# Do company valuations react to market sentiment with a lag?

According to their website, Duff & Phelps “is the premier global valuation and corporate finance advisor with expertise in complex valuation” and other fields. According to their annual Valuation Handbook – Guide to Cost of Capital, most stock valuations react to market news with a lag.

Often, valuators use conclusions of this model to make meaningful decisions about pricing company risk.

If the model isn’t true, then we will need to rethink the way we value companies — likely in a way which increases the value of closely held businesses. They will systemically overstate the risk of publicly traded corporations and therefore understate the value of closely held firms.

If the model were true, one could utilize the predictions to almost effortlessly make untold fortunes in the stock market.

I’m publicly sharing the results of my research, so I imagine you can guess where I stand on the question.

I am not comfortable using the “sum beta” methodology to estimate the riskiness of an individual stock. Any observed difference between the normal beta and the sum beta is likely the result of statistical noise. Unfortunately, this invalidates the conclusions of the Duff & Phelps methodology. Their industry risk estimates are likely biased in an upward direction.

I didn’t want this to be the result. I wanted to find an easy way to consistently beat the stock market, but I’m going to have to keep looking.

# The Rules of Expectations

As promised, here are some rules for working with expected values, first in words and then in math. All of these can be verified in excel. I’ll also include a list of things that are not rules for working with expectations. These are all especially relevant in valuation if you have multiple uncertain parameters you are combining through probabilities. These also come into play while making total rows at the bottom of complex schedules. Sometimes they won’t foot, and this post will help you understand why.

The expected value of a constant is a constant.

$E[c] = c$

The expected value of two random values is equal to the sum of the expected values.

$E[X + Y] = E[X] + E[Y]$

The expected value of a random variable times a constant is equal to the constant times the expected value of the random variable.

$E[cX] = cE[X]$

Please note that this doesn’t hold if c is not a constant.

$E[XY] \neq E[X]E[Y]$

Remember these rules, as you will be tested on them.