Understanding 'Risk Management & Trading Psychology'

Lesson -> The Kelly’s Criterion

14.1 - The Percentage risk

We looked at three very important techniques for sizing positions in the last chapter. Each technique was unique. These three techniques were:

  • One unit per fixed amount
  • Percentage Margin
  • Percentage volatility

Each method works differently, and they can produce completely different results when combined with an equity estimation technique. It is up to you to decide which equity estimation technique and which position sizing method works best for your needs.

Before I get started, let me mention another method for sizing positions, the "Percentage Risk" method. This technique is used by many traders, and it's simple and intuitive.

The percentage risk method is based on your own estimation of the 'loss' you are willing to take for a trade. This is often called the "Stop Loss" for the trade. Stop loss is the price at the which you close a trade and take a loss. As a function stop loss risk, the percentage risk technique controls how large the position is.

Let me use the stock futures as an example and show you how it works. In fact, this is a great trade setup.

Image 1

Here's an intraday chart for Tata Motors. The frequency is 15 minutes (14 Sept 2017, at 11:30 AM).

Let me tell you why this trade is worth looking into.

Tata Motors currently stands at 393.65, which is an excellent price zone, considering it has already tested the same level twice.. This makes 393.65, an intraday support price for Tata Motors. In the past, Tata Motors stock price fell when it tested 393.65. This means that it is possible for the price to test 393.65 again and bounce back to the 400 level.

Do you also notice the low volume of retracements between 400 and 393.65? I have discussed why I love trades like this in the Technical Analysis module. You might want to read this module if you haven't.

These factors are enough to convince traders to buy Tata Motors Futures at 393.65.

What, if the trade goes in the other direction? What is the stop loss?

I see some support at 390/+, so I'd be happy setting this stop loss.

It's not complicated at all, as you can see.

The trade would then be -

Stock: Tata Motors Limited

Trade Long

Trade Price: 393.65

Minimum 400

Target value 6.35

Stop loss Price: 390

Stop loss value: 3.65

Reward to risk: 1.7 (which would be great for intraday trading)

Lot Size: 1500

Margin Requirement: 73.5K

Let's say I have Rs.500,000 and I want to buy Tata Motors lots. The margin per lot is Rs.73,000.

Technically, one can purchase up to 6.8 lots or 6 lots.



The question is, would you risk your entire capital for this trade? This is a stupid thing to do. If the trade goes wrong, it would result in a loss of Rs.32850/- (3.65 * 1.500 * 6).

Also, you would lose:


=6.57% of your capital for one trade

No matter how great a trade setup is, it's not wise to put so much capital at risk. Professional traders should not expose more than 1 to 3 percent of their capital to risk on any trade. This rule is the basis of the "Percentage risk" position sizing technique.

Let's now define the maximum loss per trade in terms of percentage of total capital. It could be 1.5% at this point. This means that on this trade, I will bear the maximum loss.

1.5% * 500000


This means that I do not intend to lose more Rs.7500/- on any trade. This is the maximum loss limit.

We know that the stop loss is 390. With an entry price 393.65, the stop Loss in Absolute Rupee terms would be -

393.65 - 390

= 3.65

Per lot, the loss is -

3.65 * 1500

= 5475

If the stop loss is activated, I would take a hit in the amount of Rs.5475 per lot.

To determine the amount of lots I could accept for the risk I am willing to take, I need to divide the maximum threshold with the loss per trade.

= 7500/5475

= 1.36

This trade allows me to buy as many lots as I like, at a cost of Rs.73,000.500/- margin deposits.

It is prudent to reduce the capital blockage and revise the maximum loss threshold for the next trade. Let's identify the new maximum loss threshold.

500000 - 733500

= 426,500

1.5% * 426500

= 6397.5

This will allow me to calculate the stop loss and multiply it with the lot size. I then divide the maximum risk, i.e. 6397.5, by the loss threshold to determine how many lots I can trade in.

And so on!

You might be interested in how the trade turned out. Here you go -

Image 2

Trades like this are my favorite, even if the price is not close to the stop loss J. As I mentioned earlier, this trade was a conviction. I now want to discuss the next topic: How do you position size if you are convicted of a trade? In such cases, what should I do to expose slightly more capital?

Kelly's Criterion is here!

