Expected Value (EV) and How your Econ Profs Duped you

EV is the anticipated average value of your investments over a long period of time. Long term here refers to infinity and beyond.

Since you are reading this, let us gift you a $1 and open a Zerodha account for you. And as hypothetical as the previous statement is, consider that you get a magical stock, ‘MAG’ which only either doubles or halves every month with a 50/50 chance. You have no way of predicting which way it would go, the only liberty you have is to rebalance* your portfolio at the start of every month.

Given this, how would you invest your money so that you get decent returns after 20 years (240 months)? 

The EV principle says that on an average you would get: $2 (doubling)*1/2(chance of that happening) + $1/2(halving)*1/2 = $1.25. 25% whopping returns over a month. According to EV, you should just sit tight and invest $1 in month one and let the compounding happen, right?

Nope. That’s where MBA profs duped you. If you follow above, there’s a 50%+ chance that you’ll end up with <$1 and only 3% chance that you’d be a billionaire. Why? Because of Kelly’s criterion. But more on that tonight.

Aside, MBA seems like a scam. Only good for finding your partner. Okay, bye for now.

Your expected (average) values do not work because outliers skew the average! Different investing styles, different results. After 20 years, investing style A (let’s call it, IA) might give $100, IB $1, IC $0.1, and probably some I(infi) would give a billion dollars. Your professors are right about EV only when you’ve had infinite iterations because some of those billion dollars plus outcomes are so good that they lift the entire average. But this is never the case in real life. YOLO, you never gonna live foreva.

The most likely outcome is seldom the average outcome. So, to escape this ‘lottery’ situation you need a strategy. Kelly ‘the genius’ found just that. At the start of each month, rebalance your portfolio so that exactly half the money is in cash and the other half in MAG. 50-50. This is Kelly’s criterion.

In real life, invest 50% in risky assets (stock, MFs) and 50% in safe assets (FDs, Blue chip MFs). Whatever is left or gained after that month/ period, divvy that up again 50-50. There’s a 50%+ chance of you ending up a millionaire with this strategy, against a measly 10% chance you had when you followed your prof’s EV strategy.

This works even if the stock doesn’t double and half as in the mentioned example. What if there’s more than 2 investment options? Works then too. Kelly knew this because he built an entire mathematical model around this.

SIPs also provide approximately the same advantage. 

So, that’s it.

Been a geeky day, innit? Take this as an exception please.