A few months ago, I tagged along with my wife and daughter as they went on a tour of the Federal Reserve Building in downtown New York. While the highlight of the tour is that you get to see large stacks of US dollars in the basement of the building, I considered making myself persona non grata with my immediate family by asking the guide (a very nice Fed employee) about the location of the interest rate room. That, of course, is the room where Janet Yellen comes in every morning and sets interest rates. I am sure that you can visualize her pulling the levers that sets T.Bond rates, mortgage rates and corporate rates and the power that comes with that act. If that sounds over the top, that is the impression you are left with, not only from reading news stories about central banks, but also from opinion pieces from some economists and investment advisors. I know that investors, analysts and CFOs are all rendered off balance by low interest rates, but I will argue that the techniques that they use to compensate are more likely to get them in trouble than solve their problems.

**The what: Interest rates are at historic lows across the globe**

There is little to debate. Interest rates are lower than they have been in a generation and you can see it in this graph of the US 10-year treasury bond rate going back several decades:

US 10-year T.Bond rates at the end of each year |

But it is not just the US dollar where low interest rates prevail, as illustrated by the German government 10-year Euro bond rate, the Japanese government 10-year Yen bond rate and the Swiss Government 10-year Swiss franc rate trend lines:

Ten-year Government Bond Rates: End of each period |

In fact, on the Swiss Franc, the 10-year bond rates rates have not just dropped but have hit zero and kept going to -0.09%, leading to the almost unfathomable phenomenon of negative interest rates on long term borrowing. A world where savers have to pay banks to keep their savings and borrowers are paid money to borrow turns everything that we have learned in economics on its head and it is therefore no surprise that even seasoned investors and analysts are unsure of what to do next.

**The why: Its not just central banks**

Why are interest rates so low? I know that the conventional wisdom is that it is central bank policy that has driven them there, but is that true? To answer that question, I decided to do go back to basics.

*The Fundamentals*

While market interest rates are set by demand and supply, as they are in any other market, there are fundamentals that determine that rate. In particular, the interest rate on an investment with no default risk (a guaranteed or risk free investment) can be written as the sum of two components:

Interest rate on a guaranteed investment = Expected inflation + Expected real interest rate

This is the simplified version of the classic Fisher equation and it is true by construction. In fact, many analysts use it to decompose market interest rates; thus if the US treasury bond rate is at 2.00% and expected inflation is 1.25%, the real interest rate is backed out at 0.75%. In the long term, I would argue that a real interest rate has to be backed up by a real growth rate in the economy. After all, you cannot deliver a 2% real interest rate in an economy growing at only 1% a year in the long term, though you can get short term deviations between the two numbers. Thus, in the long term, the interest rate on a guaranteed investment can be rewritten as:

Interest rate on a guaranteed investment = Expected inflation + Expected real growth rate

How well does this simplistic equation hold up in practice? Testing it is hard, especially when you can observe only

__actual__inflation and real growth but__not expected__inflation and real growth. However, we also know that expectations for inflation and real growth are driven, for better or worse, by recent history; thus expected inflation increases after periods of high inflation and decreases after periods of low inflation, thus making actual inflation and real growth reasonable proxies for expected values. The final number we need to test out this relationship is the interest rate on a guaranteed investment, and we use the US 10-year treasury bond rate as the stand in for that number, with the concession that the last 5 years have shaken investor faith in the guarantee.Source: FRED (Federal Reserve in St. Louis) |

Even if you take issue with my proxies for expected inflation (the actual inflation rate in the US each year, as measured by the CPI), real growth (the real growth rate in US GDP and the interest rate on a guaranteed investment, the graph sends a powerful message that risk free rates are driven by inflation and real growth expectations. If expected inflation is low and real growth is anemic, as has been the case since 2008, interest rates will be low as well and they would have been low, with or without central bank intervention.

*The Central Bank Effect*

Do central banks have influence over interest rates? Of course, but the mechanisms they use are surprisingly limited. In the United States, the only rate that the Fed sets is the Fed Funds rate, a rate at which banks can borrow or lend money overnight. Thus, if the Fed wants to raise (lower) interest rates, it has historically hiked (cut) the Fed Funds rate and hoped that bond markets (treasury and corporate) respond accordinly. One way to measure the effect of Fed action is to compute the difference between the actual US treasury bond rate each period and the “intrinsic” treasury bond rate (computed as the sum of inflation and real GDP growth that year):

Source: FRED |

Note that the Fed Funds rate hit zero in 2009 and has stayed there for the last five years, effectively eliminating it as a tool for controlling rates. Perhaps driven by desperation and partly motivated by the savior complex, the Fed has turned to a relatively unused tool in its arsenal and bought large quantities of US treasury bond in the market for the last five years, the much-talked about Quantitative Easing (QE). While it is true that T.Bond rates have stayed below intrinsic interest rates over the last 5 years, the effect of QE (at least to my eyes) seems to modest.