14.2 - The Kelly’s Criterion

The Kelly Criterion's background is interesting. John Kelly, who was at the time working for AT&T's Bell Laboratories, suggested it in the 1950's. Kelly's Criterion was actually suggested by John Kelly in the 50's to assist AT&T with long-distance telephone noise problems. Professional gamblers used the same theory to determine the best bet size. This same theory quickly made its way into the stock market, where professional traders and investors use Kelly's Criterion to size their bets. This is perhaps one of the few tools that both investors and traders use frequently.

I don't understand how the transition from Telecom into stock markets took place. I am a Telecom Engineer by training .... but I can't seem to grasp how Kelly's Criterion managed this transition between these two worlds J

The Kelly's Criterion helps us to estimate the optimal bet size or the percentage of our trading capital.

  • We know a lot about the bet that we are about to place
  • We are able to take that specific bet with an advantage

Let's take a look at Kelly's Criterion using an example. The Kelly's Criterion equation is a formula whose output is a percentage. Also known as the Kelly's percent. Below is the equation.

Kelly% = W – [(1-W/R]


W = Winning Probability

R = Win/Loss ratio.

  • The total number and percentage of winning trades divided by the total trades is the winning probability.
  • The win/loss ratio is the average profit from winning trades divided with the average loss from negative trades.

Let's look at an illustration. Let's say I have a trading strategy that produces the following results. For simplicity sake, let's assume it is a trading platform to trade one stock, Tata Motors.

Sl NoSign DateResultP&L (in Indian Rupees)
013 rd SeptWin+ 5,325
024 th SeptWin+2,312
035 th SeptWin+4,891
046 th SeptLoss- 6,897
0511 th SeptWin+1,763
0612 th SeptLoss-3,231
0713 th SeptLoss-989
0814 15 SeptLoss-1,980
0915 15 SeptWin+8,675
1018 th SeptWin+4,231

These are the data.

W = Total Number Of Winners / Total Trades

= 6/10


R = Average Gain / Average Loss

Average gain = Average [5325. 2312. 4891. 1763. 8675. 4231].

= 4,532

Average loss = Average [6897. 231, 989. 1980]


R = 4532/3274

= 1.384

A number higher than 1 is always preferable as it means that your average gains exceed your average losses.

Let's bring these numbers back into the Kelly's Criterion equation.

Kelly% = W – [(1-W/R]

= 0.6 - (1-0.6)/1.384

=0.6 - [0.4/1.384]

= 0.31 or 31%.

According to the original school of thought, Kelly's percentage represents how much capital one should expose in order to trade. Kelly's Criterion recommends a capital exposure of 31% for Tata Motors' 11 th trading.

This can make things a bit tricky. For example, a trading system that is extremely accurate could have a Kelly's Percentage of 70%. This would mean that there would be a 70% capital exposure to the next trade. I find this a rather stupid thing to do. You may wonder why? You may ask why not? After all, a system with 70% accuracy can be great so why not maximize your bet?

Because there's still a 30% chance of losing 70% of your capital.

This is why Kelly's criterion can be modified. Let's go back to the percentage-risk position sizing method we discussed earlier in this chapter.

A technique where the trade exposure is less than 1.5% or any other percentage of capital is called a percentage risk. Kelly's criteria permits us to adjust the exposure to up to 5% (or any other proportion you consider appropriate).

What does this all mean? This means that I wouldn't expose more than 5% capital for any trade. Capital exposed can range from 0.1% up to 5%. So how do I decide?

Here, we can use Kelly's percentage. If the Kelly's percentage was 30%, then I would expose 30% of 5%, or, in other words, expose 1.5%. If the Kelly's percentage was 70%, I would expose 70% of 5% or 3.5% of the capital trade.

The Kelly's percentage is higher, and vice versa.

This concludes the discussion on position size. I hope you have gained a good understanding of the importance and the techniques for sizing your bets through the previous 4 chapters.

Moving on to "Trading and investing Biases".

To Summarize

  1. Percentage Risk is an intuitive and simple method of sizing position.
  2. You need to determine the maximum risk as a percentage capital. This is then divided over the stop-loss to get an idea of the capital that one should be exposing to trades.
  3. Kelly's Criterion indicates how much capital can be exposed for a trade
  4. For optimal results, one can combine Kelly's Criterion and percentage risk