Formulas Distort Valuation if Inputs are not Free Market Inputs

Some of our most basic equations for understanding stock values start to lose their grounding when you have a zero bound on interest rates. Let's start with the capital asset pricing model. It is usually expressed as follows:

c02_I0001

where

rf = Risk-free rate

βa = Beta of the security

rm = Expected market return

R (a) = Return on the asset

When the risk-free rate is zero, very low market returns will justify many stock purchases. When most stocks are good because they are on average yielding more than fixed income, very slight rates of growth can be used to justify very high stock valuations. This happened in 1929, and it was not good for investors. This is particularly true where real interest rates after inflation are negative. But negative real returns for fixed income signal an economy in distress. The world economy is very much in distress, with fixed income bouncing along at near deflationary prices. To buy time, the Fed and the European central banks have gone on a liquidity spree, lending freely to banks at nominal rates, and recently the Fed told us it would keep interest rates low through 2014. What happens when these low risk-free rates affect other rates used to understand value?

For example, the most frequently used calculation in discovering the value of a stock is Gordon's growth model for discounted dividends: ...

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