As the economy comes back to life, all eyes have turned towards Janet Yellen and the Fed and Fed-watching has become the central focus for many investors. While that is understandable, it is worth remembering that in today's economic environment, with low inflation and real growth, the removal of the Fed prop will not cause interest rates to pop to 5% or 6% . In fact, based upon the numbers in the most recent year, the intrinsic interest rate is 3.08% and if the central banking props disappear, that would be the number towards which US treasury bond rates move.

Given the evidence to the contrary, it is puzzling that investors continue to hold on to the belief that central banks set interest rates and can change them on whim, but I think that the delusion serves both sides (investors and central banks) well. Investors, whipsawed by market and economic forces that are uncontrollable, feel comfort in attributing the power to set interest rates to central banks. It also allows investors to attribute every phenomenon that they have trouble explaining to central banking machinations and interest rates that are either "too high" or "too low". Quantitative Easing in all its forms has proved to be absolutely indispensable as a bogey man that you can blame for the failure of active investing, the rise and fall of gold, and bubbles of every type. Central banks, which are really more akin to the Wizard of Oz, in their powers, than Masters of the Universe, are glad to play along, since their power comes from the illusion that they have real power.

Given the evidence to the contrary, it is puzzling that investors continue to hold on to the belief that central banks set interest rates and can change them on whim, but I think that the delusion serves both sides (investors and central banks) well. Investors, whipsawed by market and economic forces that are uncontrollable, feel comfort in attributing the power to set interest rates to central banks. It also allows investors to attribute every phenomenon that they have trouble explaining to central banking machinations and interest rates that are either "too high" or "too low". Quantitative Easing in all its forms has proved to be absolutely indispensable as a bogey man that you can blame for the failure of active investing, the rise and fall of gold, and bubbles of every type. Central banks, which are really more akin to the Wizard of Oz, in their powers, than Masters of the Universe, are glad to play along, since their power comes from the illusion that they have real power.

*The Crisis Effect*

There is another factor at play that may be more powerful than central banks, at least over short periods, and that is the perception of a crisis. Whatever the origins or form of the crisis, investors respond with fear, and flee to safety. That "flight to quality" often manifests itself in declining interest rates on bonds issued by governments that are perceived as "higher quality", and may push those rates well below intrinsic levels. Looking at the chart where we outline the gap between the T.Bond rate and its intrinsic value, the quarter where we saw the US 10-year treasury bond rate drop the most, relative to its intrinsic value, was the last quarter of 2008, where the crisis in financial markets led to a rush into US treasuries. That translated into a precipitous drop in treasury rates across the board, with the 10-year rate dropping from 3.66% on September 12, 2008, to 2.2% at the end of 2008, and the T. Bill rate declining from 1.62% to 0.02% over the same period.

Source: FRED- Constant Maturity Rates on 3-month and 10-year treasuries |

**The Interest Rate Effect**

The level of interest rates matter for all of us, as investors, consumers and businesses. For investors, interest rates drive expected returns on investments of all types through a very simple process:

Expected Return (r) = Interest rate on a risk free investment + Risk Premium

That expected return then determines what we will be willing to pay for a risky asset, with lower expected returns translating into higher prices. For businesses, these expected return becomes hurdle rates (costs of equity and capital) that they use to decide not only whether and where they should invest their money but plays a role in how much they borrow and how much to return to stockholders (as dividends or buybacks).

If the risk free rate drops and you leave the risk premiums and cash flows unchanged, the effect on value is unambiguously positive, with value rising as risk free rates drop. Thus, if you have a business that has $100 million in expected cash flows next year, with a growth rate of 4% a year in perpetuity and an equity risk premium of 4%, changing the risk free rate from 6% down to 2% will have profound effects on value. It is this value effect that has led some to blame the Fed for creating a "stock market bubble" and analysts across the world to wonder whether they should be doing something to counter that effect, in their search for intrinsic value.

While the mathematics that show the link between value and interest rates is simple, it is misleading because it does not tell the whole story. As I argued in the last section, interest rate movements, up or down, almost never happen in a vacuum. The same forces that cause significant shifts in interest rates affect other inputs into the valuation and those changes can reduce or even reverse the interest rate effect:

To illustrate, the 2008 crisis that caused the T.Bond rate to plummet in the last quarter of the year also caused equity risk premiums to surge from 4.37% on September 12, 2008 to 6.43% on December 31, 2008. In the figure below, I back out the expected return on stocks and the equity risk premium from the index level each day and the expected future cash flows for each month from September 2008 to April 2015. Note that the cost of equity for the median US company rose in the last quarter of 2008, even as risk free rates declined.

