Power Laws and Luxury Goods

As Chris Anderson knows, once you start thinking in terms of power laws you start seeing them everywhere. But it's worth drawing a distinction between power laws as a meme and power laws as something mathematically well-defined.

After posting a piece on power laws in the housing market, I got an email from one of my more devoted readers (OK, my father) asking if I had the vaguest notion what I was talking about:

I would like to know if there is any statistical basis for the alleged "power law distribution" of house prices in different cities or whether it is just journalese (as in "exponential" which is one of the most misused words around).

Good question. And the answer is, frankly, "just journalese". Specifically, I would never try to discern the distinction between a power-law distribution and a lognormal distribution – when I use the term "power law", I basically mean "something with a much longer and fatter tail than your standard Gaussian bell-curve distribution".

Let's get away from housing and think about luxury goods. And let's look at the tail -- specifically, at the top 1% of the market. (Either the market in general, or any market in particular, such as wristwatches, for example.) Now look at the top 1% of that top 1%.

If your distribution is Gaussian, there isn't an enormous amount of difference between the top 0.01% and the top 1%. It's there, but the top 0.01% won't be more than two or three times as expensive as the top 1% generally. But if you have a power-law distribution going on, then the top 0.01% will be vastly more expensive, maybe 100 times more expensive, than the top 1% generally. If you have a lognormal distribution, then you'll be somewhere in between.

The power-law thesis is that many parts of the world are moving away from normal distributions and towards distributions which look much more like lognormal or power-law distributions. Check out Merrill Lynch, which has just launched a luxury-goods "LifeStyle Index", a "tradable certificate" which tracks the earnings of the luxury-goods sector.

The performance of the index has been back-tested from January 2000 against the major broad benchmarks for the global consumer discretionary sector, namely the MSCI World Consumer Discretionary index. The average outperformance of the index versus its benchmark currently stands at almost 8 percent despite a similar volatility and a dividend yield that is 20 percent higher on average. This performance illustrates the theoretical efficacy of the index together with the inherent value of brand names associated with luxury goods and lifestyle stocks.

In other words, this index is a bet that the rich will continue to get richer, and that as and when they do so, they're likely to splurge on ostentatious displays of wealth from established brand-names.

Not a stupid bet to make, although of course if the stock market is already pricing in those future earnings gains, Merrill's index isn't going to continue to outperform.