Monday, July 29, 2013

Building Your Own Index with Individual Stocks

Long-time reader, Gene, asked the following good question
“Have you considered making a pseudo index fund by buying perhaps 15 large-cap stocks from each of Canada and the USA that would mimic an index? Not ideal for a growing portfolio, but for a relatively-stable account, and low commissions, it could save money on fees. Drawbacks are that it would be harder to increase or decrease holdings, and the savings wouldn't be huge over already inexpensive ETFs.”
Gene is right that a carefully-run stable portfolio of stocks can cost less in fees than index ETFs. However, an important issue is how well such a portfolio would track its index. For an answer here, I turn to Meir Statman’s paper How Many Stocks Make a Diversified Portfolio? Table 1 of this paper shows how the standard deviation of portfolios varies with the number of stocks you own.

At this point, I need to diverge to a topic that few investors understand well: volatility losses. Consider a very simple example. In case 1, if you have a $100,000 portfolio and earn 0% two years running, your portfolio value stays the same. But in case 2, if you gain 10% (to rise to $110,000) and then lose 10% (to drop to $99,000), you’ve lost 1% overall. In both cases your average return is the same (0%), but the volatility of case 2 induced a 1% loss. This is what I mean by volatility loss.

A simple rule of thumb is that the yearly volatility loss due to compounding is about half the square of the standard deviation. So, in Statman’s Table 1, the index has a volatility of 19.158% (or 0.19158). The volatility loss is then 0.0184, or about 1.84% per year.

The table has no entry for 15 stocks, but if we average the lines for 14 and 16 stocks, we get that the standard deviation of a 15-stock portfolio is about 22.465%. This corresponds to a volatility loss of 2.52% per year. This is 0.68% per year more than the index’s volatility loss. However, I pay only 0.21% per year in MERs on my ETFs. So, it’s clear from this analysis that I’m better off with my ETFs.

Of course, Statman based his table on a particular historical period of stock returns. If we repeat the analysis using different data, we’ll get different results. However, the gap between 0.68% and 0.21% is large enough that any analysis that results in the 15-stock portfolio being better is likely contrived.

This is the primary reason why I don’t try to construct my own index. Other reasons are ease of maintaining a portfolio of ETFs and a much reduced likelihood that I’ll get overconfident and tinker with individual stocks.

13 comments:

  1. And the #1 reason why you don't build your own index is so you don't have to think about things like "square of the standard deviation". :)

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    1. @Glenn: Good one. Unfortunately for some investors, not thinking about the square of the standard deviation is what leads them to try to construct their own index.

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  2. Interesting to see the math proves yet again that ETFs are best if you want to match the index. We have lots of our savings invested that way.

    I still like picking stocks, though, but I expect to make less money than if I bought the index. My goals are (a) to have fun (b) to get some pieces in place to have income when we need it (c) to try to avoid some of the volatility of the index by buying ultra conservative investments. Reason (a) is probably the truest reason. : )

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    1. @Bet Crooks: I think that fun is a big reason why many people pick stocks. I prefer much cheaper entertainment such as traveling to Florida in the winter to golf.

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    2. Ah but you're comparing to playing with much more money than I am risking. I couldn't get to Florida much less play golf with the amount I have at risk! (Luckily I'm a very bad golf player so I don't have to be too jealous.)

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  3. Tracking the index cannot just mean having the same volatility / standard deviation after a year. The returns must be the same day to day.

    Problem is, of course, a 15 stock portfolio wouldn't resemble the index and returns would not track the TSX. I tried taking a look (http://howtoinvestonline.blogspot.co.uk/2013/06/building-your-own-index-etf.html) at the practicalities of making a portfolio of 26 stocks that would look much like the TSX, mimicking sector and cap-weight representation. It would require quite a big portfolio ($100k plus) and would be a hassle to track and trade to keep in line.

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    1. @Canadian Investor: Of course, adding more stocks helps, but it still leaves a portfolio with slightly higher volatility which leads to higher volatility losses. So, I wouldn't try this even with a $1M portfolio.

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  4. Good post Michael.

    I'll continue to invest in stocks for some time, but I'm also increasing my positions in indexed products as well since I've got enough shares, in my opinion, in a few Canadian companies.

    With close to 25 CDN stocks, I'm practically running a large- to mid-cap CDN index though.

    Mark

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  5. I recently found a broker which may help with building such a "mutual index fund" They allow you to create a portfolio of 30 stocks and then you can set your desired allocation for every and each individual stock within the portfolio and then you can start investing buying the whole portfolio. They will automatically spread your contributions / investments among all 30 stocks based on your selected allocation. I just recently wrote about the broker on my blog and I think it is a great idea. I would help with your task greatly.

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    1. @Martin: I'll stick with the index ETFs to avoid expected portfolio losses from inadequate diversification.

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    2. And to minimize fees! (as well as avoid losses)

      I have a few units of a index mutual fund that I keep as an exercise in stupidity/while I wait for it to re-surface from the gloomy depths. I bought it about 20 years ago. For the past 2 years it has not gained one dollar. Why? Because of the outrageous fee. Yes, this is a bank mutual fund. If I sold it, I might get enough to take my kids out to lunch, but not with my husband, too, so I'm just watching it with the same repulsed fascination with which I watched a monkey slug caterpillar climb up a chair at the cottage.

      Ah investing what a hobby!

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  6. Hello Michael,

    Thanks for answering my query of last week with a whole post. I think it made for an interesting topic, for sure. It took awhile for me to wrap my head around it, but I think I understand that if (a big if) a smaller number of stocks average the same annual return as a large number of stocks, they will most likely do so with more volatility, which will decrease the compounding annual return. The roughly 0.5% disadvantage the volatility gives versus a more divirsified portfolio could only be overcome by luck, which over the long term becomes less and less likely.

    I realize I'm just summarizing your post, but just making sure I understand it. Thanks again for tackling this question.

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    1. @Gene: Good summary. This is an issue that few investors seem able to understand.

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