Relationship Of Risk In Multiple Portfolio Betting Strategies

In the "nature of risk" I said that "Once you understand how this relationship applies to ONE bet in a portfolio mixed with a percentage cash and a percentage towards that SINGLE bet, you can start to develop your understanding to account for multiple bets at a correlation between 1 and zero. We will cover that next." This is the spreadsheet I developed and in it, we take a hypothetical coin flip where heads you win 20% ROI on your capital, tails you lose 10% and 2% of the time you lose everything. 49% chance of a win, 49% of a loss and 2% of catastrophe. You can make 1 of these bets a month or 12 a year. The results: With One Single Bet the "ideal" amount is 47% of your capital on one bet. The expectation in that scenario is that you gain an average of 10% over the course of a year. With the multiple bet strategy, at zero correlation you can risk 19.16% of capital for EACH of 5 bets and you expect to yield 25% per year. If you have a more typical correlation of 70%, your return goes down to about 17% per year.  
If you are overwhelmed by numbers, this means that you earn more by betting with more than 
one stock at a time risking significantly less per bet but risking more total. In spite of risking more total, the actual volatility/risk is expected to be the same.

Why do things work this way that MORE bets at a lower correlation earns a better return better? The kelly criterion (see nature of risk) is such that for INDEPENDENT bets (zero correlation) you can roughly risk the kelly on each bet as a percentage of the REMAINING capital (capital remaining AFTER the previous bets). For 10 bets the way this would work is if the kelly was 10%, you could risk 6.5% per bet over 10 bets or around 65% of capital at risk. The way this is determined is 10% of capital is risked on the first bet, then 10% of remaining 90% capital or 9% on the next bet, and then 8.1% on the next bet. As this continues you could average this out over 10 bets to be 6.513% per bet for every bet. Or you could do this over 5 bets and the amount per bet would be nearly 8.2%. The reason the capital remaining has to be calculated and you can't just risk 10% per bet across 10 bets using all capital up is because there is the possibility that every single one of those bets losses. In the normal kelly, bet one at a time, after every single loss you can properly adjust the risk downward by taking 10% of the remaining capital which would then have been reduced to 90% after the first loss, and so on.You can make sure each consecutive bet is smaller if you wish, but I prefer remaining consistent with the option for a "half bet or 1/4th bet). Ultimately I want to cut whatever "average" number in half at a minimum as a "full bet" even though it does not represent a "Full Kelly".

We also know that if you were to risk 10 bets at a correlation of 1 the sum of all bets would equal the kelly criterion if we used bets at a correlation of 1. It would be like opening 10 positions of the same ticker symbol, and so the sum of each position must not exceed the kelly.

Now with use of this knowledge you can construct a weighted average and determine the amount given a correlation of 50% to be 50% between the two, and 70% being 70% of the value of a correlation of 1 and 30% of the value of the zero correlation number and so on. The point of this knowledge is to quantify the value of correlation and to understand the relationship. When it comes to actual betting you will often find more bets at a lower correlation is better with less risk. However, when fees are involved 10% of a $5000 account would be to put $500 at risk. If you pay $5 fees TWICE that's $10. $10/$500=2% loss. So every trade you break even loses 2%. If you gain 10% or $50, $10 represents 20% of that. When modeling the expectations, it's important you plug in the results adjusted for the amount of capital at risk. The formula doesn't do this yet, but I plan to adapt it at some point. For now, even a $5000 account doesn't get you tremendously far if you are position sizing properly unless you are very, very good. The amount that each trade limits you over time is tremendous, and that is the danger of "compounding costs".

Fortunately, I have gotten to the point where I can produce on trades. With many starting out with even less, they are going to have to be very smart about how they build their income gradually and safely while they wait to accumulate more to deposit. If you are investing, and can use a DRIP program to effectively dollar cost average in without incurring fees, you can get started with a very small amount. If you are trading you need more. Just how small of an account could one who has experience start with and actually hope to grow it? I am working on the spreadsheet so I can run the math and include the effect of fees. With some adjustment we can determine the amount when trading becomes profitable, and also when trading becomes profitable to the extent that it expects to produces more than investing.