# Fair-Value Weighting an Index

First: This is impossible! No-one knows the true fair value of a company, so keep in mind the purpose of this demonstration is strictly academic, theoretic and shouldn’t create a pandemic. (Rhymes coutesy of Fiona…)

In yesterday’s post, we looked at how our cap-weighted index overweighted the overvalued companies and underweighted the undervalued companies, thereby magnifying our pricing errors in the exact opposite way that one would desire. Today we are going to re-weight these same stocks based on their fair value.

# Take Two

We will take the same values from yesterday: Stock A and B both have a fair value of \$10, but Stock A is priced in the market at \$20 and Stock B is priced in the market at \$5. If we weight them in our index based on their fair value, then they will each represent 50% of our new index. (The total fair value of the entire index is simply the sum of the fair values of the constituents, so with each stock having a fair value of \$10 the fair value of the entire index is \$20 – with each stock having a fair value of \$10 they must each have a 50% weighting.)

Now, if the stock market prices converge to fair value we will find the following:

Stock A goes from \$20 to \$10, and 50% of our index has fallen 50%.

Stock B goes from \$5 to \$10, and 50% of our index has risen 100%.

The net effect is that you have gained 25%. Remember that the market cap-weighted index had a net effect of losing 20% in the same scenario.

# So What?

Good question – it’s all academic since we will never know what the fair value of an index is. However, the question now posed should be: is there a way to approximate fair-value weighting better than cap-weighting? This is the goal of “efficiency weighting” – which can take many forms. Cap-weighting works if you assume CAPM works, and markets are efficient all the time – in which case you believe that future prices are randomly distributed around current prices. Given that CAPM has been invalidated and that the father of EMH (Efficient Markets Hypothesis) basically rejects all three froms as individually good enough (Strong, Semi-Strong and Weak), it seems like a question worth exploring. According to Harry Markowitz, efficiency weighting assumes that current price is randomly distributed around fair value. (More on this later.)

Tomorrow I will look at one method of efficiency weighting which demonstrates one possible way of approximating fair-value weighting…

Preet Banerjee