I recently ordered and received Ralph Vince's The Handbook of Portfolio Mathematics. Vince's deep mistrust of gambling makes it more opinionated and moralistic than any other math book I've encountered. It's a little odd that he despises the practice of what he passionately studies, but it makes it interesting. For example from the introduction:
I truly love this stuff. I hope my passion for it rings contagiously herein. However, it sits as dead and cold as any inanimate abstraction. It is only your ... [tennis metaphor] that gives them life.It reminds me of a Blink 182 song.
There are gems throughout, such as "reinvesting can turn a winning system into a losing one but not vice-versa" and "in a positive expectancy situation the trader/gambler is posed with the question of how best to exploit the positive expectation" which is essentially the purpose of what is termed money management. The explanation of the martingale betting strategy is interesting. If I go to Vegas I would like to test it. Basically one doubles down on every losing bet so a single winner puts you ahead. Rarely one will lose everything but most of the time one will come out ahead. The expectation gain is negative. It's sort of like the converse of the lottery. The section on probability distributions also provides clear practical explanations.
The Amazon reviewer who gave the book two stars (the only non five star review) for being too mathematical apparently has next to no math background since everything is explained (sometimes excruciatingly) very simply with almost no greek letters or sophisticated functions. His use of the acronyms TWR and HPR obscures some of the calculations- I would prefer the math to be more formal (however, I read textbooks for fun).
The charts on pages 134-149 are great for persuading yourself that going above the "optimal f" [percentage of total capital to stake on each trade/bet] does not actually increase profits. Basically it says that even with a positive expectation of profits, in the long run it can be most profitable to only bet a minority stake of your total capital. The chart on page 119 also helps explain this idea. I had come to many of the same conclusions as Vince in my previous two money management modeling exercises, on finding optimal position sizing via Monte Carlo analysis and in my Trading Objectives entry. It feels great reading something which elaborates and carries forward ideas I discovered independently.
I recommend buying Vince's book or checking it out from a library since it really helps guide your intuition about gambling theory. Basically any reader with background in trading or basic probability will be able to understand it. Right now I'm about halfway through, I will review more once I'm further. I'm always looking for good books so feel free to recommend anything.
4 comments:
Max - I read this book and was unimpressed with a lot of it on my first read. I agree there are some good concepts in there though. The book i really liked in the portfolio math & position sizing realm is Van Tharp's 'The Definitive Guide To Position Sizing'. You have to go to his website to get it.
He basically advocates using the t-score of the expected value per trade to analyze a system's potential performance. I think this is good, but would modify the formula to account for # of trades/period & reduce the benefit that a large number of trades has on the std. error portion of the t-score formula.
Regards,
Eric
Eric,
Thanks for your suggestion. I'll probably get that book once it goes on Amazon. The t-score would be a good way to get an idea of what results to expect from a system.
Regards,
Max
Max,
I didn't see this posting in your blog until now. Please let me qualify for my disdain for gambling.
I've been surrounded by compulsive gamblers and the tragedy they create since I was born. Later, as a margin clerk, I would have wives come to my workplace and beg to "Please call me if my husband starts trading options." I am averse to proffering gambling situations because they prey on human weakness (as too the absence of enforceable usury laws in the US -- I find we a culture than when it comes to loss created by human weakness, we DO condone it because, "No one had a gun pointed at their head.")
This plays out into gigantic and destructive monsters, such as we saw in late 2008 requiring the rich daddy of TARP to bail out the loser son's gambling losses.
Anything that requires an offset through the course of the transaction is gambling. If I buy stock in a company, and short sales are prohibited, there is no co-running offset on the trade. Similarly, if I buy real property (post-Kelo in the US, however, we can no longer do this as real property has no more intrinsic value to it than a bag of smoke) in a country that honors landholder's rights, whoever sold it to me can walk away, they no longer have a vested interest in it. But when there is a vested and opposing interest to a transaction -- it's gambling, and, historically, always results in calamity attributable to that very himan weakness.
To-wit, TARP.
Intrerestingly, I am unable to think of a position any tradable that comports to this definition (whereby there is no concurrently-running offset with an opposed interest in the position) that is not bound on the left side at 0.
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