Trading Principles - 3

In my previous post (Trading Principles - 2), we discussed two concepts:
(1.) Chance of winning
(2.) Risk:Reward

OK, lets move ahead.

Sometime last year, a friend asked me what I thought about the market direction. I replied that I thought markets would go up in the near term. So he further asked me whether I had bought in anticipation of this move (being long, in trader terminology). I replied in the negative saying that I was actually short on the markets.

My friend appeared puzzled, perhaps he thought I was being a 'wise guy'. In reality, I was being totally honest. But what explained the discrepancy between my views and my action?

Lets say you toss a fair coin. If you get a heads, you get paid Rs. 2. If you get a tails, you lose Re 1. Would you play this game of chance?

For a fair coin, there is a 50% chance of getting either heads or tails.
So if play this coin toss game 100 times, you can expect 50 heads and 50 tails.
For each head, you win Rs. 2. So for 50 heads you will win Rs. 100
For each tail, you lose Re. 1. So for 50 tails, you will lose Rs. 50.
After 100 tosses of this fair coin, you will win Rs 100 and lose Rs 50 for a net gain of Rs 50.
So if you play this game 100 times, you can expect to win Rs. 50.
Hence, the EXPECTED VALUE of the gain from a single toss of the coin is Rs 50 divided by 100 = Rs. 0.5.

You can expect to win 50 paisa for every toss of the coin. This is called the EXPECTED VALUE (E) per toss of the coin toss game. Surely, you would like to play this game, as many times as possible. The more you play, the more money you can make.

Likewise, each investment/trade has an expected value. If the expected value is positive, a profit is expected on the trade and it is worth taking. If the expected value is negative, a loss is expected on the trade and the trade is not worth taking.

Let us take a couple of examples.

Trade A has a 70% chance of winning and a 30% chance of losing. The win per trade is Rs 100 but the loss per trade is 400.
The expected value (E) for this trade is (0.7)*(100)+(0.3)*(-400) = -50
Trade A has a negative E value. i.e. this trade is expected to lose you money even though it has a 70% chance of success. Thus a high chance of success does not equate with making money.

Conversely turn the above trade on its head. Take trade B that has a 30% chance of winning Rs 400 and a 70% chance of losing Rs 100.
E for this trade is +50.
So even with a low chance of winning, the trade makes you money.

Perhaps now it might make sense why I was short on the markets in spite of thinking that the markets would go up. I was expecting that if the markets went up, they would not go up much. But they went down, they would go down a lot. The Expected Value favoured a short position.

It does not matter much, if over the long run, you are more wrong than right (% success rate) or vice versa. What matters is how much you make when you are right and how much you lose when you are wrong (a high average profit:average loss ratio).

So how do we use this to make real life decisions? Suppose you have a one year time horizon. At the end of 1 year, you expect the Sensex to have a 50% chance of going up by 30%. But there is a 50% chance of it going down by 20% as well. Should you buy?

The expected value from this trade is 0.5*30%-0.5*20% = 5%

This is positive. So should you buy since E has a positive value?

Do not forget the opportunity cost. You could put your money into a bank fixed deposit and get an assured 8% (assuming the bank does not default). So in actual terms, the opportunity cost for making the Sensex trade is higher than the expected benefit from this trade.

An investment must then must not only have a positive expected value but it must be higher than the best opportunity cost. Clearly, it does not make economic sense to buy into the Sensex with these kind of statistics.

What if your time horizon is 5 years?

Say, over 5 years, there is a 90% chance of the Sensex doubling in value. But there is a 10% chance of the Sensex going nowhere. The E for this trade is 90. The opportunity cost @8% per annum is 47. So over a longer duration, the trade makes sense.

(Hence the importance of a personal time horizon for any investment.)

So what lessons can we derive from the above discussion?
(1). More important than % success rate is the reward:risk relationship. It is easier to find investments and trades that have a low success rate than one that has a high success rate, provided you obey point no. 2 below, which is
(2). Let your profits run but cut your losses short. Look at trade B above. Many investors do the converse. They sell quickly when they have a profit, lest the profit should evaporate. But they hang on to losing investments in the hope that prices will come back. In effect they follow the strategy, 'cut your profits short but let your losses run'. Typical phenomenon are short term trades becoming long term investments, Buy-and-hope investing, not willing to accept a loss, etc. All lead to the poor house!
(3). Seek and act on only those investments that have a positive E value. Finding such trades requires possessing an edge in the markets. An edge comes from experience, vision and ability to foresee, access to information, plan and discipline, patience, perseverance, or all of the above, and more.

Till next time, happy investing!