a tail piece. Because, there is a very apt tail piece available! 

Here is a new job description. Measure the heights of 2775 people ( equal to the sample size of the trading days ) randomly and pass the collected  data through the processes we used for analyzing the Nifty closing prices. We may find that the average, median and geometric mean of the new data may fall anywhere between five or six feet. This is comparable to similar values obtained by us with respect to the Nifty in the Chart 3.

However, the question is whether we will be able find people with heights of seven to nine times the average in the sample or anywhere else. But why?  For example the true range is having an average  of 2.63 ( Table 3) and an extreme value of 22.55 ( Table 2 ) and the ratio between them is 1: 8.5. Anyone knows that finding a human being with a height which is  8.5 times the average is an absolute impossibility. Statisticians say that the data like the heights of people is distributed normally. It simply means that most of the data points will be near the average and chances of finding a 45 feet human being is impossible.

Statisticians say that financial data series like equity  prices or indices have long tails. This simply means that  most of the  data points when plotted on a graph will fall near the average but some of the data points will be very far away from the average and those points may  look like long tails in the graph !!

That brings us back to question of whether the discussion needed a tail piece. And it is settled now !
Beware of long tails in trading !! And sometimes the tail may wag the dog as well !!!

Cheers and Prosperous Investing and Trading!!!
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