Archive for February, 2009

No Free Lunch Theorems

Tuesday, February 24th, 2009

“The Difference” has reminded me of No Free Lunch (NFL) theorems. These theorems state that solutions always depend on the problem being solved, and that there is no such thing as a general solution.

I hear this from NFL: logic informs us about reality by resolving contradictions, and you need a source of contradictions to start with. That source would be assumptions. Of course, the wrong assumptions combined with logic would misinform instead of inform, and it isn’t obvious what the source of “correct” assumptions is.

A related, interesting note: Occam’s razor demands simplicity in assumptions, not the logic.

Book Queue

Tuesday, February 24th, 2009

At the end of January, I got a carton of books:

  • How’d You Score That Gig?: A Guide to the Coolest Jobs-and How to Get Them
  • How to Be Alone: Essays
  • The Snowball: Warren Buffett and the Business of Life
  • The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies (New Edition)
  • The Partnership: The Making of Goldman Sachs
  • Life Entrepreneurs: Ordinary People Creating Extraordinary Lives (J-B Warren Bennis Series)

all of which had popped up on some blog or another in my rss stream. I’ve quickly gone on to dismiss “Life” and “Score” as mindless anecdotal drivel, and am currently reading “Essays” and “Difference”, alongside “Matter” by Iain Banks.

I’ve found “Difference” to contain interesting points, but so far have found it ineffectual in rekindling my waning respect for toy models. The toy model logic in the book is very combinatorial, which to me means that conclusions depend a lot on the particular favor of factorizability assumed. I have continued to be troubled by the idea that modeling is weak as a general approach to understanding because of the sheer number of starting assumptions that is typical. “Essays” is not a book that can be read fast, and I am enjoying “Matter” very very much.

Sci-fi like “Matter” really raises my spirits. That I find such a source of meaning in something I cannot deny is pure escapism is something which I think should trouble me. The first Culture novel I read, “Consider Phlebas”, was not that good, and yet I had enjoyed it for the glimpses of the Culture universe it offered. “Matter”, on the other hand, is thoroughly enjoyable.

Warren Buffet’s misleading buy-the-index logic

Saturday, February 14th, 2009

Warren Buffet, in his 2007 letter to shareholders, argues that index investors make the average return:

Naturally, everyone expects to be above average. And those helpers – bless their hearts – will certainly encourage their clients in this belief. But, as a class, the helper-aided group must be below average. The reason is simple: 1) Investors, overall, will necessarily earn an average return, minus costs they incur; 2) Passive and index investors, through their very inactivity, will earn that average minus costs that are very low; 3) With that group earning average returns, so must the remaining group – the active investors. But this group will incur high transaction, management, and advisory costs. Therefore, the active investors will have their returns diminished by a far greater percentage than will their inactive brethren. That means that the passive group – the “know-nothings” – must win.

In this paragraph, there is an average over stocks and an average over investors. Both are weighted averages – the stocks are weighted by market value, and the investors have their stock return weighted by the market value of the stocks they hold. These two averages are exactly the same.

In fact, this logic holds for any set of assets you’d care to define. For example, it is true for the set of all stocks that start with the letter A (‘A’-stocks). If you held just ‘A’-stocks in your portfolio proportionally to their market caps, you would earn the same returns as the average ‘A’-stock investor, provided you weighed their ‘A’-stock returns by the market value of ‘A’-stock they had.

However, you would never just buy stocks that started with the letter A because the risk-return ratio for that would be inferior, as you would be bidding for those stocks against people who are diversifying away risk using a wider range of assets. In fact, even stocks as an asset class is completely arbitrary given the many other asset classes which could be used to diversify risk.

The best risk-return possible using only stocks is not achieved by weighing by market value, because the other players are not restricted to only using stocks. This is not a new idea. According to Wikipedia, the world stock market as of October 2008 was $36.6 trillion, while the world derivatives market was $480 trillion and the bond market as of 2006 was $45 trillion. Therefore, it certainly isn’t the case that a primarily stock portfolio is anywhere close to market cap weighting. Also, I simply do not think disregarding the usage of stock derivatives for mitigating stock risk is plausible.

The “average stock return” justification for buying the index is fallacious because the choice of asset class is completely arbitrary.

Frameworks and Graphs

Sunday, February 8th, 2009

Many frameworks consist of boxes with arrows drawn between them. When people introduce a framework, they usually start explaining what each arrow means, e.g. how A -> B represents the specific ways in which A influences B, going down a list of possible interactions.

There is  a different way of looking at the information which the framework provides, which is not what’s in the arrows which are drawn, but rather in the fact that some arrows are missing. Every missing arrow is an assumption that the two factors concerned do not affect each other directly, and these are the assumptions which simplify and accelerate understanding.

Frameworks where every possible arrow has been drawn are uninformative in this regard, and can be replaced by a simple list.

Theory of the Firm, Transactions, and Commoditization

Sunday, February 8th, 2009


In simplified terms, the theory of the firm aims to answer these questions[1]:

  1. Existence – why do firms emerge, why are not all transactions in the economy mediated over the market?
  2. Boundaries – why the boundary between firms and the market is located exactly there? Which transactions are performed internally and which are negotiated on the market?
  3. Organization – why are firms structured in such specific way? What is the interplay of formal and informal relationships?

Part of question 2: the boundary between firm and market is sharp iff firm-firm interactions can be characterized by a few simple dimensions like price and quantity – we call these transaction-based interactions, and call such products commodities. When we don’t know how to reduce the interaction, the idea of a “market” is not useful, and we call those interactions relationship-based.

It’s a false spectrum, because “transaction-based” is a lot more informative than “relationship-based”, which really means “everything else” – we say “relationship-based”, but I think it is more aptly described as “non-transaction-based”.

Why isn’t there a Case-Shiller ETF?

Friday, February 6th, 2009

I met a college friend, an economist who works at a REIT, for lunch. The discussion turned to Case-Shiller ETFs, how there aren’t any. I speculated that the difficulty of bridging the huge liquidity gap between an ETF and residential real estate has something to do with it. In the case of the paired funds that MacroShares was slated to launch but never did, maybe the amount of buffer needed would have been too big.

Basically, the arbitrage mechanism behind a Case-Shiller index would have such high liquidity premium that it would hardly track the real thing.

Unverified, but related: my roommate has informed me that the GLD ETF is currently worth a lot more than its contractual gold equivalent.