Shannon's Demon and how returns can be created out of thin air

Quick summary:<p>&gt; To illustrate this concept, you could consider a simple coin-flip game where you make a 50% return on your money if the coin lands on heads, or lose 33.3% of your money if the coin lands on tails.<p>Let&#x27;s say you bet $100. Your expected outcome is 100 * (1&#x2F;2 * 3&#x2F;2 + 1&#x2F;2 * 2&#x2F;3) = 108.33. Greater than 100. That&#x27;s all there is to it, the &quot;magic&quot; comes from the made up security which can generate such amazing returns.

How returns can be created out of thin air... when you have a bet with EV +8.333% of the money you put up.<p>You can be assured that the possibilities of a portfolio balanced between a set of logarithmically random walking assets -- if one were to believe that individual stocks&#x27; behavior had such behavior -- is a well-contemplated concept in finance.

There is a much easier way to grasp what is happening here.<p>Often in finance, securities are assumed to follow something like a geometric Brownian pattern. This is the idea behind the Black-Scholes model, for instance. This means that you view your price ticker as a random Gaussian walk (e.g. Brownian motion) when your ticker is placed on a logarithmic scale.<p>One way to think of this is that, given some (sufficiently large) unit of time, you have an equal chance of your security either doubling or halving in value. Or being multiplied&#x2F;divided by 1.5, or 1.1, or any other figure you like, given whatever unit of time you like.<p>It&#x27;s really easy to see how this basic pattern has a positive expected value. Suppose you put $1 into a fair coin toss game, and if you win it doubles and if you lose it halves. You stand to win $1 or lose only $0.5, thus the expected value is $1.25.<p>Now suppose, to keep it simple, you have a ridiculously volatile security which doubles or halves in value every day. So the ideal trading strategy is to choose some betting amount, say $1000, and just put it in at the start of the day. Then the next day, just reset your position size to $1000, either taking your $1000 in profit or kicking in another $500 to cover losses. You will quickly become a trillionaire.

Author should attempt to backtest this using historical data and see if it actually generates a return in the real world(with taxes factored in as well).

As far as I can tell, the term “Shannon’s demon” is fairly recently made up. I learned this as the Kelly criterion. Here’s the original paper:<p><a href="https:&#x2F;&#x2F;www.princeton.edu&#x2F;~wbialek&#x2F;rome&#x2F;refs&#x2F;kelly_56.pdf" rel="nofollow">https:&#x2F;&#x2F;www.princeton.edu&#x2F;~wbialek&#x2F;rome&#x2F;refs&#x2F;kelly_56.pdf</a><p>To “Shannon’s demon’s” credit, the first word of that paper is Shannon, but that’s about it. Kelly and Shannon were different people, and the paper makes no mention of demons.<p>This also has nothing to do with making returns out of thin air. It’s about how to avoid <i>losing</i> your returns by betting too much at once, and how to optimally choose the size of a bet.

Is this not what hedgefunds were designed specifically to execute for clients? Presumably using this strategy as their own internal beta or benchmark, and then finding uncorrelated volatile assets and trades to execute the same thing to generate alpha for themselves, and charging ~2&#x2F;20 fee struture on it.<p>Literally value machines. Hence their demand for exotic products with uncorrelated volatility characteristics for risk pairing. I superficially get it now. I can see how someone could get the bug for this.

You don;t necessarily have to be able to spot the trick to know there is one. If you know that the expectation value of any combination of bets is just the sum of the expectation values of the original bets, you&#x27;ll know there cannot be a way to combine zero-expectation bets to get a positive expectation. Because no matter how you sum up zeroes, you&#x27;ll end up with zero.

Smoke and mirrors, the first plot is log scale, and thus demonstrates exponential growth in your portfolio. no rebalancing necessary, there no free lunch here, just a manipulator using graphs to manipulate.

Pairs trades are amongst the most common elementary quant strategies, which is why all equities are so damn correlated and which destroys the apparent arb described in the article.

This reminds me of that gambling strategy where you double your bet every time to make up for losses. This seems to reduce to timing the market.

This is why gambling is stupid.. Do everyone a favor and invest in yourself - real skills to give back to the world.<p>“can actually make it possible to generate positive returns at the portfolio level, even when all of the portfolio’s individual holdings are expected to produce zero, or even negative, returns over time.” -False<p>The illusion comes from the fact that, for small n you can flip heads and tails the same number of times and still have over half the money you started with - whereas with the invest all strategy you would have lost everything. For a fair coin, as n approaches infinity you still win nothing either way though. That graph is completely misleading. We can represent the amount won as the recursive sequence<p>X_(n+1) = X_n + (X_n)&#x2F;2<p>def recursive_sequence(n):<p><pre><code> &quot;&quot;&quot; Money won after winning n times in a row&quot;&quot;&quot; result = 1 # money we start with rebalance_ratio = .5 for i in range(0,n): result += result*rebalance_ratio return result </code></pre> for i in range(1,10):<p><pre><code> temp_profit = recursive_sequence(i) net = temp_profit &#x2F; 2**i # assuming you loose as many times as you won after percent = abs((temp_profit-1))*100 print(f&quot;savings after {i} heads:&quot;, recursive_sequence(i), f&quot;\npercent profit: {percent}&quot;,&quot;\n....money after loosing n times after: &quot;, net, &quot;\n&quot;) </code></pre> You can see what this gives for a rebalance ratio of 0.5. Anything more or less just increases or decreases your volatility. “How returns can be created out of thin air” is literally a scam - not true. That’s a tulip bubble. Sure you can get rich off one if you fool enough people. You need to flip a coin 2^(n+1) – 2 times to get heads n times in a row. Same for tails… Your “rebalancing” is only increasing the number of attempts it takes to not win anything ie. the time you waste flipping coins instead of spending time with people. I feel embarrassed for spending as much time as I did on this. At least I learned something… savings after 1 heads: 1.5 percent profit: 50.0 ....money after loosing n times after: 0.75<p>savings after 2 heads: 2.25 percent profit: 125.0 ....money after loosing n times after: 0.5625<p>savings after 3 heads: 3.375 percent profit: 237.5 ....money after loosing n times after: 0.421875<p>savings after 4 heads: 5.0625 percent profit: 406.25 ....money after loosing n times after: 0.31640625<p>savings after 5 heads: 7.59375 percent profit: 659.375 ....money after loosing n times after: 0.2373046875<p>savings after 6 heads: 11.390625 percent profit: 1039.0625 ....money after loosing n times after: 0.177978515625<p>savings after 7 heads: 17.0859375 percent profit: 1608.59375 ....money after loosing n times after: 0.13348388671875