Predictions, Probability and Position Sizing

Most of us know that Astrology is bunkum and yet that doesn’t stop us from reading what the astrology section of the Sunday newspaper. Reading that does no harm, Right. After all, its more of just keeping ourselves aware or more of a time pass in nature.

Prediction in markets happen regularly and here there are two types of prediction. The Implicit kind and the Explicit kind. Let me explain each with a example.

We trend followers are staunch believers in fact that future cannot be predicted and we can only rely on the past and take signals based on what we believe the trend is. But the moment we make a trade, we are Implicitly predicting that price will move in the direction our trade dictates. If it does, we have caught the right trend and we make money, if it doesn’t, we call it a Whipsaw, scratch out the trade and await a fresh signal for the next trade.

On the Explicit side are strategies such as Elliot which not only spell out where the markets should / shall go but also the time frame within which it will reach such a target. Take for instance this prediction by Mark Galasiewski, a very well know Analyst from Elliott Wave International

On April 13, 2009 speaking with CNBC TV18, he made a very famous predicition

See Sensex at 100,000 in 15 yrs: Elliott Wave International

The prediction contains two elements required to make a trade. A target price and the target time. Given these two parameters and assuming you have confidence in the said analyst, the next question would be, “How much to Bet”

On the day, he made that call, Sensex was close to 11,000 mark and hence this prediction if it were to come true would mean a CAGR return of 15.85%. Here is the thing, 15.85% isn’t extraordinary returns.

CAGR Returns since Inception of Nifty Bees (then managed by Benchmark and now by Goldman Sachs) is 16.62% (as of Aug 2016). While we don’t know whether the next 15 years will provide similar returns, we at the very least have a number we can work with.

In April 2010, Chris Roberts of Mizuho Securities Asia Limited made a similar prediction, this time we have a chart providing us a better guideline as well

But lets go back to 2009. Markets are down but definitely not out and you believe in the said analyst prophecy. So, what next – Buy Nifty / Sensex would be the way forward – but the bigger question is, how much to bet. Should you bet 10 / 20 / 30% of your existing portfolio or go all out and bet 100% or go still further, Sell your House and invest everything?

The reason why people are so attracted by Real Estate is due to not the percentage of returns (which has been good till very recent times) but the amount that one sees as the outcome. But unlike stocks, in real estate, the minimum required is way higher.

When people invest into houses / land, most of the time they are betting way more than 100% of their networth (since most go with a loan, its actually multiple times their networth). Would you do that with Sensex or Nifty (lets not take stocks since we all know that not all stocks are the same) and if not, why not?

The biggest fear is the fear of not knowing what the future holds, especially decades from now. While the same risk exists in Real Estate, we comfort ourselves saying that even if the worst happens, I still will be able to hold onto the asset.

Its a fact that most world markets have at some point or other seen a 85% draw-down from peaks. While our data (public) exists only from 1979 and has a max draw-down of around 50% thrice and in those times, even the guy who has strongest belief may find it tough to hold onto his investments let alone add.

A fun fact (Fun b/c I am not sure about the source of the data): Indian markets fell 73% from their peaks of 1920 and recovered only by 1945 (25 years).

Lets cut back to our original problem. If we have a forecast, how do you action the same? This question was what engrossed me in a twitter match when I replied to a particular prediction by a Analyst who is the head of Research at a major brokerage firm

There were essentially two questions that I posted.

1. What is the probability that we shall reach 9410 by Diwali
2. Based on that probability, what should be the position size of the same.

The analyst who made the above prediction came back with the following reply

“Isn’t position sizing matter of capital allocation and risk appetite rather than probability of success?”

In my opinion, probability of success is what should drive capital allocation and not the other way round. In the above example, I based on distribution of returns calculated that at best there was a 11% probability of 9410 coming into play in the next month. Using VIX, Vasishta (@Uptickr) gave a even lower probability of 5%.

Given the above numbers, what should be your bet size. Do note that since the original forecast was made, the markets are down 4% (target was 5.5% approx) making the original prediction look like a one to one on a risk reward basis

So, why is position sizing important? As @ReformedBroker tweeted the other day,

Replace the word hedge fund manager and place yourself there. What do you spend the maximum time upon?

Selecting the right securities are betting big when you think you have found the one that will provide the returns you think you deserve.

Switch on the Idiot Box and all you can see is analyst upon analyst predicting either where Index would be n days from now or which security should one buy.

Probability of Returns is always two sided. One way to calculate the probability of returns is to use Chebyshev’s Inequality, but that will still give you the probability of returns and not provide you with a way to determine how much position size should be taken based upon the historical reliability of your signal.

The simplest position sizing when you are dealing with a portfolio of stocks is to have uniform capital allocated to each and every pick.

But what if you are trading a single ticker like Nifty or Bank Nifty and come across predictions such as the one above? How do you decide how many contracts to buy for every Signal?

With Deepawali coming up, every Television channel will be pulling up every analyst they can to provide them with a view on the coming year and a list of stocks that investors should buy for the year ahead. So, should you go ahead and buy those stocks and if so, once again, how much should you be betting?

As Investors and Traders, we love predictions and if you are on Television, what better way to get noticed than make either a very dire forecast (like Marc Faber does every year) or make staggering bullish forecasts that once again make news.

While I have no idea if anyone has created a data set of predictions by brokerage houses and the error ratio’s, out in United States, Salil Mehta writing his blog Statistical Ideas, provided a humongous amount of data and aptly named the post as “Strategists: full of bull“. If some one were to do a similar anlaysis in India, I don’t think one would find any major difference in the hit rate of such predictions.

The key to position sizing in any asset class / stock / index / sector is conviction. Think of a experiment you can try out at home. Announce to your family members that you have 20 Lakhs with you and will invest that into buying a 1 Crore property (by taking a loan 4x your investment). If you are part of a normal Indian family, you should receive more queries on property than query on whether it makes sense financially taking such a big loan.

Now, what if a few days later say that you have dropped the idea of buying the home but will invest the same into market (remember, no loans, only investing what you already have saved). The reactions now will be way different and more or less you will be taken as a gambler who is out to destroy his savings.

The difference comes from the conviction we folk have in Real Estate / Gold vs investing in Equity. Conviction cannot be build while having faulty premises that fail at critical times.

Postscript: Thinking deeply, felt that unfair to name a single individual just because I was engrossed in a debate with him while the rest of the guys get a free pass. I have hence removed the tweet. My Apologies.