How to measure if investors are diversified in a stock market?

Question

My question is related to this question but it is not the same. Consider the US stock market. How can I tell if people trading in this market hold properly diversified portfolios? Is there some literature on this? I cannot find anything.

Answer 1

I think the first step is to define what you mean by "properly diversified". A traditional/fundamental standpoint would be that the portfolio is comprised of many different sectors, industries, ect. The more "quant-like" approach and in my opinion, a more realistic approach, is to understand correlation between portfolio assets and the dynamics of said correlation. A key observation would be that correlation between assets tends to increase when the market falls. In a practical sense, one might look towards beta-weighted delta (perhaps to the SP500 or to the predominant index in the market being modeled) as a proxy for correlation. Now that we are comparing apple to apples (all our delta is weighted towards a single index), we know what our exposure is vs. the "market" (our index).

As for determining what other people are doing, the answer is not clear and a very quick search seems to yield few results. Here's a little exercise, if you will, that might help:

1. Assume we have an index like the SPY to beta weight.
2. Assume the beta-weighted delta of a participant's portfolio is a proxy for diversification.
3. Assume that participant's only hold assets within the index.
4. As the market goes up, it is natural that long-delta participants will lose delta (sell for profit) and short-delta participants will gain delta (buy to cover losses). The opposite is true for a down market. Participants who are delta neutral stay neutral.

Depending on the initial distribution of long and short portfolios, the amount of selling for profit/buying to cover losses or vice versa may or may not be evenly distributed. Therefore, the lack of uniformity in the distribution would create more pressure to the long or short side of the market as a whole (again this is a strong supply and demand-like assumption). One could potentially develop a metric of sorts that takes a guess at the initial distribution of portfolio deltas via the buy/selling levels as the market moves (one would need to define "buying/selling levels).

Overall, going through a process like this can't hurt and maybe it would produce something useful if certain constraints can be relaxed. The method I have outlined is naive and I hope someone can point out some terse work on this question.