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# The Fed's Valuation Model

The economists of the U.S. Federal Reserve (Fed) use a relatively simple model to value the financial markets. It is often said that the stock market and the bond market are interconnected in that one is an alternative vehicle to the other, with money flowing between them. That is the basic assumption underlying the Fed’s model for assigning a relative value to these two markets. The model assumes that investors regard stocks and bonds as competing assets; as intelligent, logical and reasonable persons, they will naturally choose the market that offers the better return.

To determine the relative values of the two markets, the model compares the return of 10-year government bonds with the average return of stocks, the latter simply being the inverse of the price/earnings ratio, i.e. the earnings/price ratio. So if a federal government bond offers a return of 5%, to be of equal value the stock market would have to be trading at a multiple of 20 (1/20 = 5 % or 1/0.05 = 20). According to this theory, there cannot be a long-term, sustained value differential between the two markets, and since the U.S. Federal Reserve uses this model, many investors do likewise. Continuing with the same example, if 10-year bonds offer a 5% yield, and the stock market is trading at a multiple of 15, the stock market would be considered undervalued, because it is offering a return of 6.7% (1/15). Being intelligent, logical and reasonable, investors would then make an arbitrage trade, selling their bonds and buying stocks until the imbalance corrected itself.

In a study published in Quarterly Review of Economics and Finance, university professor Javier Estrada tested the validity of the relationship between the return of bonds and the return of stocks in 20 countries. If the Fed’s model is valid, there should not be significant return differential between the two markets over the long term. One would even expect a negative correlation between the two returns. But that is not the conclusion that Javier Estrada reached; instead, he found a close correlation between the two returns in most countries.

The university professor also tested the model as a tool for forecasting stock market returns. He assumed that when there is a big return spread between the two markets, the tendency towards a balance should be a useful tool to predict the relative performance of these two asset classes. Here again, his conclusions were surprising, because he found the model to be a useful forecasting tool in only one out of 20 countries: the United States.

In conclusion, the stock market and the bond market are alternative investment vehicles, but it is perhaps the appetite for risk that determines money flows between these two types of assets, rather than the relative return differential.

## The author

### Marc Desnoyers

B.Sc., M.B.A., C.F.A