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.
- What is the probability that we shall reach 9410 by Diwali
- 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.
I’m completely with you regarding real estate but have given up on explaining it to anyone. I realize it’s *my* waste of time.
But coming to position sizing, it’s a matter of confidence/conviction but I’d rather put it as probability since that’s the only way of meaningfully quantifying confidence/conviction. Now if you have a good system, it’s essential that it gives some indication of the probability also. If your system is only giving you buy/sell calls but not the probability then you need to tweak your system or do some more backtesting to get some sense of probability.
Of course all probabilities and systems are highly prone to black swans, so you always run the risk of everything failing at once … gotta make sure you’re protected against that also.
15+% CAGR is nominal returns in INR not real returns or returns in USD. This is a little misleading if the inflation itself was 10%+
In trading, we always deal with probability. Even if probability of something to happen is 80%, the possibility of it happening r still 50%. This is the way how I look at trading. And that is the reason we all prefer to use SL.
Here in above case 9410 is confirmed means he is too much convinced of it happening. Same was my view at that time. With recent down action in markets, I am changed from confirmed to cautious. But I am still of opinion that 9500 is possible. My basis r, the uptrend started since 6825 is still intact. It will reverse after a close below 8518 spot as per me. So despite down action the probability of happening 9410 r still high as previous low isn’t broke yet, but again possibility of it happening is still 50%.
So how to position urself in this case? Well, because this is very low risk entry right now as ur SL is very near, if u divide ur positions into 4 parts, one should deploy 1st part here as u r testing waters as despite high probability, actually the possibility of happening that is just 50%. Rest 3 parts one should deploy when previous high is crossed and confirmation comes, while trailing the SL.
Now coming to the part of conviction of investing in real estate versus stocks. The chances of going ur property value to near zero r very less and that makes people confident of investing in property. When u want to invest same amount in stocks, u r not sure whether that particular stock will really go up when Index really goes higher. We have always seen examples when despite index goes up, not all stocks go up equally. In real sense actually some of the stocks might be going down as well while index is going up. And perhaps that makes people nervous about investing in stock market despite target and timing r clear. And majority of time property is generally bought for some use which lasts for 20 or more years of usage where fluctuation of property rarely makes anyone nervous.
So volatility of stock market is which makes it less attractive to the people as compared to real estate. I am pretty sure if someone has some funds which they can easily afford to loose and buy stocks out of it and forget and keep them for lifetime, chances of success of such positions r pretty higher as compared to tracking portfolio regularly and disturbing it frequently.
So all in all, somehow stock market carries elements of casino and one can only use the funds which they can afford to loose in stock markets while real estate is lucrative even if u bet ur whole income because of the duration for which it will be used as u r less worried about the depreciation at all if comes.
urban real estate – Limited supply increasing demand. Long term bet (investment). Entry/exit barrier is high and hence low liquidity. Every one wants to own a Makhaan after spending on roti and kapda.
Equity – Ever increasing supply to match demand. Variable demand. Low entry barrier and hence high liquidity.
conclusion : both dwell in different domain. If one has money to invest, the choice is not equity or real estate, it is generally real estate and then others.
Ulag
Well, to pick the bones, split the hair…. I gotta question “What exactly is confidence”, a confidence that supposedly drives the allocation? When you quantify ‘confidence’ the resultant number is simply a ‘probability.’ Even in the dumbest case as “RJ gave me this tip,” its as simple as hoping that RJ’s punching numbers will still give me some profit.
Most people, read traders, come up to the level of analyzing probabilities. “May go up, may not go up” But what truly differentiates awesome traders from wannabes is the risk-management of the position. So, if you have a finite X capital, how will you position yourself for losses. That’s stop loss. But SL is level 1. Its basic minimum common sense. Saving-the-skin risk management. SL protects your corpus, does not by itself grow it. What does protect, is smart and does grow your corpus is the Position sizing.
Position sizing, in my books (haha), simply means that “given this probability and this much of possible loss when I am wrong, how much should I invest?” Fair enough to say, this comes very close to being the HG! Its just too much key of a question not to be asked.
You said it all Sir
>> “given this probability and this much of possible loss when I am wrong, how much should I invest?
Prashanth,
Firstly, its not appropriate to criticize someone using someone’s twit(view) gone wrong. You can always make your point without naming anyone. Have you not hit any stop loss recently due to your signal gone wrong?
Secondly, Property was/is and will remain most favorite asset class of Indians. Buying property in Mumbai is akin to buying a FMCG stock like HUL/Nestle which mirrors inflation, Has lower draw-downs in downturn compared to say equity and above all sentimental value due to Indian culture where in you are looked down if you live on rent. Theoretically our entire population is aspiring to buy home one day.
Thirdly, Position sizing for trading is most difficult decision for Nifty and I can guarantee you will not hit jackpot that easily with the kind of probability of success it has but same is not very difficult with individual stocks as we have seen in case of RJ etc. You buy 5 beaten down stocks based on whatever signal you follow and wait for few years, 1-2 stocks will turn out to be out-liner changing your life for ever.
I agree. Was wrong to pick up a public tweet and we still don’t know whether he will be right or wrong (its still nearly a month away). Have removed the tweet picture.
With regard to my own trading, my last trade was one of a disaster (posted on twitter too, double whammy). But when my system predicts that markets shall move up again, my position size will be similar to the one taken earlier since one bad trade doesn’t change the odds by too much.
RJ / Buffett were great capital allocators first and good stock pickers later. While I have no clue about RJ, Buffett initial letters (Partnership) do make it more clear as to the big bets he was ready to take based on his conviction of the company.
I agree with Brij . In trading risk management is more important. Cut your losses and run your profits. This will grow your trading corpus. Position sizing will automatically come under risk management. For example, I have bought on Friday as I fell panic low of 8558 was tested and a higher bottom @ 8565. Now my sl is 8565. I will hold the calls with sl of 8565 and then I trail.