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Hafoch Ba D'Kula Ba: Portfolio Diversification in the Torah

In a mishnah in Pirkei Avos (5:6) (popularized by Shweky ; - ), Ben Bag Bag states "Hafoch ba hafoch ba, de'kula ba - Turn it and turn it, for everything is in it." In other words, all of the wisdom of the world can be found in the Torah, albeit often expressed cryptically and with brevity - leaving it to Torah scholars to tease out the details through diligent study.

Over the years, I've found Ben Bag Bag's statement to be very true, and have been zocheh to find all sorts of wisdom and insights embedded within the gemara and other Torah sources ranging from mathematical concepts to principles of psychology.

This week's parsha - Vayislach - offers validation of Ben Bag Bag's principle. For starters, it's well known that sages throughout Jewish history have studied Yaakov's preparations for his confrontation with Esav prior to their own negotiations with foreign governments (indeed, as per an idea floated in an earlier post, there seems to be elements of game theory operating in the story of the confrontation between Yaakov and Esav that could be highly instructive in terms of how each dealt with the dilemmas they faced given the imperfect information they each possessed about the other's intentions and merits).

What's less well known is the nugget of sophisticated financial advice that the gemara extracts from the parsha.

Following the return of his messengers, Yaakov remained uncertain of Esav's intentions (alluded to in the text of the parsha which refers to Esav alternatively as "Esav" (symbolizing malicious intent) and "achi - my brother" (symbolizing friendly intentions)). Just in case Esav was preparing for battle, Yaakov split his camp into two parts so that should Esav attack one, the other camp could flee (32:9).

R' Epstein in Torah Temima says Yaakov's strategy forms the basis for a bit of business advice in Baba Metzia (107b), where R' Yochanan states that a person should divide his agricultural assets into 3 parts - one third wheat, one third dates, and one third vines.

As Rashi elucidates, in years in which one or two of those crops perform poorly, the others will prosper, thereby mitigating one's losses. In other words, diversify your holdings across equity asset classes with dissimilar patterns of return - which happens to be the bedrock principle of modern portfolio theory ("a theory of investment which tries to maximize return and minimize risk by carefully choosing different assets") (see also Wikipedia entry on diversification).

Unfortunately, the Talmud does not expand on R' Yochanan's brief statement, but at least we see that our sages were aware of fundamental principles of asset diversification.

Interestingly, I came across an abstract of an article in the Journal of Portfolio Management, which referred to R' Yochanan's rule as the "1/n rule for n assets," which assigns equal weight to each asset in a portfolio of "n" assets. The article compares the 1/n rule to modern (and far more complex) portfolio strategies such as the Markowitz diversification model.

Another article I found argues that the "1/n" rule (which ignores the mathematical complexities underlying modern portfolio theory, and is thus often referred to as "naive" diversification) actually performs well in practice, and results in reasonably diversified portfolios "that are surprisingly close to some point on the efficient frontier." (since I am no finance maven, that last statement leaves me scratching my head, but I invite any "finance" experts to chime in).

IMHO, seems to me that the recent financial crisis - triggered by banks using enormously complex models that were apparently poorly understood - suggests that maybe a return to "good 'ol" Talmudic finance may not be such a bad idea.


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