# Cap-Weighting Magnifies Your Exposure to Pricing Errors In The Wrong Ways

Market Capitalization Weighted indices have a significant structural flaw. Namely, they overweight your pricing errors when they are unfavourably wrong and they underweight your pricing errors when you are favourably wrong. Allow me to demonstrate with a simplistic example.

# Example

Let’s suppose we have 2 stocks in our stock market and that we magically know the true value (or fair value, or intrinsic value) of each. They each have a fair value of \$10/share, but stock A has a stock market price of \$20/share (market participants have bid the price up) and stock B has a stock market price of \$5/share (market participants have bid the price down).

If we assume that the market is fairly efficient for the most part, then it isn’t crazy to see what would happen if the stock prices converged to their fair value prices (\$10/share in both cases). First we have to see that our index is heavily weighted to Stock A which now represents 80% of our index (\$20/share and a the total market is only \$25). Stock B is similarly calculated to be only 20% of our index (\$5/share out of a total market cap of \$25 for the index).

If Stock A were to retreat from \$20/share to \$10/share, then 80% of our index will have lost 50% in value.

If Stock B were to increase from \$5/share to \$10/share, then 20% of our index will have gained 100% in value.

The net effect is that you will have lost 20% overall.

# You Can Have Good Pricing Errors and Bad Pricing Errors

In this little example, our universe had only two stocks and in fact only two shares (one share per company). The company that was over-priced (\$20 stock market price versus \$10 fair value) had a very high weighting in our index simply because a market cap weighted index is constructed such that weighting is dictated by market cap (duh!). In this case we were over-exposed to this over-pricing error. The company that was under-valued (\$5 stock market price versus \$10 fair value) represented very little of our index, so our exposure to the stock that was going to go up was diminished.

Preet Banerjee
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• Michael James

I like your example to illustrate the effect of weighting errors always working against you. However, it applies to some degree to any kind of weighting system, not just cap-weighting. Any time you try to assess intrinsic value, but get it wrong, you will buy too little of a stock that is better than you think it is and too much of a stock that isn’t as good as you think it is. The important question is whether a given method of assessing intrinsic value is better than approximating intrinsic value with the market cap. This is often easy to do in hindsight, but harder to do looking forward.

• Preet

You hit the nail right on the head with your last two lines. I’ll go into weighting based on fair value next (which is impossible to do as you know) and then look at the alternatives.

• Sean

Hey Preet, this is quite an interesting concept, especially since I’m tending to weight the equity portion of my portfolio regionally by market cap. Can you accurately measure/predict the fair value of an entire market or index though (vs. small/mid/large-cap in a single market)? Hopefully I’m making sense here… your example is just blowing my mind at the moment…

• Preet

Hi Sean – “accurately”: you’d never know. There are those who are trying to figure out the next best proxy (I’ll give you a big hint, one of them is fundamental indexing). More to follow on this over time.