How much of a stock should I buy ? (how to calculate position size)
This is by far the most important question in investing.
Just think about it for a minute.
Your logic could be completely wrong about an investment and the stock price still can go your way for many other reasons. After all your investment can only go in 1 of 3 directions: up, down or stay "flat".
Nevertheless this calculations are a good starting point.
I should also mention "Half Kelly", half Kelly basically says " Kelly works in theory but you should be careful so as a rule of thumb bet just half of what Kelly formula tells you". In some back tests Kelly formula beats Half Kelly, sometimes Half Kelly beats Kelly. Remember you are calculating odds. You could also go broke using either one of them. But it all depends on the odds, which brings me to my next point.
Just think about it for a minute.
Your logic could be completely wrong about an investment and the stock price still can go your way for many other reasons. After all your investment can only go in 1 of 3 directions: up, down or stay "flat".
Let's imagine you decide to buy an imaginary stock, lets call it "123".
123 is going through bad times but you read the 10k´s, 8Q´s, investigate the new companies president, interview customers and former customers, etc. And your conclusion is that they are going to be able to attract clients again at the same volumes that they did before, they are going through a one time solvable problem.
Today the price of the stock is at $10 and you think that eventually (tricky word "eventually") it will get back to $60+, as they where a couple of years ago.
Here is the irony of the whole matter. As far as you know there could be a little group of gnomes making quote at the other side of your terminal. All you see is a little dot bouncing around your computer screen.
How could the story go? you could be completely wrong in your appreciation. 123 doesn't get their customers back, but in a turn of unexpected events competition goes out of business. Now 123 raise prices and people stayed! You and everybody is perplex, nobody saw that one coming. Then investors decide it's a bargain and jump into your stock... now is trading at a premium than similar companies.. etc. You were wrong on your thesis, still you made a lot of money. There are many more things that could happen that you can think about, because you are only human!
So trying to find reasons for the movements in a stock is mostly an illusion,
On bad days, "experts" on tv open their "bad news" drawer and pull out some explanations, while on Good days they open their "good news" drawer and show you some explanations.
I´m not saying doing your research (we call this process "scuttlebutt") does not work. It does. Just look at the most successful people in investing. It gives you an edge, but maybe not the way you first think about it.
Scuttlebutt allows you to wait and hold when everybody else doesn't, and allocates a percentage of your portfolio that would make those movements significant to you.
What really gives you an edge in investing is
1) long term view (because it allows you to take few quality decisions in a lifetime, and there's less competition there because it goes against human nature to do so.)
2) the size of your position
Academic Study after study show (not that we needed an academic study to get this concept) that the more active you are (the more you trade) the less likely you are to make serious money in the long term, due to fee´s.
Today the price of the stock is at $10 and you think that eventually (tricky word "eventually") it will get back to $60+, as they where a couple of years ago.
"You don't trade the markets....you trade your beliefs about the markets." - Van Tharp
Here is the irony of the whole matter. As far as you know there could be a little group of gnomes making quote at the other side of your terminal. All you see is a little dot bouncing around your computer screen.
How could the story go? you could be completely wrong in your appreciation. 123 doesn't get their customers back, but in a turn of unexpected events competition goes out of business. Now 123 raise prices and people stayed! You and everybody is perplex, nobody saw that one coming. Then investors decide it's a bargain and jump into your stock... now is trading at a premium than similar companies.. etc. You were wrong on your thesis, still you made a lot of money. There are many more things that could happen that you can think about, because you are only human!
So trying to find reasons for the movements in a stock is mostly an illusion,
On bad days, "experts" on tv open their "bad news" drawer and pull out some explanations, while on Good days they open their "good news" drawer and show you some explanations.
I´m not saying doing your research (we call this process "scuttlebutt") does not work. It does. Just look at the most successful people in investing. It gives you an edge, but maybe not the way you first think about it.
Scuttlebutt allows you to wait and hold when everybody else doesn't, and allocates a percentage of your portfolio that would make those movements significant to you.
What really gives you an edge in investing is
1) long term view (because it allows you to take few quality decisions in a lifetime, and there's less competition there because it goes against human nature to do so.)
2) the size of your position
Academic Study after study show (not that we needed an academic study to get this concept) that the more active you are (the more you trade) the less likely you are to make serious money in the long term, due to fee´s.
Fee´s are also compound interest, they just work against you.
Don't believe me? Take 100 richest people in the world and see how many companies they traded? Most of them just hold one, maybe those companies hold other companies in them, but if you look at them you'll find they don't jump around every couple of weeks selling and buying new ones. They stay with what they understand.
Don't believe me? Take 100 richest people in the world and see how many companies they traded? Most of them just hold one, maybe those companies hold other companies in them, but if you look at them you'll find they don't jump around every couple of weeks selling and buying new ones. They stay with what they understand.