Source: Damodaran.com (Implied ERP) |

The expected return on equities has stayed surprisingly stable (around 8%) for much of the last 5 years, nullifying the impact of lower interest rates and casting doubt on the "Fed Bubble" story. As the crisis has receded, investor concerns have shifted to real growth, as the developed market economies (US, Euro Zone and Japan) have been slow to recover and inflation has not only stayed tame but turned to deflation in the EU and Japan. Thus, looking just at lower interest rates and making judgments on value misses the big picture.

**Reacting to Low Interest Rates**

Given that low interest rates have shaken up the equation, what should we do to respond? Broadly speaking, there are four responses to low interest rates:

__Normalize__: In valuation, it is common practice to replace unusual numbers (earnings, capital expenditures and working capital) with more normalized values. Some analysts extend that lesson to risk free rates, replacing today’s “too low” rates with more normalized values. While I understand the impulse, I think it is dangerous for three reasons. The first is that "normal" is a subjective judgment. I argue, only half in jest, that you can tell how long an analyst has been in markets by looking at what he or she views as a normal riskfree rate, since normal requires a time frame and the longer that time frame, the higher normal interest rates become. The second is that if you decide to normalize the risk free rate, you have no choice but to normalize all your other macro variables as well. Consequently, you have to replace today’s equity risk premium with the premium that fits best with your normalized risk free rate and do the same with growth rates. Put differently, if you want to act like it is 2007, 1997 or 1987, when estimating the risk free rate, your risk premiums and growth rates will have to be adjusted accordingly. The third is that unlike earnings, cash flows or other company-specific variables, where you are free to make your judgment calls, the risk free rate is what you can earn on your money today, if you don’t invest in risky assets. Consequently, if you do your valuation, using a normalized risk free rate of 4% (instead of the actual risk free rate of 2%), and decide that stocks are over valued, I wish you the very best of luck putting your money in that normalized treasury bond, since it exists only in your estimation.__Go intrinsic__: The second option, if you believe that the market interest rate on government bonds is being skewed by central banking action to abnormally low or high levels is to replace that rate with an intrinsic interest rate. If you buy into my estimates for inflation and real growth in the last section, that would translate into using a 3.08% “intrinsic” US treasury bond rate. To preserve consistency, you should continue to use the same inflation rate and real growth as your basis for forecasting earnings and cash flow growth in your company and going the distance, you should estimate an intrinsic ERP, perhaps tying it to fundamentals.__Leave it alone__: The third option is to leave the risk free rate at its current levels, notwithstanding concerns that you might have about it being too low or too high. To keep your valuation in balance, though, your other inputs have to be consistent with that risk free rate. That implies using forward-looking prices for risk (equity risk premiums and default spreads) that reflect the market today and economy-wide growth and inflation rates that are consistent with the current risk free rate. Thus, if you decide to use 0.21% as the risk free rate in Euros, the combination of inflation and real growth rates you have to assume in the Euro economy have to combine to be less than 0.21%. Doing so does not imply that you believe that nominal growth will be that low but ensures that you are making the same assumptions about nominal growth in the numerator (cash flows) as you are in the denominator (through the risk free rate).__Leave it alone (for now)__: The last option is to leave the risk free rate at current levels for now but adjust the rate in the future (perhaps at the end of your high growth period) to your normalized or intrinsic levels. Here again, the key is to make sure that your other valuation inputs are consistent with your assumption. Thus, for the period you use the current risk free rate, you have to use equity risk premiums, growth rates and inflation expectations consistent with that rate, and as you adjust the risk free rate to its normalized or intrinsic levels, you have to adjust the rest of your inputs.

To illustrate the four options when it comes to risk free rates, I value a hypothetical average-risk company with an expected cash flow of $100 million next year, using all four options. The inputs I use for the company under each option are summarized below, with the value computed in the last column:

The four choices yield different values but the most interesting finding is that the value that I get with the “leave alone” option is lower than the values that I obtain with my other options. Consequently, those who argue that we need to replace the current risk free rate with more normalized versions because it is the “conservative” path may be ending up with estimates of value that are too high (not too low).

