Price Multiples. Correlation with EG and Req Return.

CFA Level II
#1

Hi, I cant get the following sentence to make sense (From Schweser):

" Price multiples are positively correlated with expected earnings growth rates and negatively correlated to required returns. Therefore, price multiples rise with increases in expected future earnings growth and with a decrease in any of the components of the required rate of return (the real rate, expected inflation, the risk premium for inflation uncertainty, or the equity risk premium). As a result, the equity risk premium declines during economic expansions and rises during recessions".

How is this possible?

Lets take P/E for a company. Price: 100. Earnings: 10.

P/E = 100/10 = 10.

If earnings now grow to 20. The P/E ratio will be 5. I.e. earnings grow P/E ratio falls. Isn’t this a negative correlation and not a positive one?

Same with the Required Rate of Return. If req. return increases, P will be lower due to being discounted at a higher rate. Causing P/E to also fall. I.e. a positive correlation and not a negative one?

#2

Think of it using the justified P/E ratio (leading).

P/E = 1-b / r-g

Using that it’s easier to see that if g increases the denominator decreases and P/E increases.

Similarly, as r increases the denominator increases and P/E decreases.