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Luck | Portfolio Yoga

Expectations, Probability and Reality. Can you really make 100 Crore by Investing 10 Lakh

Most kids coming home from their exams don’t expect anything less than a First Class. Parents don’t expect anything less than their ward getting into the IIT’s of the world. Investors assume that they can easily generate returns that would put even Warren Buffet at his prime to shame.

On Twitter, experts for most of the time seem to showcase how great their stock selection / trade selection was – look at how the stock bounced right off the support. Fundamental biased investors generally are eager to show how easy it was to know that the stock was a fraud, post the event even though when the stock was actually doing far better than the market, there are few sane voices questioning the same with data.

When the market was running up in the years prior to 2018, Mutual Fund managers were more than happy to show how great investing is. Now that the Large Cap Index in itself is still doing good but stocks have crashed, the excuse is that it’s “darkest before dawn”.

The reason investors aren’t able to stay the course is not because they are greedy or lack discipline but because they were misled on the expectation of the returns they could achieve for the risk they took.

Thousands of home buyers today have either paid or still paying for houses that may never be delivered. They weren’t greedy other than being dreamy about owning their own house – they were misled when it came to the risk they took when they signed on the dotted lines.

On the very long term, markets have gone up and hence if you keep investing, you will do well is the mantra of every analyst in town.

Take a look at the chart below – this chart is the Total Return Index of S&P 500 since 1871. The growth is just amazing with hardly any drops.

But the reality wasn’t so easy queasy. Can you see the small dip during the early 1930’s? Well, that was what is today known as the great depression. A famous pic from those times

By the time, the low was made, the Dow was down a preposterous 89% from its peak. US hadn’t seen a crash of that magnitude before or later. Yet, the Index recovered and those fortuitous to be holding on to the survivors would have made it back. But do we really expect ourselves to survive such a carnage without a change in the way we invest?

While the Bombay Stock Exchange is the oldest stock exchange in Asia, we don’t have data on stock prices of historical years. Sensex which is the bell weather index came into life only in 1986. Since 1986 to today, the Compounded Growth rate has been 13.50%.

To make that 13.50%, you should have been able to participate in the Sensex for the last 32 years and going through long periods of negative return. In other words, you would have been required to be a Saint. Of course, all this is theory since there was no easy way to participate in the Senex other than to construct the same on your own in the same weights. The first index fund came into life only in July 1999.

Acclaimed Guru and Stock market expert, Ramesh Damani recently gave a talk with the clickbait topic

How to make 100 crore by investing 10 lakh: Ramesh Damani

He talks about the huge advantage of starting to invest early and has the following side

Staring to save early is good but does that really provide the edge. There are two things worth noticing in the slide – One, the period of Savings and two, the small number at the last which says “Interest Compounds at 15%”.

Sensex has compounded at 13.50% and since this doesn’t include Dividend Yields which can come to 1%, 15% seems pretty much achievable. But does the static convey the real picture?

While I don’t have data on Sensex PE in 1986, in January of 1991, Sensex was trading at trailing four quarter price earnings ratio just below 10. We have seen this low a number only once post 1991 and this was in 1998. Neither the crash of 2000 nor the crash of 2008 brought down the market to such a cheap level.

Ramesh seems to have taken the 15% number from Sensex of the past 30 years. But the larger question is whether the last 30 years is representative of the next 30. No one knows how the next 30 – assuming you are saving for your retirement will generate.

But was Karishma really able to out-perform Kareena? Lets run it through real Sensex numbers to see how they performed. Remember, Karishma saves for just 7 years while Kareena saves for 27 years. If both invested in debt yielding 15% CAGR, this holds true – but markets don’t give out 15% or even 13.50% returns year on year.

Since we have only 33 years of clean data, lets give Karishma the first 7 years (1986 to 1992). For Kareena, we shall start investing in 1992 and invest till 2017. So, how do they fare by end of 2018?

Karishma has invested 50 thousand for 7 years which is equal to 3.5 Lakhs. This is now worth a fabulous 1.58 Crores – in other words, her investment has generated a XIRR return of 14%.

Kareena started off in 1993 and invested until 2017 for total investment of 12.50 Lakhs. Her current value is a mere 70.50 Lakhs. XIRR comes to 11.50%.

So, what happened. How did Kareena beat Karishma even though she invested for a longer period and through multiple bull and bear markets? Is this all the magic of Compounding?

The reason is simple – from when Karishma started to invest till date, index had a CAGR growth of 14.13%, for Kareena this number comes to 10%. In other words, much of the difference can be accounted by the timing.

Karishma started to invest when Sensex was around 500 levels and ended her investment when Sensex was around 2500. For Kareena, the start point was at 3350 and ending at 34,000.

