Israelsen on Diversification (Part 3)

I want to offer one further critique of Craig Israelsen’s performance data included in the last post.

As shown in the table, over 15 years the 12-asset portfolio outperformed the 7-, 4-, 2-, and 1-asset portfolio (in that order). But was this a statistically significant result?

In response to my question, Israelsen wrote:

     > The issue of statistical significance pertains to
     > differences among samples that are drawn from a
     > population (inferential statistics). As the
     > different portfolios are not samples, the issue
     > of statistical difference in the returns is not
     > relevant. In other words, the return of the 1-
     > asset portfolio is not the mean return of that
     > type of portfolio, it is THE return of that
     > portfolio. Same logic for the 2-asset, 4-asset,
     > and 7-asset portfolio. In essence, any
     > difference in the returns is material.

I think Israelsen has a good point but I am still uneasy about his numbers. To get the returns presented, I would have to start investing on the exact same day he did. This is highly unlikely.

Alternatively, Israelsen could have created samples by studying rolling periods. This involves calculation of multiple returns over stated time intervals starting on different days. He could calculate a mean and standard deviation of all sample periods, which could then be compared using inferential statistics.

By providing one static return as Israelsen did, I believe he leaves the door open to fluke occurrence. Without knowing how likely different portfolio start dates are to dramatically affect average annual returns, no robust conclusions can be drawn. I believe Perry Kaufman made this same mistake in an article discussed recently.

I also believe Israelsen missed the point of diversification because he did not discuss drawdowns. While diversified portfolios may not result in higher annualized returns, I do believe standard deviation of returns (otherwise known as “risk”) decreases when non-correlated assets are combined.

Put another way, liked hedged portfolios I expect diversified portfolios to “lose” most of the time. This was mentioned in Part 2. However, with lower drawdowns the probability of investors holding positions through the rough times is increased. The worst outcome would be dumping the portfolio and locking in catastrophic loss from a market crash and missing a big market rebound that may be just over the horizon.