The Line Between Aggressive and Crazy
rhsfinancial.com
rhsfinancial.com
Gwern details this extensively here: https://www.gwern.net/Coin-flip well worth checking out.
The actionable takeaway for me is to try and solve this problem with some machine learning approaches, since it's simple enough that we compare to exact solutions, but also interesting enough.
The takeaway from a social point of view is that even people working in finance are not very good at playing these games individually. (The companies they work for might still be doing much better as a collaborative effort, and with more simulations and backtesting used.)
No, you're just bringing up a separate issue from the one implied by the parent.
Your own risk tolerance, the values of your life, the opportunity costs outside of this one -- those are real complexities but we ignore them to answer a question about how best to maximize your bankroll within the current situation.
If you have 100 dollars..and you lose 50% of it on a fair coin bet, you now have $50.
Say you play again..You win. Youll only have $75 ($50 times 150%.)
Thats the basis of risk analysis. That losing and winning arent equal for finite bankrolls just because their probabilities are equal.
In the Haghani & Dewey 2016 experiment log utility is violated in two ways:
- A $250 cap on payouts.
- The fact that $250 payout to participants was on TOP of participant's current wealth, making utility approximately linear.
Now everything financial has been analyzed to death and nobody can make money with technical analysis.
This article is more about how you manage risk and learning what your personal risk tolerance is. If you take more or less risk than you "should", then all else equal, you'll wind up with less money.
Besides, these are not "just" math PhDs, but math PhDs backed by some of the largest private equity trading firms in the world, armed with multiple datacenters of 5000 blades each, running machine learning algos and playing "what if" scenarios 24 hours a day, to build rulesets and aligned structured positions so they can scrape news feeds and react in milliseconds.
Anyone who thinks they can sit at home and day-trade with these sharks without being fleeced is a fool. But then, anyone who is a fundamentals trader and is still in this outrageously irrational market is also a fool.
One of the first things I learned as a trader: "The market can remain irrational longer than you can remain solvent."
Plugging in an average stock market performance (over last 20 years):
Return: 8% Standard Deviation: 17.72% Risk free rate: 3% (guess)
This gives f = 1.59.
This means the optimal strategy is to be putting 159% of your money in an ETF index?
This strategy is in stark contrast with the typical 70%-30% allocation of investments. How do we reconcile this? Intuitively, the function of your age needs to be included in this equation (I think somebody commented on this already).
For a consumer, the rate of funding would be higher, however.
Alternatively, where can I get my 3%? No ICOs please ;-)
no single security provides the risk-free rate but perhaps a (small) portfolio of securities could get you the risk-free return.
3% is more accurate for the cost of margin loans or the opportunity cost of pre-paying a mortgage.
Putting 160% would mean using a leveraged S&P 500 ETF.
Plus, many investors can't stomach the losses of a 100% equities portfolio, let alone something levered up.
>How do we reconcile this? Intuitively, the function of your age needs to be included in this equation (I think somebody commented on this already).
Age is a proxy for funding amount. A lot of investment goals aren't just "maximize the amount of money I get". They often care about things like "I need to spend $X/yr in retirement". So your investment goal should also put some weight on how likely it is to sustain that, and a higher bond percentage at higher investment amounts will do that.
That is not necessarily true regarding leveraged etfs.
Leverged ETFs when used as a substitute for being fully invested can be more safe than being fully invested in the non-leveraged version. The idea being one puts 1/3 of their capital in the 3x S&P 500 ETF and the 2/3 in T-bills. The maximum loss, no matter what, is still only 33%.
Ruin (if it is defined to mean 100% loss of capital) is impossible with a leveraged etf [it just means your wealth asymptotically approaches zero], but it is possible with margin debt.
If you rebalance daily in order to maintain your desired stock exposure, you end up owning the S&P 500 as your buy and sell orders of the levered ETF counteract the ETF's buy and sell orders on the underlying index to maintain its leverage. All you're doing is paying higher fees, trading costs, the spread on T-bills vs institutional margin costs, and realizing capital gains and losses pointlessly.
What you want is to buy call options on the S&P 500 index. The market is far more efficient here and way better for you.
Funny how this seems also to work as an argument against Pascal's wager.