While I prefer the "leave alone" option, I think that the other approaches are defensible, if your macro views are significantly different from mine. The danger, as I see it, comes when you mismatch your assumptions, with two of the most egregious examples listed below:

Note that while each input into these mismatched valuations may be defensible, it is the combination that skews the value vastly downwards or upwards. If you use or do intrinsic valuations, checking for input consistency is more critical than ever before.

**Bottom line**

So, what is the bottom line? Like almost everyone else, I find myself in uncharted territory, with interest rates approaching zero in many currencies and like most others, I feel the urge to "fix" the problem. There are three broad lessons that I take away from looking at the data.

__Central banks tweak interest rates__. They don’t set them. Consequently, I am going to spend less time worrying about what Janet Yellen does in the interest rate room and more on the fundamentals that drive rates. I will also grant short shrift to anyone who uses central banks as either an excuse or looks to them as a savior in their investing.__When risk free rates are abnormally low or high, it is because there are other components in the market that are abnormal, and I am not sure what is normal__. For investors in the US and Europe who yearn for the normality of decades past, I am afraid that normal is not returning. We have to recalibrate our assumptions about what is normal (for interest rates, risk premiums, inflation and economic growth) and pay less heed to rules of thumb that were developed for another market (US in the 1900s) and another time.__As investors, we can rage against interest rates being too low but it is what it is.__We have to value companies in the markets that we are in, not the markets we wished we were in.

**Data to download**

Spreadsheets

## 19 comments:

Hi Mr. Damodaran,

Thank you for the honest reminder about the FED's true power when it comes to hiking interest rates. My question is regarding your november's valuation of lukoil. Are you planning on selling your shares since your updated valuation ( March 2015) presents a vale per share of 42.53 while the current stock is trading at 49.33 (15% premium) ?

Thanks

Tim

The fed has 1.7 trillions dollars of Mortgage back securities on its balance sheet as on 31st dec 2014. While its not engaging in QE the fact that its keeping these assets off market must be a stimulus in itself. It must also clearly impact interest rates. So if the feds actions were unwound wouldn't the interest rates shoot up to at least the long term historic rate

Can you please clarify for me what the distinction between your Intrinsic Interest rate and the Nominal GDP? It looks like it would be the same... Thanks.

You say: In the long term, I would argue that a real interest rate has to be backed up by a real growth rate in the economy. After all, you cannot deliver a 2% real interest rate in an economy growing at only 1% a year in the long term, though you can get short term deviations between the two numbers.

I have seen this statement many times. It is not self-evident to me. I would appreciate it if you could provide some kind of demonstration for this statement.

UniverseofRisks,

You are right. There will be a liquidity impact from a Fed unloading of bonds, but the Chinese government also owns trillions in treasuries. If I had to worry about a destabilizing influence, maybe it is the latter than I should worry about,

On real interest rates, here is the way I was taught real interest rates in Econ 101. If you borrow a 100 bushels of wheat today from me, I will let you do so only if you agree to return more than a 100 bushels a year from now. In other words, a real interest rate has to be backed up by real goods and services. Think of it as the rate that would exist even in a currency-free economy.

Finally, you are right. My intrinsic interest rate is equal to the nominal GDP in my calculation, but the set up is flexible enough that you can make it richer, by bringing in better estimates of expected inflation and expected real growth.

The required return on equities is partly a function of the growth rate assumption.

How did your assumed cash flow growth assumption behave post-crisis? I wasn't sure if you used some analyst measure (5yr EPS growth expectations?); a nominal gdp growth rate associated with a lower risk free rate; or just the same assumption as pre-crisis. If you could make that explicit, it would help to better understand how the derived ERP has remained stable.

the fisher equation implies:

real interest rates = nominal interest rates - inflation

At the same time, it states that monetary policy has no effect on real interest rates.

However, aren't nominal interest rates determined by the demand for money (liquidity preference) and its supply, which is stimulated by the FED?

Here has an interesting (and also a recently and actual one) interview with LIAQUAT AHAMED about the power of central banks.

Liaquat Ahamed is the author of the book "Lords of Finance: The Bankers Who Broke the World".

https://www.youtube.com/watch?v=5qmeLUKqX0g

"

We discuss the lessons learned and ignored from the powerful central bankers of a century ago. Financial Thought Leader Liaquat Ahamed, the Pulitzer Prize winning author of Lords of Finance discusses the differences and similarities between central bank policies today and those leading up to the Great Depression".Iranian banks are paying 20-22% on 1-year deposits. Given the impending deal, the currency is unlikely to collapse much further. And for a foreign person, the high-inflation argument is weak because you will not be spending the money there anyways. Why aren't more non-US persons (who are otherwise subject to US sanctions) depositing money with Iranian banks? Can you get money in or out? The answer is yes, through exchange bureaus.