Since both of them investe in the same instrument, we can get a better understanding by looking at how many Sensex units Karishma got for her 7 years of investment and how many years it took Kareena to accumulate the same.

Karishma over the seven years accumulated 440 Sensex units (Investment divided by Sensex). Kareena was able to accumulate just 195 Sensex units over her entire investment.

It’s similar to someone investing 50 thousand in Eicher Motors when it was a small cap stock versus investing 50 thousand when Eicher became a large cap. Return generated by the early investor is tough to match. As the adage goes, the early bird get the worm.

Personal Finance blogger, M. Pattabiraman had a very interesting video where he showcases how timing can influence returns for SIP’s.

Mutual Fund SIPs will not work without luck!!

Given what we now know and understand, what then should one have expectation of returns. Let’s assume if you were to invest a sum of money with a horizon of 10 years, what expectation you should have at the end of 10 years.

A lot depends on where you invest, but for simplicity sake let’s assume that you invest in a large cap fund that shall mirror Index returns.

Lets start with a much smaller time frame than 35 years – 10 years is seen as Long Term and if we can get things right in this time frame, we may as well have a chance to get things right on the longer time frames as well.

For this analysis, I shall use Nifty 50 weekly data which starts in mid 1990. Using weekly gives me more data points than monthly and hence better granularity. What is the range of returns we have seen for a period of 10 years?

The answer is that it can range between a negative 1.60% to a positive 20.28% with average return being 11.65%. That range of returns is just too wide to use it for figuring out how much can we get for our investment ‘n’ years later.

Here is a chart that plots the data (n = 959).

How to read the chart?

The chart showcases the percentage of weeks where investment would have yielded the returns as shown in the Horizontal (x-axis). To get a better measure, you can simply cumulate to the bar you think is the return you need and subtract the same from 1. This is your probability of getting such a return.

So, the probability your return is greater than -1.58% will be 99.69%, the probability that your return would be somewhere near 20% is 0.52%. If you were to take a view of a coin toss, the 50th percentile so as to speak will lie at around 13%.

While just blindly investing in a growing market will at some point of time provide you with strong positive returns, the inability to project the same can hamper our ability to stay the course. When we are hit with draw-downs, the last thing we calculate is that if the current return is well within the overall bell-curve of returns possible.

Assuming that 6% is the minimum returns we wish to generate from equity, what were the historically bad years to start a 10 year investment in Nifty 50?

We had 156 weeks where investing would have yielded a return of less than 6% after 10 years. The worst years to invest were 1994 followed by 1993 and 1992. Compared to this, 2007 / 08 which too makes a presence was a walk in the park. Investing in almost any day of 1994 and greater than 80% of the days of 1992 and 1993 would have generated returns below 6%.

Comparatively, just 7 weeks of 2007 (bunched around November and December) and 2 weeks of January (first couple of weeks) were the worst weeks.

As much as we think we know the future, it’s one thing to know and quite another thing to live through the same. Draw-downs take a toll not just in terms of money lost (notional or not) but also has a massive impact on our confidence.

The great Stephen Hawking was diagnosed with ALS when he was 21. This being a non-curative disease, Doctors at that time gave him a life expectancy of 2 years.  He lived for 53 years more.

In an interview to New York Times magazine in 2004 he said

“My expectations were reduced to zero when I was 21. Everything since then has been a bonus.”

From Warren Buffett to Rakesh Jhunhunwala to Ramesh Damani, I doubt anyone invested with intention of using the proceeds at the end of ‘n’ year for specific purposes. Having zero expectations from your investment in markets can be tough, but if you were to accept that, the task of becoming a better investor becomes easier for nothing the market throws at you will impact you negatively.

 

Trading System Performance – Skill or Luck

So, you have finally devised your trading system which seems to have produced good returns in the back-testing you have conducted and is ready for trading with real money. Pat yourself on the back since regardless of what happens next, you have taken a step towards being a better trader by using a rule based strategy than implementing a discretionary strategy where every rule has a exception and every failure is easily rationalized.

By accepting that we have our limitations which can prevent us from succeeding in markets, we are able to make our trading more process driven and one where mistakes aren’t rationalized but seen through the eyes of it being either a part of the system or the failure of the system. Either way, the results showcase how good or bad your system is (assuming you take every trade and do not try to over-ride your own system).

While a back-test is a good way to analyze as to whether the system has any merit or not, it is not the end of testing but actually the beginning. It is said that if you were to give typewriters to monkeys, its just a matter of time before one of them hits all the right keys and gets you a Shakespeare’s plays in order.

Or as the character Dr.Alfred Lanning in the film I, Robot says “Random segments of code, that have grouped together to form unexpected protocols”. If one keeps testing ideas, especially using optimization feature, one is bound to hit the right system. Its just a matter of time.

