During a recent CNBC appearance,

Warren Buffett (Trades, Portfolio) said the following about the relationship between interest rates and equity valuations:

“The valuations make sense with interest rates where they are. In the end, you measure laying out money for an asset in relation to what you're going to get back. And the number one yardstick is U.S. governments. And when you get 2.30% on the 10-year, I think stocks will do considerably better than that. So if I have a choice of the two, I'm going to take stocks at that point. On the other hand, if interest rates on the 10-year were 5% or 6%, you would have a whole different valuation standard for stocks.

Interest rates are gravity. If we knew interest rates were going to be zero from now to judgment day, you could pay a lot of money for any other asset. You would not want to put your money out at zero… It's been a powerful factor. And the longer it persists, the more people start thinking in terms of something close to the rates they've seen for a long time. The one thing I'm sure of is that over time stocks from this level will beat bonds from this level…

And everybody expects interest rates to change, but they've been expecting it for quite a while… If three years from now interest rates are 100 basis points higher, then stocks will still look cheap at these prices. If they're 300 or 400 basis points, they won't look cheap.”

As usual, Buffett has succinctly covered a lot of ground. The purpose of this article is to look at the relationship between interest rates and equity valuations – and the impact it has on forward returns once the valuation has “reset” to a higher level.

Let’s look at an example to get a feel for the math behind Buffett’s first comment (“*In the end, you measure laying out money for an asset in relation to what you're going to get back*”). We are looking at a business that will generate a stream of cash flows over the next 50 years (100% returned to investors each year) that starts at $100 and increases by 2% per annum.

In the first scenario, investors demand an 8% annualized return (IRR) from the investment based on a spread over the risk-free investment; let’s assume 300 basis points over a long-term treasury yield of 5%. Based on those assumptions, this business (stream of cash flows) has a fair value of $1,600. At that price, investors will earn the 8% per annum that they require for taking the incremental risk of owning something other than the risk-free bond.

In the second scenario, the yield on long-term treasuries permanently declines from 5% to 2.3%. If the spread between the risk-free rate and our investor’s return requirement is held constant at 300 basis points, our IRR – the required rate of return we demand when paying for this stream of cash flows – falls from 8% to 5.3%. As a result of this change, the price we are willing to pay for the business increases to $2,460 – more than 50% higher than fair value in the first scenario.

The takeaway is a lower hurdle rate allows us to justify a materially higher price *for an identical stream of cash flows*. In the real world, we have seen the hurdle rate decline because the yield on the “number one yardstick” – U.S. treasuries – has been stuck near historic lows for five-plus years.

In summary, lower interest rates justify higher equity valuations. Looking at the numbers, the implied multiple increased from 16 times to nearly 25 times (pretty significant multiple expansion). There is nothing new or shocking here; I think this point is widely understood by market participants.

So there is a clear argument for a higher valuation (and stock price). But what does that mean for our forward return expectations? As an investor, what should I expect after Mr. Market accounts for the lower hurdle rate and the stock price (or index level) increases from ~$1,600 to ~$2,500?

The discount rate in our calculation makes the net present value of our future cash flows equal to zero. That rate is unchanged over the measurement period. When we use (or accept) a lower discount rate, **we are building in a lower expected (required) rate of return over the life of the cash flows (business)**. I am not sure that point is always appreciated. The next time you hear someone say lower interest rates justify higher equity prices, you should finish the sentence for them: “Lower rates justify higher equity prices *because today’s gains are eating into future returns*.”

If our stream of cash flows is unchanged, a higher starting valuation (stock market gains from multiple expansion) is ultimately a “cost” that results in lower forward rates of return. Those lower future returns are deemed acceptable by market participants since the alternative (long-term treasuries) have become less attractive as well. The point is that there is a clear trade-off between the starting valuation (price) and return expectations.

When someone measures equity prices against bond yields, it is important to appreciate what they are saying. We must remember to differentiate between *relative* valuations and *absolute* returns. Failing to make this distinction could prove costly for investors. Stocks can appear cheap on a relative basis and still be expensive on an absolute basis (by which I mean priced for significantly less than historic rates of return).

Finally, assuming rates will hold near current levels has a material impact on the fair value estimate for equities. If that assumption ends up being incorrect, investors may be in for a surprise. Here’s how

Seth Klarman (Trades, Portfolio) put it in “Margin of Safety”:

“At times when interest rates are unusually low, however, investors are likely to find very high multiples being applied to share prices. Investors who pay these high multiples are dependent on interest rates remaining low, but no one can be certain that they will. This means that when interest rates are unusually low, investors should be particularly reluctant to commit capital to long-term holdings unless outstanding opportunities become available,with a preference for either holding cash or investing in short-term holdings that quickly return cash for possible redeployment when available returns are more attractive.”

**Conclusion**

If treasury yields muddle along in the low single digits, investors can justify paying a lot of money for a future stream of cash flows. The owners of common stocks should not expect historic rates of return in perpetuity if starting prices (valuations) adjust for this factor.

On the other hand, if long-term rates move materially higher **and **stock prices adjust to earn a spread above the long bond, equity investors could be in for a rude awakening. It seems ill-advised for investors to become more confident that rates will stay low in the future simply because they have been low in the recent past.

There is one additional factor worth considering that I've overlooked: does a period of materially lower long-term interest rates have any impact (positive or negative) on the future cash flows to be received by equity investors? That is a discussion for another day.

I will leave you with Buffett’s prediction:

“If three years from now interest rates are 100 basis points higher, then stocks will still look cheap at these prices. If they're 300 or 400 basis points, they won't look cheap.”

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