Is a trade worthwhile?

A money gamer is constantly swinging between fear and greed. Greed is the primary drive for making a trade while fear always tortures the trader after making the trade especially when leverage is involved. As greed, ie., the desire to making profit, is the motivation of the trade while the fear comes from a loss resulting from that trade. After all, it is all about risk management.

There are many aspects in terms of risk management like the evaluation on macro economic situation eyes on the interest rate development, world economy and the fundamentals involving the outlook of the related asset or down to the trading strategy like the entry price, size of position, gearing and hedging etc. All these things are meant to deal with how a trade is executed. However, the most important point is still not yet addressed. It is whether or not the trade is worthwhile at all or should the trade be made at all.

There are some articles addressing how worthwhile a trade is by the concept of expected value (EV). Simply speaking, EV= (Probability of Gain) x (Take Profit Gain) ] + [ (Probability of Loss) x (Stop Loss Loss). According to those articles, higher the value better the trade is. However, it seems EV is good in comparing two or more alternatives of trade yet it still has not addressed to the point whether the trade is worthwhile or not unless the result is negative. To explain, below are two EVs with similar value but quite different scenario of winning/losing probability and the amount of gain/loss.

EV1=(0.1*$1000)+(0.9*-$10)=91.9
EV2=(0.9*$213)+(0.1*-$1000)=91.8

The two EVs are in similar value but do they give the punter similar risk and return? Apparently no! The scenario in EV1 resembles betting in lottery while EV2, as a local vivid metaphor puts it, win a candy but lose a factory (贏粒糖輸間廠). In EV1, the chance to win is slim (0.1 prob) but the reward is $1000 while a very high chance (0.9 prob) to lose but the loss is $10 only. The opposite is the EV2, despite of a high chance (0.9 prob) of winning however the reward is only $213 but as long as it loses then the loss is $1000 despite there is only 0.1 probability. In EV1, one risks his $10 to bet on a potential return of $1000 while in EV2 one is risking to lose $1000 in the hope to win $213 yet the EV value for the two cases are almost the same. Perhaps there is argument on the probability of the winning and losing in the two equations.

Probability is only the summary of the history of how likely the happening of something based on past record while history will not necessarily repeat in the future in the exact same fashion as it was in the past for a particular event. 0.1 probability of losing in EV2 means statistically there was one failure out from the 10 occasions in the past but it does not mean there must be one failure in every 10 occasions. For example 10 failures could scatter randomly throughout 100 occasions. There could be 2 failures in the first 10 occasions but none in the next 10 occasions yet the probability is still 0.1.  If the failure just happened to fall onto the one the punter places his betting, so sad then. One must remember probability is good for the long run but absolutely not effective as what it suggests in any one particular occasion. Apart  from this nature of probability but there is also black swan that makes probability is not so effective in term of reliability.

While it is good to win the jackpot in the lottery but we must avoid the scenario of winning a candy but to lose a factory when in failure. So when evaluating a trade(or a bet), the odds probably should be reviewed first. In EV1, the odds is 1000:10 while it is 213:1000 for EV2 or 100 vs 0.213 respectively. Judging from the odds alone then apparently EV1 is more favourable but there is only 10% chance to win the $1000 and 90% chance losing $10 in EV1 while it is 90% chance winning $213 and 10% chance losing $1000 in EV2. So what are the justified odds for these two sets of probabilities?

The formula to obtain odds from probability is O=1/(1-P) so the justified odds are 10 and 1.11 for EV1 and EV2 respectively. By comparing the offered odds of 100 and 0.213 for the two scenarios so it is clear that the trade(or bet) of wagering $10 in the hope of winning $1000 with just 0.1 probability is still a good deal and thus worthwhile. Simply speaking, only when the offered odds is greater than that derived from the winning probability then the trade (or bet) is worthwhile. In fact this is the underlying principle of value investing as remarked by Charlie Munger that value investing is looking for a bet with 0.5 winning probability but odds at 3:1 and hoping to find this misquoted odds. I think many of the so-called value investors do not even know this principle so resorting in nagging at the intrinsic value of a stock.

By considering the odds and probability altogether perhaps can give a better evaluation on how worthwhile a trade(or bet) is than can the Expected Value.