1) Key figures
There are a number of key figures that can be used to evaluate a share on the basis of fundamental data: Earnings per share, price/earnings ratio, price/sales ratio, price/book ratio, PEG ratio, debt/equity ratio, F-score, etc. Of course, all these key figures have their justification and together provide a large and comprehensive picture of a company.
Share prices are currently on a downward spiral and we keep hearing things like "it's not at all rational that Alphabet's share price is falling, it's already totally undervalued!" In today's post, we want to look at the share price using just two key figures to try and make the current price movements plausible. As a mathematician, I also want to do "something with numbers" and not always just talk about stock market psychology ;D
2) Modeling the share price with two key figures
As is well known, the so-called P/E ratio - i.e. the price/earnings ratio - is the ratio of share price to earnings per share (EPS)[1],[2]:
P/E ratio = share price / EPS.
According to the great mathematicians Carl-Friedrich Gauss and Leonhard Euler, however, this is equivalent to
Share price = P/E ratio * EPS.
What initially looks like a gimmick already explains an extremely large number of effects that we are currently experiencing. We will now concentrate only on the two key figures P/E ratio and EPS.
As a quick warm-up exercise, let's do a little math: Microsoft ($MFST) is currently trading at a P/E ratio of around 26. The earnings/year per share (i.e. EPS) is $9.58. Consequently, we arrive at a share price of approximately 26*9.58$ = 249.08$.
3) Interpretation P/E ratio
The price/earnings ratio is a measure of the multiple of the profit of the last financial year at which a company is valued on the stock exchange [1]. However, it can also be interpreted differently: If a company has a P/E ratio of 10, it will take 10 years for the company to generate the value of its shares as profit. In the above example of $MSFT, it would therefore currently take around 26 years to generate the value of all Microsoft shares as profit. This interpretation may seem obvious, but it contains an interesting approach: the P/E ratio can therefore be interpreted as a kind of "expected return". To understand this better, let's look at the reciprocal of the P/E ratio and call this the "earnings yield" [1]. For Microsoft, this earnings yield is currently around 1/26 ≈ 0.0385 = 3.85%. This earnings yield can be interpreted - as the percentage suggests - as an interest rate with which the capital invested today earns interest. If the company's profit increases while the P/E ratio remains the same, the share price will also increase and, put simply, my invested capital will earn interest at this return on profit.
The short mathematical fact check shows that
- the lower the P/E ratio, the higher the earnings yield
- the higher the P/E ratio, the lower the earnings yield
4) Share prices vs. central banks
As most of us will have noticed, the "interest rate turnaround" is currently being initiated at the central banks. Put simply, this means that our money in the savings account is earning interest again. We therefore receive a "return" for simply putting our money in a savings account. The attentive reader will already have noticed that the interest rate set by the central banks (the so-called prime rate) influences how and where investors invest their money. To put it simply: the lower the interest rate, the more attractive shares are; the higher the interest rate, the less attractive shares become.
Let us remind you of the following equation, which contains the two important key figures:
Share price = P/E ratio * EPS.
But now we return to share price determination. Important: for the remainder of this section, we will initially assume that EPS remains constant. Let's assume that the key interest rate is - as in recent years - close to 0%. Investors' money then increasingly moves into shares. The principle of supply and demand causes share prices to rise. If other conditions remain unchanged (i.e. EPS remains the same), this means that the P/E ratio rises. Roughly speaking, therefore, low interest rates always go hand in hand with higher P/E ratios for shares.