There are few people that have made a fortune with many small trades decision but they are not as wealthy and they constantly have to find a new strategy because short term strategies lose their edge and fast.
So finally: how much of a stock should you buy?
So finally: how much of a stock should you buy?
After all, as a small investor this is really what you can control the most.
chances of winning = % winning times = how many time out of a hundred would you win? 30%? 3%?58%?
chances of losing = % losing times = how many time out of a hundred would you win? 30%? 3%?58%?
Multiple of risk = they amount of money you can win divided by the amount of money that is at stake. = $ win/ $ risked
An example with "company 123":
Theory: Kelly formula
% of your portfolio (kelly formula) = chances of winning - (chances of losing/ Multiple of risk)
chances of winning = % winning times = how many time out of a hundred would you win? 30%? 3%?58%?
chances of losing = % losing times = how many time out of a hundred would you win? 30%? 3%?58%?
Multiple of risk = they amount of money you can win divided by the amount of money that is at stake. = $ win/ $ risked
An example with "company 123":
We expect to lose all of our position if we are wrong, that's $10 per share, but if we are wrong we expect to sell at $60 per share. So we divide our possible gain by the amount at risk.
First decide what's that opportunity cost (let say it´s 6%) and how many years you are going be in the stock not receiving this (as we mentioned before 3 years) = 6%* 3 years =0.06* 3 =0.18 = 18%
This works for simple interest... what about compound interest?
(100%+6%)^3 = 1.06^3 = 1.1910 = 100% + 19.10% … so 19.10% every year.
Multiple of risk with opportunity cost = Multiple of Risk - opportunity cost = 6 - 0.1910 = 5.809
Multiple of Risk = Win amount / Risked amount = $60/$10 = 6
*A note on "risked amount": notice that I could risk less than $10, say I only want to risk $3, then I would set a stop loss at $7. Now even though I need to pay $10 for each stock, I only plan to lose up to $3. Then the formula would look like this: Multiple of risk = $60/3 = 20.
So let's imagine that I think there's a 30% chance that 123 can turn around in 3 years.
% of your portfolio = 30% -(70%/6)
% of your portfolio = 0.3 -(0.7/6)
% of your portfolio = 0.3 -(0.1166)
% of your portfolio = 0.1834
% of your portfolio = 18.34%
So there you have it! the theory!... but as the saying goes "In theory... theory works".
In reality we are missing something. What about your opportunity cost?
What is your opportunity cost? how much would you make with your second best idea.
I order to make this more real. we have to add
% of your portfolio = % winning times - (% losing times/ Multiple of risk with opportunity cost)
¿How does Multiple of risk with opportunity cost looks like?
This works for simple interest... what about compound interest?
(100%+6%)^3 = 1.06^3 = 1.1910 = 100% + 19.10% … so 19.10% every year.
Multiple of risk with opportunity cost = Multiple of Risk - opportunity cost = 6 - 0.1910 = 5.809
now lets calculate a more realistic position (taking on account you opportunity cost)
% of your portfolio = % probability winning - (% probability of losing/ Multiple of risk with opportunity cost)
% of your portfolio = 0.3% -(0.7%/5.8)
% of your portfolio = 0.3 -(0.7/5.8)
% of your portfolio = 0.3 -(0.1206)
% of your portfolio = 0.1794 = 17.94%
So what's the problem with Kelly formula? why do I call it theory?
% of your portfolio = 0.3 -(0.7/5.8)
% of your portfolio = 0.3 -(0.1206)
% of your portfolio = 0.1794 = 17.94%
So what's the problem with Kelly formula? why do I call it theory?
Very simple, there are two big assumptions with this:
- you are accurate on your percentages and
- you are able to play multiple times the same probability game. This makes sense when odds are not moving, a game of cards, etc. But in real life anything can happen, and industries are coorelated
Nevertheless this calculations are a good starting point.
I should also mention "Half Kelly", half Kelly basically says " Kelly works in theory but you should be careful so as a rule of thumb bet just half of what Kelly formula tells you". In some back tests Kelly formula beats Half Kelly, sometimes Half Kelly beats Kelly. Remember you are calculating odds. You could also go broke using either one of them. But it all depends on the odds, which brings me to my next point.
"Garbage in, garbage out" - Proverb
The problem is not Kelly formula. I would be more worried about the odds you assign to your results (they are subjective after all).
As a starting point in your research I suggest you should always start (but not finish) with a normal distribution in your head.
2.5% chance of an excellent outcome to your investment
13.5% chance of a good outcome
34% chance of a better than average outcome (tricky.. what is average varies in everybody's mind, But I use options pricing to eyeball the "probability" the market is giving a stock to reach certain price in certain time).
34% chance of a worst that average outcome
13.5% chance of a bad outcome
2.5% chance of chaos
