With record highs in stock markets being reached recently, the question that dawns any intelligent investor is this: is the stock market over-valued or not? The other question is, does it matter?
These are difficult questions to answer.
And it’s made harder to answer when investing legends seem to contradict with each other. People like Seth Klarman thinks markets are bubbly. News that valuation indicators such as Shiller P/E and Buffett Indicator (Total US Market Cap / US GNP) indicate over-valuation keeps showing up. Yet the person who “invested” the Buffett Indicator” seems to think we’re not at bubble territory, which is also agreed by index fund legend John Bogle.
And ultimately the reason why these questions are so difficult to answer is because the perceived truth involves so many moving parts, so you need to understand the relationship between all moving parts and also come up with your own assumptions to come to a conclusion.
To begin to understand how people get their sense of valuation from, we need to understand absolute valuation and relative valuation.
Let’s start with absolute valuation.
Absolute valuation means you value if something is over-valued based on a predetermined investment hurdle rate. It could be 10% (which Warren Buffett uses), or it could be 6% (Joel Greenblatt’s minimum hurdle rate when 10 year US treasury yields less than 6%).
The rationale for a predetermined investment hurdle rate is that when compared to the essentially risk-free interest rate of 10-30 year US treasury bonds, what return should I get from non-US treasury bonds in order to justify and compensate for the risk I’m taking?
So in this sense, the US stock market isn’t over-valued since according to Stanley Druckenmiller, the US stock market’s current valuation is supposed to be where it is relative to a near zero interest rate. And this conclusion is very straightforward if we look at the following graphs using today (Apr 25th 19:43 HK Time) as an example.
(Screenshot from http://www.multpl.com/)
(Screenshot from http://www.multpl.com/shiller-pe/)
(Screenshot from http://www.multpl.com/interest-rate/)
(Screenshot from http://www.multpl.com/30-year-treasury-rate/)
First let’s look at the P/E ratios of S&P 500.
The current P/E is 20.70 and the Shiller P/E (10 Yr inflation adjusted average earnings) is 27.38 . If we were to treat stocks as bonds, then the yield or interest rate of the S&P 500 would be roughly between 3.65% – 4.83% (100 divided by P/E gives you Earnings Yield), which is higher than the 10-30 Year Treasury Rates  of 1.93% – 2.62%.
So from a theoretical point of view, if stocks were risk-free, then the maximum value we should be willing to pay for stocks should be all the way up to 38.17 – 51.81 P/E.
The question that dawns from this exercise is, how much excess return (or minimum hurdle rate) is appropriate to compensate for the risk in investing in non-risk free investments such as stocks?
If you have the perspective that as long as stock returns can be higher than the risk-free interest rate by a certain percentage (eg. higher by 50% – 100%), then we are probably entering slightly under-valued to fair value territory .
If you have the perspective that once the risk-free interest rate’s 50% premium is below 6% (eg. if 10-30 Year Treasury Rate was 3.5%, it’s 50% premium would be 5.25%) you demand a minimum of 6% return as your minimum hurdle rate, then the stock market is at over-valued territory.
But frankly speaking, this is an over-simplified way of seeing whether the stock market is over-valued or not, and I’m not even done with talking about absolute valuation nor begun to talk about relative valuation.
There are two more considerations that require our attention, namely taxes and method of return.
Firstly, taxes are not levied against US treasury bonds, so not only does non-risky investments have to compensate the risk with excess returns compared to a risk-free interest rate, it also has to compensate for the tax effect.
Secondly, if stocks don’t return money to shareholders in the form of dividends, then the only way a shareholder can generate a return is either through earnings growth and/or positive sentiment (eg. higher P/E multiple).
If shareholders are to make most of their money through earnings growth and/or positive sentiment, then further excess return needs to be demanded to compensate for potential of negative sentiment destroying market value faster than earnings growth can grow against.
So the more complete way of seeing whether the stock market is over-valued or not is to determine how much excess return (or minimum hurdle rate) is appropriate to compensate for the risks and costs in investing in non-risk free investments such as stocks? After all, the risks are many and costs of tax cannot be ignored.
 The reason why current P/E and Shiller P/E is both used is because criticism of P/E as valuation tool is that it is extremely easy to manipulate earnings through accounting shenanigans while at the same time earnings can also be volatile from a year to year basis. The criticism of Shiller P/E on the other hand is that 10 years as a period to average out earnings is too long since serious earnings recessions that happened over a short period of time were captured, thus distorting the output value. A range would give a better picture.
 Similar reason to the point above in that interest rates maybe overly high or low if looking at only one class (eg. 10 Year only or 30 Year only) of long term US treasury bonds. Also everyone has different definition of how long constitutes long term.
 If 10-30 Year Treasury Rates is 1.93% – 2.62%, then stock returns need to be 2.90% – 3.93% if you demand 50% excess of risk-free interest rate or 3.86% – 5.24% if you demand 100% excess of risk-free interest rate.
Not advice. No offer. Do not rely. May lose value. Risky. Conflicts hidden/obscured. (Borrowed from Terrence Yang‘s Disclaimer on Quora)