*Originally published: January 2021*

When it comes to determining a fair value for equities, interest rates are an important variable to consider.

As rates rise or fall, they affect the appropriate valuations for different stocks in different ways. This article provides a brief overview of how that works.

## The Equity Risk Premium

Equities are not priced in a vacuum; they are always compared to other alternatives.

Specifically, safe sovereign bonds are the main comparison. If you live in a developed country and buy sovereign bonds and hold them to maturity, your only risk is inflation risk. There’s virtually no chance of nominal default, since the issuer of the bond is also the issuer of the currency. There’s typically plenty of liquidity in developed sovereign bond markets as well, so these are considered pristine collateral. In particular, the United States 10-year Treasury yield has been a de facto benchmark for a long time.

Suppose you could get a 5% annual yield on a 10-year Treasury note, and annual inflation is about 2%. You’re making a positive 3% real yield, which is great for a risk-free investment. What would it take for you to buy, say, a dividend stock instead?

The answer is you’d need a much higher than 5% expected return from that stock in order to take on increased volatility and business risk. Maybe, for example, you would do it if you could get a 9% expected annualized return over the next 10 years. In other words, you would be demanding a 4% equity risk premium, meaning a 4% better annualized return than the risk-free alternative, in order to take on that increased volatility and uncertainty.

Now, suppose a decade later, you’re in an environment where you only get a 1% annual yield on a 10-year Treasury note, and annual inflation is about 2%. You’re making a -1% real yield, which is a gradual destruction of purchasing power. In fact, you could say the price-to-earnings ratio of that 10-year note is 100, since you’re only getting a 1% return on your capital per year. Naturally, you’d be reaching for some other store of wealth. What would you pay for a good stock?

Well, if you still want an equity risk premium of 4%, then you’d be willing to buy stocks that only offer the prospect of 5% long-term annualized returns. In other words, you’d be willing to buy rather highly-valued stocks, since you’re comparing them to very highly-valued bonds and have few other options for liquid mainstream investments.

However, in doing so, the investor must consider the probability that interest rates will rise, and reduce the valuations of their stocks during their holding period.

**Cyclically-Adjusted Earnings Yield**

There are various ways to measure an equity risk premium.

The most complete way is to do discounted cash flow analysis or other return assessment of a specific investment, and compare that to the 10-year Treasury note yield to maturity.

However, investors also want a high-level snapshot of general conditions, so we need some basic calculations to compare broad equities vs Treasuries. For that, a popular calculation is the S&P 500 earnings yield (the earnings per share divided by the share price) minus the 10-year Treasury note yield. That can also be adjusted to use the forward consensus earnings yield instead of the trailing yield.

My preferred way to measure the equity risk premium, however, is the cyclically-adjusted earnings yield of the S&P 500 minus the current 10-year Treasury yield.

This is because S&P 500 earnings in any one year, especially during a recession or a brief economic boom, can be a poor representation of their average earnings capability over a full business cycle. So, this calculation takes the inflation-adjusted average of the last ten years of earnings, and divides that by the current share price. That gives you the cyclically-adjusted earnings yield, which can then be compared to the 10-year Treasury rate.

This chart shows the cyclically-adjusted equity risk premium in blue, and the forward 10-year annualized returns of the S&P 500 over 10 year Treasury notes in orange:

*Data Sources: Robert Shiller, Federal Reserve, Standard & Poor’s*

The lowest that this version of the equity risk premium ever reached was in 2000, at -4%. That’s why the Dotcom bubble was so silly; you could get a 6.5% yield on a Treasury note, but investors were paying a cyclically-adjusted earnings yield of less than 2.5% for the S&P 500. Then, equities crashed. Treasuries were clearly the better buy there.

This current period in the 2020s is more difficult for people because despite the fact that stock valuations are so high, bond valuations are so high as well, and investors are stuck between a rock and a hard place. They have to venture into things like value stocks, commodities, or international equities if they want something resembling a historically normal price for things.

## Interest Rates vs Equity Valuations

Professor Robert Shiller has arguably the best long-term dataset and model for equity valuations over time. He popularized the cyclically-adjusted price-to-earnings ratio, or “CAPE ratio”. The CAPE ratio is the stock price divided by the inflation-adjusted average of the past ten years worth of earnings per share for a company. In other words, its the inverse of the cyclically-adjusted earnings yield that I mentioned in the previous section.

And you can calculate the average ratio for an index of stocks, like S&P 500.

