Position sizing and risk: the maths that keeps you in the game

Two investors can own the same shares, buy them on the same day and end the decade in completely different places. The difference is rarely the shares. It is how much of each they held, and what they did in the one bad year. Position sizing is the least glamorous subject in this course and the one that decides whether you are still around to use the others.

The arithmetic nobody shows you

Losses and gains are not symmetrical. Lose 10 percent and you need an 11 percent gain to get back to where you started. Lose 20 percent and you need 25. Lose 50 percent and you need to double your money just to break even. Lose 75 percent and you need a 300 percent gain, which for most people means the money is gone.

If you lose	You need to gain back
10%	11%
20%	25%
33%	50%
50%	100%
75%	300%

This table is why survival comes before returns. A portfolio that avoids the 50 percent hole does not need to find the 100 percent recovery, and the people who compound money for decades are, almost without exception, people who never had to.

Decide the loss before the purchase

Here is the discipline in one sentence: before you buy anything, decide how many rupees you are prepared to lose if you turn out to be wrong, and let that number set the size.

The common rule is 1 to 2 percent of your total capital per idea. With 5 lakh rupees, that is 5,000 to 10,000 per position. Now the position size falls out of the arithmetic. Suppose a share trades at 500 and the chart work from the Intermediate course suggests that below 460 your thesis is broken. Your risk per share is 40 rupees. Divide 5,000 by 40 and you get 125 shares, a position of 62,500 rupees, about 12.5 percent of your capital.

Notice what the formula does when the stop is wider. If you decide you are wrong at 400, the risk per share is 100 and the position shrinks to 50 shares. Volatile shares get smaller positions automatically. That is the point. Traders formalise it with a volatility measure such as the average true range, but the principle needs no indicator: the wilder the thing, the less of it you hold.

If you do not use stops

Many long-term investors never set a stop loss, and that is a legitimate choice if the research is real. They still need limits, just different ones. Cap any single position at 5 to 8 percent of the portfolio at cost. Cap any sector at 20 to 25 percent. Hold enough names, somewhere between 15 and 25, that one disaster is a bruise rather than an amputation.

And count correlated holdings as one bet. Three private sector banks are not diversification; they will fall together on the same RBI announcement. Two IT services companies are one position in the rupee and in American corporate spending. Ask what single piece of news would hurt several of your holdings at once, and treat that cluster as one position when you apply the caps.

Expectancy, or why the hit rate is a trap

People judge a method by how often it wins. The number that matters is expectancy: the win rate times the average win, minus the loss rate times the average loss.

A method that wins 40 percent of the time can be very profitable if the winners average three times the size of the losers. A method that wins 80 percent of the time can be ruinous if the losers are ten times the winners. The second profile is exactly what selling options produces, which is why the Advanced lesson before this one dwelt on it: a long row of small green months, then a single red one that takes them all back and more. Write down your last twenty decisions and compute the expectancy. It is more honest than your memory.

Leverage changes the rules, not just the numbers

Everything above assumes the worst case is losing the money you put in. With margin trading or futures and options, that assumption breaks. A 3 percent gap down in a stock future held on 15 percent margin is a 20 percent loss on your money before the market has even opened for you to react, and if the gap is 15 percent the broker’s call arrives before breakfast. Forced selling at the worst possible price is how leverage turns a bad week into a permanent one.

The 1 percent rule still works with leverage, but only if you compute the risk on the full contract value, not the margin. Most people who blow up did the sums on the margin.

Kelly, and why half of it is enough

There is a formula from the 1950s, the Kelly criterion, that computes the mathematically optimal fraction of capital to risk given your edge and your odds. Its main lesson is counterintuitive: beyond a certain size, betting more with a real edge reduces your long-run growth and eventually guarantees ruin. Nobody knows their edge precisely, so practitioners who use Kelly at all use half of what it suggests. For most investors the takeaway is simpler. Even when you are right about a company, there is a size at which being right does not save you.

The behaviour part

Rules only work if you follow them at the moment they are inconvenient. Three habits help. Write the exit before the entry: the price, or the event, at which you will admit the thesis failed. Never add to a losing position without a written reason that is not “it is cheaper now”. And keep a journal of every decision with the reasoning at the time, because in a year you will not remember why you bought, and the journal will show you which of your reasons actually predicted anything.

The worksheet

Six lines, one per holding, done tonight:

1. Total capital, and 1 percent of it in rupees.
2. The price at which you would admit each holding was a mistake.
3. The rupee loss from here to that price, per holding.
4. That loss as a percentage of total capital.
5. Each holding’s weight, and the largest sector’s weight.
6. The one news event that would hurt the most holdings at once.

If line 4 is above 2 percent anywhere, or line 5 shows one name above 10 percent or one sector above a third, you have found the thing to fix before buying anything new.

Try this before moving on

Fill in the worksheet for whatever you own, even if it is two shares bought last month. Then move on to the tax chapter, which deals with the one certainty in all of this: whatever you make, the tax department has a view on it.