Stock markets are undervalued (when considering bond yields)
It is widely believed that US equity markets are again exhibiting what Alan Greenspan once called irrational exuberance. The S&P 500 price/earnings (P/E) Ratio is hovering around 30. The more trusted Shiller P/E Ratio (also known as CAPE, where the earnings are based on 10 years of profits, inflation adjusted, rather than just on the last year) is hovering around 31. This means that the price of a share today equals the sum of the next 31 years of the company’s earnings per share (assuming future earnings continue at the average rate of the last 10 years).
The Shiller P/E of 31 is double the 20th century average Shiller P/E ratio of 15.2. QED markets are overvalued.
Or are they? Expensive is a relative concept. You cannot determine if shares are expensive based on the P/E ratio, without considering prevailing interest rates, for two reasons. Firstly, when you decide to invest in shares you are weighing the opportunity cost versus investment in bonds. If bond yields are lower, shares become more attractive.
Secondly, the fundamental value of a share is based on discounting future earnings. The rate of discounting of future income should always be based on prevailing interest rates. If interest rates are lower, then the future value of earnings are less discounted and, again, shares are worth more.
What does the bond market look like today? Pretty dire. Treasury inflation-protected security (TIPS) that are guaranteed to pay you $100, index-linked, in 10 years are, bizarrely, trading for $110. Yes, those bonds are currently trading at a real yield of about -1%. Over 10 years you are guaranteed to lose about 10% of your money. People are paying to delay gratification.
Looking at negative real bond yields, the stock market suddenly sounds more attractive.
Given that interest rates are currently around zero, and real (inflation-adjusted) interest rates are negative, might the current high valuation of shares be rational?
Answering that question numerically is challenging in that shares are valued using P/E ratios, while bonds are assessed by their yields. If we could introduce a P/E ratio reflecting the yields of bonds, we could compare share and bond valuations more directly.
I suggest PETRY — the P/E implied by Treasury Real Yields.
The idea is simple enough. Consider a safe perpetual annuity of exactly $1 per year, index linked. Calculate the net present value, by discounting at the market real interest rate, as seen by 10 year TIPS yields.
(inclusion of diagrams is optional)
At a 5% yield we get a “PETRY” P/E ratio of 20. But as the interest rates fall to zero, there is no discounting of future earnings, and a perpetual annuity actually has a value tending to infinity!
Today real interest rates are negative. So the naive PETRY is infinite. If a company is expected to survive forever, even without any growth beyond inflation, it’s value today is unlimited. There is no limit to the rational value of the stock market in an era of zero or negative real interest rates.
However, we of course don’t know if a company will survive forever. It would seem reasonable to disregard any future income beyond the next 30 years. When redefining PETRY to be the net present value of a 30 year index-linked annuity, we get a more sane curve with no infinities. The implied PETRY P/E slopes down from about 15 when real interest rates are 5%, to exactly 30 at 0%, reflecting the value of 30x$1 without discount, to about 35 when real interest rates are -1% and future values are at a premium.
10 year TIPS currently have a real yield of -1%. So 35 is a sane P/E ratio for the stock market, given current interest rates. You may argue that stocks have risks compared to government bonds and should be cheaper, but then again stocks also have upside: companies typically grow faster than inflation, and they may last longer than 30 years. So 35 would not necessarily be an irrationally exuberant P/E for today’s stock market.
If we look at the historical ratio of Shiller P/E as a ratio of PETRY we do see that the stock market P/E tends to be of the same order of magnitude as PETRY:
The Schiller P/E today is just 0.9 or 90% of PETRY. True, during the financial crisis and its aftermath it was even lower than that, but at other times it has been up to 1.2, so stocks still look attractive when correctly placed in the context of today’s negative real interest rates.
Let’s finish with a glance at the UK market. The FTSE 100 recently recorded a P/E of 14 and a Shiller P/E of around 13. UK 10 year index-linked gilts are trading at a shocking -2.3% yield implying a PETRY30 of 42! So UK stocks are trading at a very cheap .31 ratio, representing a 69% discount of stocks P/E relative to the P/E implied by UK government index-linked bonds.
In conclusion, the Shiller P/E (CAPE), or any other measure of stock prices, should be evaluated in the context of prevailing real interest rates. PETRY shows the P/E ratio implied by real bond yields (by taking the NPV of a safe 30 year index-linked annuity). The Schiller P/E can be viewed as a ratio of PETRY in order to value stocks in the context of the current interest rate regime. On this basis, US stocks are slightly discounted, which is perhaps appropriate given the unknowns of the pandemic, while UK stocks are surprisingly attractive.