Shiller’s long-term chart shows how the S&P 500’s CAPE ratio has varied over time, compared to the interest rate on the 10 year Treasury note:

*Chart Source: Robert Shiller, Yale*

As you can see, there is a significant inverse correlation there over the long run. High interest rates generally result in low stock valuations, and low interest rates generally result in high stock valuations.

There are some exceptions on the chart, like in the 1940s during World War II when Treasury yields were low along with stocks being cheap due to great uncertainty and high inflation. And it certainly doesn’t hold true from day-to-day; “risk off” days tend to see yields go down and stocks go down together. However, with the big picture, rates and equity valuations tend to be inversely correlated.

Similarly, if we look at US household net worth as a percentage of GDP compared to interest rates, we see a similar phenomenon:

*Chart Source: St. Louis Fed*

Household net worth (which consists of stocks, real estate, bonds, and other assets, minus liabilities like mortgage debts) was only about 330% of GDP in the late 1970s when rates were high, and topped out at over 600% of GDP in 2020 when rates went below a fraction of 1%.

All sorts of bubbles or recessions can happen that temporarily make stocks unreasonably priced, but since the market tends to return over time to a normal equity risk premium, it does make sense that equity valuations and interest rates are inversely correlated.

However, it goes a step further than that, because different types of stocks respond differently to interest rate changes.

## Interest Rate Impacts on Growth and Value

Some companies are disruptors, with new products or services, and are growing rapidly. Investors naturally pay a higher valuation for them.

Other companies are mature cashflow-generating businesses, typically with significant dividends, that trade for lower valuations. While some of them are being disrupted, other ones are doing fine, and just happen to existing in mature industries.

These are “growth” or “value” factors, and can be identified in various ways.

Which type of stock does better or worse in a given decade depends on many variables.

Valuation differentials are a key variable; if there’s a bubble in one of the factors, the other factor will likely do better in the subsequent years. In 2000, there was a bubble in growth/tech stocks, so value stocks outperformed from that peak. In 2007, there was a bubble in value/bank stocks, so growth stocks outperformed from that peak.

Changes in interest rates are the other variable, in large part because they affect valuation differentials as one of the underlying causes. In the next three examples, I’ll walk through a discounted cash flow model for a value stock, a growth stock, and a hypergrowth stock.

If you need a primer on how discounted cash flow analysis works before looking through these examples, I have one here.

**Value Stock DCF Example**

Let’s say a company earns $100,000 in free cash flow per year. It’s a steady-state business, so we expect it to grow its cash flow by 5% per year for the next ten years, and then level out at 3% annual perpetually after that. That growth is just keeping up with population and currency inflation; its market share and volume per capita are rather static.

If we discount those future expected cash flows by a 12% rate, then the value of the next 25 years of cash flows would be $1.096 million:

In other words, we would be willing to pay a price/FCF ratio of roughly 11x, if we want 12% annualized returns on these cash flows.

If we were willing to look out further, and discount a couple more decades of the company running in perpetuity, we’d get to a little bit over $1.2 million for the valuation, or a bit over a 12x price/earnings. However, for this article I’ll stick with the 25 year forecast.

Now, suppose we’re analyzing the same exact company, but interest rates are 4% lower. So, due to lack of viable alternatives, we’re also willing to drop our discount rate by 4%, and so we use an 8% discount rate. Here’s the updated chart:

The 25 years worth of discounted cash flows for this updated model would be $1.586 million. In other words, we’d pay a price/FCF ratio of nearly 16x.

That valuation is 44.7% higher than our previous $1.096 million valuation assessment where we were using 12% as our discount rate for the same company.

It’s the same company, but with a lower discount rate and thus a higher fair valuation. Keep that 44.7% number in mind.

**Growth Stock DCF Example**

Now, let’s look at a second company, with a higher growth rate.

It starts with $100,000 in free cash flow per year, but it’ll grow that by 20% per year for the first 5 years, then 15% for the next 5 years, then 10% for the next 5 years, then 5% for the next 5 years, and then 3% thereafter once it’s fully matured.

If we discount those future expected cash flows by a 12% rate, then the value of the next 25 years of cash flows would be $2.860 million:

In other words, we would be willing to pay a price/FCF ratio of nearly 29x, if we want 12% annualized returns on these cash flows.

Now, if we analyze the same company using a lower 8% discount rate, here’s what we get:

The 25 years worth of discounted cash flows for this updated model would be $4.628 million. In other words, we’d pay a price/FCF ratio of over 46x.