The question hence is, is the system performance due to Skill or pure Luck. A system that is based on some skill or market  inefficiency. A system that is based on luck is one where in the streak of profits is just purely driven by luck and its just a matter of time before the said system starts misbehaving.

So, how does one determine whether the profits that are shown in the back-test is due to it being inherently good or just a matter of luck.

There are a few ways to analyze that and I shall lay out a few of them out here. To start with, let me choose a system which will be used for the testing.

The system that I shall use for the test below is a EMA Crossover. To get the two parameters, I ran through a Walk Forward Optimization which finally gave me the 2 variables I was after.

Now that the main requirement is fulfilled, lets move onto what are the ways by which you can detect whether the performance of your system is more based on luck than skill.

The first thing to do is to test your system on other time frames / markets. No single system performs exceptionally well in all time frames / markets and hence if you are looking for a 100% score, you are bound to be disappointed. What we are looking instead is performance that is well within limits.

Lets take the EMA Cross system that we have now created. The testing was done on Daily time frame. Lets compare this to Hourly as well as Weekly and see how different the numbers will be. To keeps things simple and as well as have a standard format, we shall use Expectancy as the parameter to judge. Time frame of the Test is from 1st Jan 2010 to 1st Jan 2015.

Other test settings are

  • We trade on Close Value
  • No Commissions or slippage is included.
  • We do not compound our position size
  • We take both Long & Short trades (Always in the trade)

We shall first test the system on the Daily time frame. While the optimization was done on CNX Nifty (Spot), we shall see how the system fares on other Indices

Index Time Frame Expectancy
©Portfolio Yoga
Nifty-F1 Daily 25.84
Bank Nifty F1 Daily 212.42
CNX Auto Daily 87.64
CNX Commodites Daily 10.83
CNX Consumption Daily 16.04
CNX Energy Daily -28.55
CNX Finance Daily 95.2
CNX FMCG Daily 82.34
CNX Infra Daily 21.56
CNX IT Daily 22.04
CNX Media Daily 24.48
CNX Metal Daily 28.9
CNX MidCap Daily 255.5
CNX MNC Daily 52.34
CNX Pharma Daily 4.87
CNX PSE Daily 57.34
CNX PSU Bank Daily 98.52
CNX Realty Daily 5.45
CNX Service Daily 23.82
CNX Small Cap Daily 98.66

The system is profitable in most indices save for CNX Energy where it saw a loss. This is good since it indicates that the system is not curve fitted to Nifty.

We shall now move to testing the system on hourly data.

Index Time Frame Expectancy
©Portfolio Yoga
Nifty-F1 Hourly 7.07
Bank Nifty F1 Hourly 17.9
Reliance Hourly 0.87
State Bank of India Hourly 1.09
ICICI Bank Hourly 0.21
Tata Motors Hourly 0.89
ITC Hourly -0.24

 

 

Once again the system trumps (though if you were to observe closely, expectancy is in dangerous area for stocks such as ICICI Bank & Reliance while it out right loses money on ITC.

While we cannot decide based on above data as to whether the system is good or not, what it does show is that there is some amount of skill and its not entirely due to luck.

We next move back to Nifty F1 on Daily time frame and test the result using the Bootstrap method as well as Monte Carlo Testing.

The p-value using Bootstrap for Nifty F1 (Daily) comes to 0.55 which is way above the null value requirement of 0.05 to reject the thesis that the results seen above are based on random luck. In fact, the 0.55 number indicates that 55% of the result probability is just due to random luck and no more. This is pretty damming evidence of the fact that while our system seems to perform great, it actually is nothing more than a lucky streak.

Lets move forward and test our hypothesis using Monte Carlo Analysis. Once again, we are looking at the whether our result is based upon blind luck or is there something worth while.

Before we get into Equity Curves, lets compare and contrast a few other details.

In our regular back-test, we get a max draw-down of 19.70%. In contrast, the 95 percentile says that the probability is high that we may see a draw-down as high as 60%.

In our regular back-test we see a maximum losing steak of 7 trades while in the Monte Carlo approach, the figure comes to 20

And finally, lets look at  the various ways in which our equity curve could have been plotted. We ran a total of 10000 stimulations and as expected, chart is messy. But what is does show is the high probability (test of the lower line) of the system losing more than 50% of capital and hence running out of capital.

Eq

But should we be surprised with the answer that this system is not suitable for trading since far too many trades hinge on luck than actual skill?

Too many traders believe that one can come up with great system by just optimizing data. If only life was that simple, we would all be chilling out in our favorite place while the system kept earning for us without a sweat 🙂