Just look at the diagrams. At every valuation level (there represented as growth estimates), an overpriced stock that moves down is replaced by underpriced stock that moves up. The PE ratios of each of those stocks individually changes, sure, but the movements offset at the aggregate level. Nothing happen to the average valuations. Just count the number of stocks at each valuation level (i.e. the number of stocks in each column). It stays the same.
Backpacker, what you are thinking of is that percentages of stocks in the value, core, and growth categories will remain the same. If a stock dropped from Growth to Core, I suppose another stock would move from Core to Growth. Morningstar does that dividing stocks 1/3 value, 1/3 core, 1/3 growth. The academics define Value as the bottom 30% of certain valuation measurements.
The issue that you forget is that the P/E ratios and other financial ratios for the market as a whole can change over time. Most of the time, market P/E's for the US market fluctuate from 10 to 20, 16 is about average. The changing P/E ratios help measure investor enthusiasm. During the 2008-2009 bear market, stocks got hit so hard that some Growth stocks started hitting Value managers stock screens. So both Value and Growth got more valuey. But yet, the proportion of Value stocks, Core Stocks, and Growth stocks remained the same by Morningstar and academic definitions. So valuation measurements can drop not only at the individual stock level but also in aggregate.
Also, if the earnings estimates of one company falls and then its P/E ratio falls it doesn't follow that the earnings estimates of another company rises and its P/E ratio rises. Earnings estimates can drop for big portions of the market partially offset by many fewer companies with increasing earnings estimates. This would happen as the economy goes into recession. If investors get discouraged, P/E ratios could fall even more than what is warranted by decreased earnings estimates.
I have never given too much thought about cost of capital, I always assumed that for stocks it was about 10 percent as that is the historical returns of the stock market and that for bonds it was whatever the market rate is at the time. In other words, I have thought of cost of capital for stocks as the rate of return that investors were expecting or demanding from the stock market.
Larry is thinking of it more as being influenced by interest rates. It is a lot like doing a present value calculation discounting future earnings back to the present using current interest rates. In the formula future earnings/risk free rate + risk premium=intrinsic value. What Larry says makes sense because lower interest rates would cause a lower denominator and thus higher prices. This is what would cause higher P/E's.
So to illustrate, stock A has estimated earnings of $10/share for 2017. Lets put the risk-free rate at 1.5% and the equity risk premium at 4%. That is $10/.055=$181.82 per share. At that price, you would have a P/E ratio of 18. But that would be the intrinsic value of the stock. The actual price would be different.
Just for fun, lets see what stock A would look like in more normal times, lets say a risk-free rate of 4% and an equity premium of 7%. We will use the $10/share earnings estimate for 2017. $10/.11=$90.91. That would give you a P/E ratio of 9.
Am I doing this correctly? You can see that falling interest rates and a lower equity premium drives P/E ratios up because the denominator is decreasing. But with higher P/E's come lower future expected returns.
A fool and his money are good for business.