That valuation is 61.8% higher than our previous $2.860 million valuation assessment where we were using 12% as our discount rate for the same company.

Notice that, during the same reduction in the discount rate from 12% to 8%, the growth stock had a notably larger percent increase in its fair value than the value stock (61.8% vs 44.7%). This is because the growth stock has a larger percentage of its expected cumulative cash flows occur far into the future compared to the value stock that is more front-loaded, so a larger portion of the growth stock’s expected cumulative cash flows are subject to the multi-year compounding effect of the discount rate.

The growth stock is more rate sensitive, in other words. Whenever we have a big shift to lower interest rates, and the market expects those low rates to persist for a while, then it’s not surprising to see a surge in valuations of growth stocks during that transition from higher to lower rates.

**Hypergrowth Stock DCF Example**

Lastly, let’s look at a third company, with an even higher growth rate.

For the next five years, it won’t be profitable at all. Once it establishes positive free cash flow on the sixth year, it grows that by 30% for the next 5 years, then 20% for the next 5 years, then 15% for 5 years, then 10% for 5 years, and then 10% for the next 5 years, and so on.

If we discount those future expected cash flows by a 12% rate, then the value of the next 25 years of cash flows would be $2.589 million:

Now, if we analyze the same company using an 8% discount rate, here’s what we get:

The 25 years worth of discounted cash flows for this updated model would be $4.917 million.

That valuation is 89.9% higher than our previous $2.589 million valuation assessment where we were using 12% as our discount rate for the same company.

So, the hypergrowth stock is even more rate sensitive than the growth stock (61.8%), let alone the value stock (44.7%).

## Final Thoughts: Rates and Flows

These were somewhat arbitrary examples, with 25-year forecasting periods and 12%/8% discount rates. But they’re meant to illustrate an example of how, the higher percentage of the expected cash flows from a stock are deep in the future (due to larger growth rates), the more rate-sensitive the investment is.

And what valuation an investor is willing to pay for a set of expected cash flows depends in large part on what they can get with sovereign bonds or other “risk free” benchmarks.

So, determining how to value different types of companies in this environment depends in large part on what discount rate you use, and what you expect to happen with benchmark rates going forward.

If you expect interest rates to remain near zero for a multi-decade period, then you can infer that fast-growing companies would likely remain extraordinarily highly-priced for a long time. The growth/value forward performance gap would likely narrow, however, because interest rates would likely not keep getting persistently lower (as they’d have to go into negative yields and then keep digging down into lower and lower negative yields to do so).

On the other hand, if rates rise to, say, 3% or more, that could put considerable downward pressure on equity valuations, particularly highly-valued stocks with little or no current earnings but large expected forward growth.

**Complicating Variable: Capital Flows**

A common observation is that, despite persistently zero or negative yields in Europe and Japan, we don’t see extraordinarily high equity valuations there.

This is significantly because their equity indices tend to be more value-oriented (more financials, industrials, healthcare, energy, staples, materials, and less tech), and thus don’t benefit from the low interest rates as much, and also because equity valuations depend in significant part on international capital flows.

If we look at liquid vs illiquid investments around the world, like equities (liquid) and real estate (illiquid), we see some overlap but also some divergence.

With real interest rates low in most places around the world, real estate tends to be quite expensive in most major cities. North America, Europe, Japan, and even many emerging markets have expensive real estate markets. Their local low interest rate policies do play a role in driving up real estate valuations.

However, if we focus on equites, which are more liquid and mobile between countries, there’s less of a correlation. If there’s a global disinflationary environment, as there was over the past decade, capital can chase foreign growth/tech stocks. So, plenty of European and Japanese capital have spilled over into US growth/tech stocks.

We can see, for example, that the US stock market is increasingly owned by foreign investors (the orange area below):

*Chart Source: Tax Policy Center*

In addition to this structural trend, there are cyclical forces at play.

During strong dollar environments (based on various fiscal and monetary policies), liquid capital flows more towards US equities, whereas during weak dollar environments, it flows elsewhere. This can create a self-perpetuating cycle in one direction or another until a number of catalysts and policy changes lead to a reversal. So, US equity valuations became very high in 2000 (strong dollar period), and then emerging market valuations became very high in 2007 (weak dollar period), and in recent years US equities have once again been highly-valued in a strong-dollar period.

Between valuations, capital flows, and rate expectations, investors can build a map for themselves about the long-term forward returns prospects of various asset classes.