# Severing The Link Between Price and Weight Part I

In a recent post about market-cap weighted fixed income indices, it was noted by reader Xenko that one way to overcome overweighting overvalued companies and underweighting undervalued companies (counter to what a rational investor would desire) could be to inversely weight constituents of an index. While the original post was about fixed income indices, I’m assuming the thought was directed at equity indices so I will speak directly to that (there is an extra step with respect to fixed income indices that we’ll go over some other time).

Here is the problem with that suggestion: if you assigned more weight to a company based on its inverse cap-weighted rank then you run into the problem of running up the price of smaller cap stocks. A large market-cap stock might be worth \$50 billion and is highly liquid. If it is the largest stock by market cap in an index it will have the most weight. But if the smallest company in an index (say with a market cap of \$100 million) had the highest weight then if there were a lot of people trying to track that index their might be additional pressure on that stock’s price because it might be illiquid.

Let’s explain with an example. Let us say that the total market capitalization of all companies is \$1 trillion. The \$50 billion company would have a 5% weight in this index by market-cap and the \$100 million company would haveĀ  a 0.01% weight in this index. If we created another index which reversed these weightings so that the \$100 million company represented a 5% weight in this new index (let’s called it the ‘inverse index’ for now) and the \$50 billion company had only a 0.01% weight in this index, this wouldn’t be a problem for the \$50 billion company. But what if this index had \$4 billion worth of investors’ money pouring into it on day one because they liked the concept. The index fund traders would have to allocate 5% of \$4 billion into the \$100 million company. 5% of \$4 billion is \$200 million. This would send the \$100 million company’s stock soaring artificially. This is a problem of “index capacity”.

So in practice, this would not work.

This is essentially the same line of thinking which explains why an equal weighted index will not work as well in practice as it does in theory. An equal weighted S&P500 index would allocate a 0.2% weighting to each stock in the S&P500 index. Now, your exposure to pricing errors is randomized instead of the tendency to overweight overpriced stocks and underweight underpriced stocks. Maintaining a 0.2% weighting to each stock would have higher turnover than a regular cap-weighted index, but the same problem of capacity concerns on the smaller stocks exist as with the above example.

In the next part of this series we will look at how else we can randomize the exposure to pricing errors without these ancillary problems cropping up. (We can never eliminate pricing errors.)

Preet Banerjee
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• Michael James

“You can’t buy more than 100% of a company” should be up there with

“You can’t push a rope” and

“You can’t keep fast-forwarding on your PVR once you catch up to real time.”

• Preet

@Michael James – thanks for the chuckle! :)

• Xenko

I hadn’t thought about how the total number of investors could affect the smaller stocks like that.

I’m still curious if an inverse index would actually give a better return than the normal index, even if it isn’t practical in reality.

• Preet

@Xenko – about to answer that in the next post… stay tuned! :)

• Michael James

Xenko: Taken literally, a inverse index couldn’t outperform a normal index because you would pile all your money into a stock just before it becomes worthless. You must define some rule that limits how much money can be put into any one stock. Then it would be possible to look at historical data to see how it fares.

• Jordan

Doesn’t this index capacity problem depend on what index you are tracking? I think it could still work if you ran the inverse index on mid or large cap stocks only.

The idea sounds a bit similar to the Dogs of the Dow strategy, which beat the Dow by 2-3% a year from 1920 until the mid 90’s. That is until it got so popular that more then \$20 billion was invested in it making it implode, like Preet was mentioning.

But hey, a strategy that outperforms by 2-3% for for 70 years ain’t that bad!

The other option is even if it’s not possible for an institution to create an index because of scale, is there any advantage or out performance by inverting and creating your own index? The TSX 60 would be a good test, you could own every stock individually for about \$300/year in trading costs.

Not saying it’s worth doing, I’m just always curious about different ideas for passive out performance so I’m just throwing the idea out there that it’s not impossible.

• Preet

@Jordan – I think there are some other problems (hit me in the shower this morning!)

• Richard

The bigger question is why invert the weighting at all? If you’re going that far to avoid the larger companies in the index you’re probably expecting them to underperform with a high probability. In that case you might as well buy the bottom half of the index or move to an index of smaller companies. Or do what Preet will tell us tomorrow :)