Dear Prof.,

Is there a reason why you don't use core inflation to compute the intrinsic rate?

Thanks.

Dear Mr. Damodaran,

As you show, there is a strong correlation between long term interest rates and past growth/inflation, but there is limited evidence that a low long term interest rate means low growth in the future. The market is what it is, I agree. Thus the alternative is the actual long term bond investment opportunity today. What is then wrong with leaving the risk free rate alone, but normalize the growth rate? We do know that world GDP growth has been surprisingly stable looking at figures since before 1900.

Note: Re-posting a comment I posted this morning as appears to be lost!

On the matter of “Interest Rate Effect” on the stock market valuation:

Is it possible for the expected cash flow growth (of the entire stock market which I assume approximates the performance of economy as a whole) to be much different from the growth of “Nominal” GDP?

On an individual company basis - yes, but for the entire market?

With your calculation of the 3% or so intrinsic (un-propped) rate (which I suppose means your expectation of a 3% or so nominal GDP growth), would you consider present stock market valuation to be either embedding a slim risk premium or a higher than 3% nominal GDP growth (either more inflation or more real GDP growth)?

Ray Kumar,

For short periods, the answer is absolutely yes and it has been true for much of the market's history. The earnings growth in companies can be higher than overall economic growth, either because you are coming of depressed earnings or because higher-than-anticipated growth creates an even higher earnings growth.

Diego,

You have a good point about earnings growth and the crisis effect. There was a problem, especially during the last 3 months of 2008 and it was not that growth was not adjusting, it was because the cash flows were adjusting more slowly than the market. While I updated the cash flows to reflect monthly changes in buybacks, I am probably over estimating the ERP in the last two months of 2008.

As always a fantastic post. So far I haven't come across anything on this topic that has been so refreshing as your piece. Offering us a new perspective. Thank you.

Dear Prof. Damodaran,

thanks a lot for the interesting insights on low interest rates.

Being a German, however, I am expecting negative 10 year bond interest rates in the next weeks. I wonder what the consequences will be assuming negative eternal growth in the leave alone version of DCF models.

Thanks a lot for your answer!

Peter Hasler

Professor,

I do think the debate over the equity valuation and low interest rate is one of the crucial ones. Anecdotally, Warren Buffet today at CNBC said equities are expensive under the normal rate but it is not at the current rate.

From my experience as a professional buy-side equity analyst, when using discount CF model, it has been and is always a big question the way to pick WACC as the past historical trend of long term bond rate is incorporated in it. When rates go lower, assuming everything the same, value of equity goes up.

Moreover, as you pointed out, the long term growth rate of excess CF should be adjusted downward accordingly when real interest rate drops, but I have to say equity analysts are unlikely to change it in that way. Anecdotes include NO broker report that says long term growth rate of Apple has been revised down and valuation moves lower because of declining real interest rates. (Well,,, Apple has large net interest income and it is occasionally adjusted by a serious analyst.)

What I saw and see it the divergence between real rate and long term growth expectation. Company equity analysts use the terminal growth rate (and ROE) of excess CF at the end of forecast period and links growth rate at the end of forecast (say 5-7 years) with the terminal growth (say 30-50 years from today when the growth reaches equilibrium.)

My sense is that the current equity market valuation may be supported by such divergence and even more excessive for private equities and venture business where pensions and university endowments are allocating lots of asset – which I see as a potential and hidden risk. Equity bubble was formed in public market but IMHO this time invisible and under-regulated private and pre-public market may be becoming the stealth bubble driver.

Professor,

Another impact from low interest rate is, I think, the lowered cost of M&A deals. That may be indirectly boosting market price more than the interest rate alone indicates.

Acquirers like home buyers are looking at the cost of the deal including financing package. The current low rate environment is so attractive as a finance condition for a acquirer that it can inflate price of equity through such indirect low-rate condition.

That is even more evident in a private market as the exit price is determined by such deal in which the cost of acquiring equity is judged by the total cost including finance.

As you laid out the logic, it seems at present there is a gap between how value should be estimated and what the users of equity deals are looking at. That may be one of the risks of low rate environment we are in now.

Taking the standard DDM: P=D/(r-g). Or Div Yield=r-g

So, r= Risk Free Rate + ERP

If Risk Free Rate= g, then the DDM simply becomes: Div Yield=ERP, (currently at 2%). And most importantly , the Risk Free Rate does not feature in the equity valuation equation at all!

I dont think 200 bp is an adequate compensation given that corporate bond spreads are around 100bp to 150bp for inv grade.

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