The two critical ratios and why gambling is on the different side

I would test these two ratios first on approaching any investment system: The winning ratio and the average size of wining over losing ratio.  Take it a broader way: in order to make capital appreciation (or even in life) one needs (1) win more than lose and/or (2) average size of wins are larger than average size of losses.  Therefore, if one has the way to control the ratios she might have conscious sense to increase the chance of success even not guaranteed.  Yet if one doesn’t or know but can’t control this two ratios, I see it as taking uncalculated risk and leaning on chances – which is a critical characteristic of gambling.

Gambling is exciting, especially when you say “all in” and feel like Matt Damon (in Rounders, film, 1998). Yet gambling with financial markets poses you to both stand-alone risk in the short-term and a larger, more systematic risk of your whole investment system in the long-term.

(1) Win more than lose or the winning ratio (hereafter: Wining Ratio) is the average of frequency winning divided by the frequency of losing.  Overall if the size of wining and losing is the same, one needs win more than lose on average to make progress.  (2) Average size of wins and losses (hereafter: Size Ratio) comes to distort the first ratio.  One might frequently lose more than win on average and still make progress if averagely size of her wins is larger than her losses.  Personally, I see the later is even more important than the former, yet these two ratio distort and influence each other on a significant way so that one needs at least a harmonic balance in between of the extremes to make the system sustainable.

In the absence of the Size Ratio, one definitely needs a larger than one [1] Winning Ratio to make progress in the long run.  This is where all kinds of analysis come to play: fundamental analysis, technical analysis, forecasting, modelling, rumors, whatever. Let’s take the stock market: one cannot get in the market at anytime with whatever company.  She has to consider at least two things: first – which company to invest (this is called Selection) and second – when to invest and when to get out (this is called Timing).  With the Selection, she has to decide which way to approach: Top Down (Macroeconomic analysis to industry analysis and company picking up) or Bottom Up (relative value evaluation through ratios screening) or mostly hybrid of the two.  Then maybe she has to continue doing all kind of market research, intelligent report, competitive analysis, scenario analysis, sensitivity analysis, management meeting, modelling, valuation, to confirm she has a winning horse on her side.  Besides, on Timing side she will have to oversee all kind of markets go up and down: bond, stock, foreign exchange, to find the best bargain point of getting in.  I didn’t notice the divestment yet, but narrowly speaking, all of these works come to increase the chance of her success – if she doesn’t really care about the Winning Ratio, she must not waste too much time on these all stuff.  Getting a positive and sustainable winning ratio is a very sophisticated process.  Finally everybody just buy and sell, it’s the what that stands before making the order counts.

Now size comes to distort.  If one has a Winning Ratio of 75-25 (75% win and 25% loss that finally makes the ratio 3x) but averagely a loss is larger than a win three times – that one would statistically come to an end with a tie result.  If one has a Winning Ratio of 25-75 and makes the ratio come to 0.33x but averagely a win is larger than a loss four times – that one would statistically enjoy a positive result in the end.  This is when sizing strategy comes to play.  Sizing strategy in simple form is when to add to a previous investment.  If you buy a share in the stock market, will you add the next tranche of investment when the share goes up or goes down?  In the first case of the share goes up, bad point: you have to pay more for the same product you purchased before, good point: the market is confirming that the first purchase is right.  In the second case of the share goes down, bad point: the market is not or not yet confirming that the first purchase is right, good point: you’re pay less for the same product you previously purchased – effectively you get a better bargain point.  Because Sizing Ratio can strongly distort the Winning Ratio, get it right in sizing becomes critical for any investment policies.

From what I know, private equity firm (PE) and venture capital (VC) often average upward.  Private equity firm when invests in any business, they normally don’t come all straight equity to that business.  To hedge the business risk, they at least normally come in two tranches, a part in straight equity and another part in convertible debt.  When the business does good, they might convert the debt to next tranche of equity and effectively not get as good price as the first tranche of straight equity when they first come.  But if the business goes bad and the equity part deteriorates significantly, the convertible debt doesn’t expose to that risk unless the business goes bankruptcy so at least they expect to get the principal back with some interests.  It’s pretty the same with VCs, VCs often come to a business by several rounds of capital with tight growth measures even they all come in the form of straight equity.  Normally, they will come the first round when the VC and the new business get the first agreement.  If the business does good, they’ll get in the next equity tranche, and the process continues.  VC is notable for poor Wining Ratio but the Size Ratio comes to save them.  They may invest in 10 companies and only have one profitable (0.1x) yet that one cover all of the 9 losses and even comes with an additional gain, take the case of Silicon Valley companies like Facebook, Google, LinkedIn, to just name a few.

Hedge funds use numerous ways to mixed the Winning Ratio and the Size Ratio to form numerous different strategies.  Take HFT (High Frequency Trading) for example, HFT employed computers with algorithms used statistics and probability to enter and exit the market thousands time a day with the time per trade only from seconds to minutes.  Because the small fraction of time and target employed, HFT doesn’t expect to catch big market move, HFT is expected to catch a very small gain (a cent, 5 cents per trade, etc) in a very small period of time – because of that, HFT needs to win thousands of trades a day in order to make money.  Now take a look on the negative side: if one buys EUR/USD at 1.3000 and expect to gain 0.0005 (5 pips) how much would she expect to lose on that trade?  If one buy EUR/USD at 1.3000 and expected to exit at 1.3005 (5 pips gain) and places a stop-loss at 1.2995 (5 pips loss) – not counting the bid-ask spread, she has 50-50 chance to win and to lose 5 pips in this trade.  Now if she widens the losing side to 20 pips.  Let’s say she enters the market and buy EUR/USD at 1.3000, with target of 1.3005 in 1 minute and places a stop-loss at 1.2980 (20 pips loss).  Now she has a better Winning Ratio: in the next few minutes, very likely the market volatility will hit the 5 pips rather than hit the 20 pips on whatever direction.  But because of the size of a losing trade is four times of the size of a winning trade.  This system needs to win 4 times much in order to get back to even.  So if one employs this system of 5 pips gain, 20 pips loss per trade, one has to make sure that the Winning Ratio needs to be larger than 80-20 (4x) to make a profit in the long run, statistically.

In gambling, mostly one cannot control any of these two ratios.  In Black Jack, one generally can only control the winning ratio as well as increase the size when she has a better odd of winning marginally.  Mostly, she can only increase the size when the cards are not in hand thus expose to a bad Winning Ratio.  The same applied for Roulette and other game using dices.  Casinos state clearly in regulated rules that they offer a skewed winning ratio to players for example 40-60 winning ratio in Black Jack or 38-62 in slot machine, just for illustration.  Because they have a better Winning Ratio meanwhile one cannot control the Size Ratio, one statistically has no way to beat the casino on the long run.  I treat anything in life has this characteristic as gambling: when one can’t control the ratios and have to lean on chances.  In Poker, one can somehow influence both the ratios and because of that, casino only plays dealing role and earned fixed income – hence, not expose to market risk.  Banks do the same when they make the market: they hold risk neutral positions and earn bid-ask spread.  This might provide them less profit as exposing to the market but limit to the minimum market risk they take.

Now take a look back on other fields of life: war, battle, politics, study, career … don’t you try numerous strategies to have a better Winning Ratio and Size Ratio?

Tri Ton

Businessperson with private equity expertise. Interested in strategy and investment.

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