Rebalance or not to?

[tomsmith]

Hello everybody,



can anyone please help me with some ideas about how to divide funds when investing in 2 or more stocks?



If i decide to divide my money evenly, than it would seem rational to keep it evenly divided and rebalance it, whenever it is not even.



But if 1 of the stocks starts loosing value and eventually goes bankrupt, if i keep rebalancing, i will sink all of my money in it, ending up bankrupt.



If i never rebalance, than i end up with a ratio of funds decided by past performance, which would pose a question, why not start by dividing my funds based on past performance. But that doesn't seem to be rational as past performance doesn't indicate future performance.



I am not sure this is a good topic for this forum, but i thought that someone might have some mathematical solution to this problem.



Thanks!

[apine]

we call the answer to this question: trading!



there is no mathematical answer to this question. but here are a few ideas:

1) usually "re-balancing" is something done between sectors or asset classes. this avoids that pesky bankruptcy scenario

2) in the extreme case of re-balancing immediately, you are effectively pairs trading

3) one might have criteria for exiting one or more of the stocks. that might be fundamental or a simple stop-loss

there is a mathematical investigation into this, but it really deals with more arbitrage-like scenarios. it is in a paper by boguslavsky. try searching for it. i think it is on his site.

[Tradenator]

For more on selecting portfolio weights, see [url=/Show%20Post.aspx?PostIDKey=92879]here[/url], [url=/Show%20Post.aspx?PostIDKey=74355]here[/url], etc ... and use the search button to find many other threads on this topic.  There is a lot of good info on this site that is worth the effort of actually finding the search button and using it.  Any method here, except equal weights like you said, would require that you size positions based on historical data.  Graeme has a nice pdf on portfolio construction here (under Modern Portfolio Theory).



As apine said, there is also a trading issue here.  Surely you would close the losing position and let the winner run for a while, right?  Finally, it is well reported that trends in markets often persist, so you might want to rethink what is rational and what isn't here when it comes to using historical data to base decisions on.  Google "price momentum".  The idea is to be correct on average, and then size positions to get out when you are wrong and stay in when you are right.

[kr]

I think this is the question with the least satisfactory academic answer. MPT says where you want to be, but not how to get there. There are lots of impartial answers. You can go the route of Kelly or Optimal Portfolios. But on a practical level, you have to ask a qualitative question about when you would not be happy with a given allocation. For example:



1- believe that a static MPT is always right. This will mean you tend to buy into cheap stocks and sell off expensive ones. Saying it that way sounds a bit like being short gamma, which is kind of odd. Alternatively, think about mean reversion / "dollar cost averaging" or other such theories.

2- have a macro view, that translates into a dynamic MPT... i.e. these days maybe you'd rather be longer govies and less long equities, so rebal.

3- sector rotation theories and the cycle - i.e. dynamic MPT changes b/c certain sectors are better during different parts of the business cycle

4- other technical rebalancing strategies



I think it is a good question to discuss. I've thought about it a bit, for my own investing, but haven't been too satisfied with my conclusions.

[nodoodahs]

The simple, mathematical answer to your question is: You should backtest your ideas over a variety of rebalancing strategies, and not hold preconceived notions until you have some data.



I'm concerned by the psychology of your example, "what if" the stock falls to zero. How many stocks ever fall to zero? What percentage of stocks do they represent? Is this a realistic concern for the stocks that you are trading, during the timeframe you intend to hold them, or is this an emotional fear trying to express itself in your trading? The market is a good place to find out about yourself and how you handle fear, but it can be an expensive proposition.



About trend: Seykota would probably say that there are no trends in the marketplace; "trend" is a concept that we bring to the marketplace, in order to categorize data. I don't know that "trend" is a meaningful term in and of itself, apart from a strict definition in mathematical terms, or at least a timeframe.



On short timeframes, I dunno. I'm not a high-frequency guy. I suspect that equity trends are mean-reverting on short timeframes, especially extreme downtrends on timeframes under a week.



On very long timeframes, trends are mean-reverting. This is the concept behind asset allocation and rebalancing in longer-term portfolios. You can easily google on those words for *.pdfs and find them.



On medium timeframes, trends to persist, from what I've seen and read. This is something I'm working on with weeks to months of holding time.



Some of the papers I've read on "price momentum" (all of which should be read carefully for their definitions) suggest that annual return momentum is mean-reverting over a month and positive over longer windows (3-9 months).

[apine]

hey nodoodah, seriously you have to be kidding right? you think it is an irrational fear that a stock can go to zero? doood. really.



how about enron? anything.com? countrywide? american home mortgage? continental illinois bank? polaroid? kmart? sears? and those are just big names that come off the top of my head. there are plenty that have happened and neither you nor i know about it, or it is just a name from the past. and fyi, it can happen in a hurry.



forgetting going all the way to zero, how about traditional implosions -- say citi right now or mckesson back in the 90's. how about tyco or lucent? or cisco? or how about a mean reversion strategy between say, microsoft and exxon mobil based on historical data that you tested from, say 1986-2000 and then implement in 2001 or 2002?



that kind of thinking is exactly what gets firms in deep trouble. backtesting without thinking about what could possibly go wrong is what everybody rants against when it comes to var and other risk management debacles. otherwise all you have done is implement a var trading strategy.

[nodoodahs]

Nope, not kidding. Go back and re-read it. Nah, I'll save you the trouble.



