DeepState
Multi-Strategy, Quant and Fundamental
- Joined
- 30 March 2014
- Posts
- 1,615
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- 81
Hi So_Cynical. In terms of the basics of your thought experiment, no you did not miss anything. The reason why this particular path way did not add value is that both stocks moved upwards in the second period by exactly equal proportions. When that happens, rebal can't make money - but it doesn't lose you money either. But, as you know, stocks very rarely move up or down in identical rates of return. When they differ, particularly if they revert relative to one another from the returns prior to rebalancing, rebalancing makes money. So, given stocks move around, sometimes in the same direction as prior period to rebal (no money to be made) and sometimes in opposing directions to movement prior to rebal (money gets made), overall there is a positive expectancy [you'd see HR around 0.5 and slug >1]. But, as you know given you apply an average down strategy, this is probabilistic. Not every trade works, and some have to be cut - as per your HR being <1 (like the rest of us). I refer you to post #35 and #37 of "What has your hit and miss ration been?".
As skc mentions above, lots of things can happen but rebal is expected to provide outperformance over time, with increased likelihood with the progression of time. You are the house and offering Roulette. Anything can happen over short intervals including, say, 12 reds in a row [which is akin to a two stock portfolio in which one stock moves up by 50% per annum for a couple of years and another moving down in a mirror fashion]. It is a real scenario, but the chances of occurring are slim. Over the longer term, the casino is ahead - as you also know and any path taken to get there is just one of many that chance might have allowed.
As a rough and ready tool to progress your thought experiment, let's BS and assume that stock returns are just random numbers. Each stock return is an average return that you can set at your discretion +/- some random number. So, say, we rebalance each quarter. For quarter 1, say, Stock A has a return of 2.5% +/- 20%. You can change these as you wish. Produce a whatever-you-like (say, 5 years worth or 20 quarters) length of quarterly returns this way and you have our BS workbench approximation of a stock return. Do the same for Stock B, C, D,...maybe to 20 stocks, heck go for 50 too if this is just an experiment. These stocks can have different expected returns and different randomness around this expectation. So now you have our BS stock market. You can create a stock market with all stocks going up, mixed or all stocks going down. It doesn't matter, but you could do it if you wanted to. What matters is that the random movements in the stock prices are not wholly synchronized....and that the expected stock price movement in either direction does not exceed the magnitude of the random part of the return for the whole period [ie. pulling Reds twenty times in a row for all stocks in your portfolio]. In other words, hopefully you'll see fit not to assume that all stock prices have an expected move of +/-10% per month if each random part is +/-10% (you can see the symmetry for other figures that you could use) in the same or different directions to infinity or zero if you are trying to get something out of this. Or, you can do it with awareness of the remoteness of possibility. I'm not sure I have seen an equity market do 120% per annum ad infinitum. Individual stocks might, though, and you might wish to play with this [movement size and time concentration] in a portfolio to see what happens.
Calculate two things...
1. Each quarter, average the returns across all 20 stocks. These returns represent a rebalanced portfolio of equally weighted stocks. It doesn't have to be equally weighted, and you can do whatever you like with the weights as long as it is consistent with 2. Then accumulate these returns using compound returns. That is your total return for a rebalanced portfolio over the period.
2. Now, to calculate the return for an unbalanced buy-hold portfolio, you take the cumulative returns for each individual stock and average that. This is the buy and hold return for an initially equally weighted portfolio. Again, it doesn't have to start at equal weighting. It just has to be consistent with 1.
Keep pressing F9 and you will find that the difference between 1. and 2. jumps around. That's why it's called a probabilistic process. Any one F9 press produces one scenario. Anything can happen. Count them and you will tend to find that, most of the time, 1. exceeds 2. by a healthy margin. Keep records of it, and you'll probably find that the average difference is pretty interesting.
Although this is a BS stock market, you can feel free to progress to use real stocks and try it out. Just pick anything and give it a chance to play out over five years (it doesn't have to be five years...a longer period just helps you to see the conclusions more readily). Try heaps of different combinations of real stocks, or just try a diversified portfolio of 50-100 truly randomly selected ones. It would be helpful if you had a monkey to help you with this for authenticity. The monkey can use a dart or can point. In fact, they can do that at the end of each quarter and reshuffle the stocks (thus helping with the problem of high unemployment for primate stock selectors particularly in peripheral EZ), but keep the weighting schemes as they were, and that would be fine. For the fun of it, get the monkey trained by NASA and get it to choose amongst the stocks that lost value over the investment horizon you are testing. Choose any investment horizon over the period since stock markets were created.
Because it was a thought experiment, I imagine you don't really think in terms of two stock portfolios that move around by 50% amounts. If you are rebalancing quarterly, say, movements of 50% in opposing directions in a two stock portfolio are...remote. And you have found that it does not subtract value in your experiment.
We then come to two hoary issues:
1. What about commissions and taxes?
2. But...I have views on the market, does this override this?
1. Please feel free to model your commission for trades. In reality, you'd only rebalance significant outliers - say the 10 biggest misweighted positions each quarter as a rule of thumb. The small misweights don't matter much at all because they are...small. However, if your account size is small, commissions will be an issue. In that case, rebal works pretty well on annual periods. Go ahead and try it out (you already did, actually). So there are always ways to bring comm into small consideration. DO NOT cross the spread. These are non-urgent orders and you can just sit on the limit order book until someone comes to you for liquidity.
Taxes are interesting. If you are in pension mode, there's no issue. If in SMSF accumulation mode, then the worst case cap gain is 15%. Now check out what realistic turnover is and you'll find that it isn't much. It's all fractional stuff. Nothing like Martingale where you have to lay down exponentially larger bets as the market moves against you. Factor in the fact that you are accumulating investments...which means that you are buying at current prices and have fresh parcels. You are free to choose which tax parcels to liquidate. Hence, you just choose the most expensive, subject to the applicable tax rate to the parcel. When you allow for this and the fact that you are probably recycling dividends back into the market as well, you can generate more than adequate turnover without much cost in just about any scenario you wish to explore. When you move to max tax rate, and you are accumulating assets, then fairly similar things apply as per the SMSF accumulation. You generlally have enough room, or create enough room in your tax parcels for it not to be too much of an impediment. Given you are smart, if you found that there was a line or so that was 'locked' due to heavy tax implications for parcel harvesting then guess what...just leave them out. Things just aren't that sensitive to this stuff.
2. Does this mean that you can't express a view? WTF? Of course you can. Those simulations above are for an equally weighted portfolio. There's nothing stopping that from being any weighting scheme you want. Those weighting schemes are essentially your target weights in your portfolio. However they were derived - it doesn't matter. If you want to get a bit super-duper about it, then I refer you to Post #55 in "What has your hit and miss ration been?". It will explain the key concepts and roughing it will for your needs is just fine.
Overall it's just cream on the cake. But we are here to get phat.
Good trading to you, So_Cynical.