Now the key interest rate is being raised to 5% overnight. In simple terms, this means that we now receive 5% per year for "parking" our money in the account. We remember, however, that the inverse of the P/E ratio reflects the profit return on an investment in a company. If Microsoft currently has a P/E ratio of 26, i.e. an earnings yield of 1/26 ≈ 0.0385 = 3.85%, it is less attractive for me to invest my money in Microsoft shares than to simply put my money in my savings account. According to the principle of arbitrage, the two interest rates will adjust to each other [3]. To put it simply: nobody wants to invest their money with risk at 3.85% if they can get 5% without risk. As the key interest rate is set by the central banks, the only remaining option is for the profit yield to increase from 3.85% to 5%. Only then is there an equilibrium and the investment alternatives are of equal value in this context. If the earnings yield increases from 3.85% to 5%, this means a reduction in the P/E ratio from 26 to 20. For the share price, however, with EPS remaining the same, this means
Share price new = 20 * 9.58$ = 191.60$.
In this scenario, Microsoft's share price would fall from around 249$ to around 190$, even though Microsoft still generates the same earnings per share! This is also known in the technical literature as multiple compression. It should also be noted that the share price has not fallen by the difference in interest rates, i.e. 1.15%, but by a full 23%! Incidentally, the reverse is of course also true: if the interest rate level falls, the P/E ratio rises in proportion, so that the share price then rises again.
5) What is currently happening on the stock market
The connection between share prices and concerns about a recession or economic difficulties is simpler and more obvious. If there is a difficult economic situation, a company's sales and profit margins could develop negatively, which of course has a negative impact on EPS. Since share price = P/E ratio * EPS, the share price must naturally also fall if the P/E ratio remains the same and EPS falls.
We now come to the "big picture". We are currently in an environment of rising interest rates and economic concerns, triggered by the war in Ukraine, supply bottlenecks, high energy prices and general inflation worries. As described above, rising interest rates are leading to a lower P/E ratio and the difficult economic situation is also causing the expected profit - i.e. future EPS - of many companies to fall. These effects now combine according to "share price = P/E*EPS" to produce a much lower share price and therefore a much lower valuation for many companies.
Calculation exampleIn addition to the lowered P/E ratio of 20 at Microsoft, it is now also priced in that EPS is expected to fall by 10%. Then we have
Share price new = P/E*EPS = 20 * (9.58$*(1-0.10)) = 172.44$.
This corresponds to a share price discount of approx. 31%!
The fact that growth companies such as Shopify (P/E ratio 289), Airbnb (P/E ratio 80), Fiverr (P/E ratio 796), etc. are currently being massively punished is mainly due to the fact that their P/E ratios (if they exist at all, because profits have to be generated first) are absurdly high and therefore the P/E ratio will fall massively if interest rates rise. Even if it is of course priced in that these are growth companies, such high P/E ratios are usually no longer accepted. This then contributes very strongly to the fall in the share price: lowering a P/E ratio from 26 to 20 leads to a fall in the share price of 23%, lowering a P/E ratio from 100 to a still very high 50 leads to a fall in the share price of 50% and all this without changing any profit forecasts, because fundamentally the company remains exactly the same in this case too.
6) Conclusion and outlook
- It is possible in a very simple model consisting of only two key figures (P/E ratio & EPS) to explain the current share price movements
- high key interest rates lead to falling P/E ratios and therefore falling share prices
- poor economic situation often leads to falling expected EPS and thus falling share prices
- when high interest rates and economic concerns combine, these effects lead to massive sell-offs
This model is of course very simplified and ignores other important key figures. I am by no means suggesting that other key figures should be ignored. The aim was simply to show that even very simple models can explain the current price movements and seemingly irrational sell-offs of quality stocks. In the same way, this simple model already explains why growth stocks with high P/E ratios are disproportionately punished.
I would like to do a second, more concrete part on this soon. To do this, I will look at historical P/E ratio data and consider these in relation to key interest rates in order to have practical evidence of this phenomenon. I will probably write a small R script for this and then post an analysis of this topic here.
Sources:
[1] Wikipedia: https://de.wikipedia.org/wiki/Kurs-Gewinn-Verh%C3%A4ltnis
[2] Wikipedia: https://de.wikipedia.org/wiki/Gewinn_je_Aktie
[3] Wikipedia: https://de.wikipedia.org/wiki/Arbitrage#Markttransparenz