"Is this a realistic concern for the stocks that you are trading, during the timeframe you intend to hold them, or is this an emotional fear trying to express itself in your trading?"



Trading is probably a bad arena to act out fears in.



You name a handful of examples over many years. Decisions by anecdote aren't usually profitable. How many different stocks have traded in the NYSE, AMEX, and NASDAQ in the last two decades, and in the same time frame, how many have went to zero? What are the odds? How are those odds mitigated by diversification or perhaps an options strategy? How long does a typical case take to go to zero, and how does that interact with the chosen trading strategy?



[open Edit]



I don't deny that some stocks go to zero, and I don't deny that it is a risk that must be accounted for. I am arguing that *reasonable assumptions* must be made about that risk, in the context of a trading plan.



For example, consider a buy/hold strategy with fixed allocations, rebalanced never, for equities. The risk of a holding going to zero while being held is approximately as above, i.e., how many ever go to zero out of the total available.



Using fundamental analysis (cash flow metrics, proxy review, eliminating candidates with off-balance sheet holdings exceeding some threshold or candidates with special-purpose entities) would ameliorate that risk greatly. Earnings warnings were a key part of all of those "go to zero" cases, and such news would change many financial ratios (cash flow to price, P/E ratios), and that may be a key element of a longer-term strategy. Guess what? All of those can be QUANTITATIVE STRATEGIES in that a numeric guideline could be implemented.



Using technical analysis (stop losses, momentum, moving average filters) would ameliorate a lot of that risk as well. Enron had to drop 20% before it fell to zero, would you still be holding? It had to drop 50% before it fell to zero, would you still be holding? It had to drop 70% before it fell to zero, would you still be holding? Other than biotech stocks, how many stocks ever have a one-day move more than 20% or so?



I submit that the risk of a holding going to zero while being held is pretty damn small, in the context of most realistically-crafted strategies. One is probably more at risk from a market correction causing a majority of holdings to fall 10-20% than one is at risk from any one particular stock going completely to zero while it is being held. Hence, my supposition that the "going to zero" was an expression of fear.



[close Edit]



Speaking of strategy, what is the trading strategy? Are there stoplosses or time stops, or other downside protection? What is the timeframe? A system that rebalanced every month, with a technical momentum component, would have eliminated most (if not all) of the risks, and that's just a simple example.



As an aside, don't get me started on mean reversion strategies with an oil company and a tech company. It's that kind of stupid, mathematically masturbatory play that causes trouble. Why would they be correlated? What is the science that would anticipate the correlation would continue? What are the failsafes in that strategy? Should one monitor the mean-reversion trades for results that are outside what is expected, as a stop-loss strategy? In my work on statistical correlation, I don't accept that correlations will continue as a default, and would be likely to consider that possibility only if a reason for the correlation could be found or surmised. What would that reason be for MSFT/XOM?

[DrTarr]

What would that reason be for MSFT/XOM?



Because they both have an M in their ticker symbol!!



I agree - the possibility of going to zero is really not a concern for any trading strategy.  The possibility of going down, sure.. But zero?  Even with Enron - Kmart and anything.com a strategy would probably exit long before 0.  I don't think you would keep rebalancing into that particular stock.



If you look at it as a fear - then perhaps some king of utility makes sense.



But, as the original question mentions, rebalancing based on past performance would be MPT and the cited reference would be an excellent start for the mathemaitcal formula.  If the question is more how do I decide what stocks to buy, then the question comes back, what are you willing to put into it.  Dart Board - Buy a News Letter - Fundamental / Technical analysis?  You split up you money into stocks that you think are going to make money and the risk of going to zero is reduced by -more stocks - better research and paying attention!!

[apine]

there is a very simple strategy for the two of you: sell loads of naked puts of way otm strikes. this is going to work really well for a while. and one day...well, one day not so well. now, if you figure you'll be getting your management fees for a year or two, great. but if you actually care about the money you manage, then you might want to consider the possibility of the company going bankrupt -- or that the market might consider that a possibility for a company. check out nstk. this is not even a bankruptcy. they just got bad news. so i hardly think that this is an oddball or ivory tower concern. quite the opposite.



most important, though, is when noddodah questions the whole psychology of even considering such a scenario when entering a trade. i would find this quiet troubling in someone managing my money. "aaaah, we don't worry about any company becoming bankrupt. that's for ninnies. " by the way, this guy did not say it was a trading strategy in the sense of pairs trading or high frequency. he was talking about portfolio allocation.



which brings us to our other topic. the msft-xom trade. i love your ignorance ridiculing this. merely because you lack the imagination or have the experience to figure it out does not make it so that you should be nasty. first, people build all sorts of models out of spurious correlation all the time. but really, that was neither my point nor the reality. my point was simply that msft had outperformed the market for 15 years and then became a dud. xom did the reverse. it is perfectly rational to buy one and sell the other. OR more likely one allocates their assets to the stock or sector that they think will be more attractive. and many people thought msft would continue to outperform xom for some time. and allocated assets to msft instead of xom is a synthetic version of a pairs trade. there might not be outright losses, but there sure was opportunity cost. and no doubt the fund that bought msft and did not buy xom lost assets to the "genius" that did.

[apine]

alright. i typed above before seeing your edit.

you are making assumptions about the trading strategy which is independent from bankruptcy odds. nor do i think that reading balance sheets help with fraud.



edit - got rid of stuff -

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