Friday, March 7, 2008

Dominated Strategies and Index Funds

A strategy is said to be dominated if it is guaranteed to give the same or worse results than some other strategy. This term is usually used in game theory, but it can apply equally well to investing.

Most of the time when we have a choice between two alternatives, we don’t know for certain which choice will lead to a better outcome. Should you buy stocks or bonds? In a given year, stocks might give better returns or bonds might give better returns.

In some cases, the choice turns out to be clearer. Suppose that I offer you a bet: we’ll toss a coin, and the winner gets $100 from the loser. I see you hesitate, and I make a second offer: I’ll give you $10, and then we’ll toss the coin for $100.

No matter which way the coin comes up, you’ll be ahead $10 taking the second offer rather than the first. This means that the first choice is dominated by the second.

This doesn’t necessarily mean that you should go for the second offer. Depending on your circumstances (and whether you think I have some sort of trick coin), it may be sensible for you to reject both offers. But one thing is certain: it makes no sense to accept the first offer.

How does all this relate to index funds? If two companies both offer equity index funds based on the same index, then the funds should hold exactly the same stocks in the same proportions. The only difference between the two funds is how well their returns track the returns of the index.

The main reason for a fund lagging an index is its Management Expense Ratio (MER). If an index fund charges a 1% MER each year, then the fund must return 1% less to investors than the stocks produce.

Another contributor to index funds lagging their index is cash holdings. Funds vary in the amount of cash they keep around. Because stocks tend to give better returns than cash, over the long term, more cash means lower returns. Similar to this case is the possibility that the shares held by the index fund do not accurately mirror the index for whatever reason.

Another possibility is that the price of an index fund’s units does not accurately reflect the value of the underlying stocks. This is called a premium or a discount depending on whether the price is too high or too low.

Suppose that we have two index funds A and B that hold the proper mix of stocks, do not sell at a discount or premium, and hold very little cash. The only thing left to distinguish them is the MER. Fund A has a 0.2% MER, and fund B has a 1% MER.

This means that no matter what happens in the stock market, fund A will always give a 0.8% higher return than fund B. As an investing strategy, fund B is dominated by fund A. So why would anyone invest in fund B?

The only reasons I can see why anyone might invest in fund B come down to ignorance. Maybe fund B manages to market itself without focusing on the MER. Maybe people aren’t aware of fund A.

In theory, all index funds that track a particular index can be evaluated, and everyone should invest in the one that lags the index by the least. In practice, things don’t always work out this way.


  1. Hi, I didn't see a way of sending a direct e-mail to you, so here's a brief comment.
    THANK YOU for a brilliant series of posts. I came across your name on Larry MacDonald's blog and I am absolutely blown away by how clearly you write. I've been a DIY investor (mostly indexed across the globe) for a few years now and I've learned quite a few things from your posts. Thank you!
    Best wishes for the future.

  2. Fernando:

    Thanks for the kind words. I've enjoyed writing this blog. Whether someone chooses DIY investing or any other option, I believe that it is best to understand as much as you can. This will hopefully reduce the odds that others will take advantage of you financially.