Friday, January 2, 2015

An ERP Retrospective: Looking back (2014) and Looking forward (2015)

At the beginning of 2014, the expectation was that government bond rates that had been kept low, at least according to the market mythology, by central banks and quantitative easing, would rise and that this would put downward pressure on stocks, which were already richly priced. Perhaps to spite the forecasters, stocks continued to rise in 2014, delivering handsome returns to investors, and government bond rates continued to fall in the US and Europe, notwithstanding the slowing down of quantitative easing. Commodity prices dropped dramatically, with oil plunging by almost 50%, Europe remained the global economic weak link, scaling up growth became more difficult for China and the US economy showed signs of perking up. Now, the sages are back, telling us what is going to happen to markets in 2015 and we continue to give them megaphones, notwithstanding their  forecasting history. Rather than do a standard recap, I decided to use my favored device for assessing overall markets, the equity risk premium (ERP), to take a quick trip down memory lane and set up for the year to come.

The ERP: Setting the stage
The ERP is what investors demand over and above the risk free rate for investing in equities. as an asset class. At the risk of sounding over-the-top, if there is one number that captures investors' hopes, fears and expectations it is this number, and I have not only posted multiple times on it in the last few years but also updated it every month on my website. In making these updates, I have had to confront a key question of how best to measure the ERP. Many practitioners use a historical risk premium, estimated by looking at how much investors have earned on stocks, relative to the returns on something riskfree ( usually defined as government bills & bonds)). Due to the volatility in stock returns, you need very long time periods of data to estimate these premiums, with "long time period" defined as 50, 75 or even 100 years of data. At the start of each year, I estimate the historical risk premiums for the United States and my January 1, 2015 update is below:
Stocks: S&P 500; T.Bills: 3-mth Bills; T.Bonds: US 10-year
Geometric average is based on compounded returns
Based on this table, the historical equity risk premium for the US is between 2.73% to 8%, depending on the time period, risk free rate and averaging approach used. I will also cheerfully admit that I don't trust or use any of these numbers in my valuations, for three reasons. First, using a historical risk premium requires a belief in mean reversion, i.e., that things will always go back to the way they used to be, that I no longer have. Second, all of these estimates of risk premiums carry large standard errors, ranging from 8.65% for the 2005-2014 estimate (effectively making it pure noise) to 2.32% for the 86-year estimate. Third, it is a static number that changes little as the world changes around you, which you may view as a sign of stability, but I see as denial.

In pursuit of a forward-looking, less noisy and dynamic equity risk premium, I drew on a standard metric in the bond market, the yield to maturity:
As bond price rises (falls), yield to maturity falls (rises)
In the equity market analogue, the bond price is replaced with stock index level, the bond coupons with expected cashflows from stocks, with the twist that the cash flows can continue in perpetuity:

There are both estimation questions (Are cashflows on stocks just dividends, inclusive of buybacks or a broader measure of residual free cashflows to equity?) and challenges (Do you use last year's cash flow or a normalized value? How do you estimate future growth? How do you deal with a perpetuity?), but they are not insurmountable. In my monthly estimates for the ERP for the S&P 500, here are my default assumptions:

This estimate is forward-looking, because it is based on expected future cashflows, dynamic, because it changes as stock prices, expected cash flows and interest rates change, and it is surprisingly robust to alternative assumptions about cash flows and growth. The spreadsheet that I use allows you to replace my default assumptions with yours and check the effects in the ERP. 

The ERP in 2014
Using the framework described in the last section, I estimated an equity risk premium of 4.96% for the S&P 500 on January 1, 2014:

During 2014, the S&P 500 climbed 11.39% during the year but also allowing for changes in cash flows, growth and the risk free rate, my update from January 1, 2015, yields an implied equity risk premium of 5.78%:

At the start of each month in 2014, I posted my estimate of the ERP for the S&P 500 on my website. The figure below graphs out the paths followed by the S&P 500 and the ERP through 2014:

The ERP moved within a fairly narrow band for most of the year, ranging from just under 5% to about 5.5%, with the jump to 5.78% at the end of the year, reflecting the updating of the growth rate.

The Drivers of ERP in 2014
To understand the meandering of the ERP during 2014, note that it is determined by four variables:  the level of the index, the base year cash flow, the expected growth and the government bond rate, and is a reflection of the risk that investors perceive in equities. In the figure below, I chronicle the changes in these variables during 2014, at least in my ERP estimates.

A confession is in order. While I update the index levels and government bond rates in real time, I update cashflows once every quarter and the growth rates materially only once a year (at the start of each year). One reason for the precipitous jump in the ERP in the January 1, 2015, update is the updating of the long term growth rate to 5.58% on that date. Updating the cashflow and growth estimates more frequently will smooth out the ERP but not change the starting and ending points.

Perspective: Against history and other markets
When I stated earlier in the post that the ERP was the one number that encapsulated investor hopes and fears, I was not exaggerating, since every statement about the overall market can be restated in terms of the ERP. Thus, if you believe that the ERP at the start of 2015 is around 5.78% (my estimate but you can replace with yours), your market views can be laid bare by how you answer the following question: Given what you perceive as risk in the market, do you think that 5.78% is a fair premium? If your answer is that it (5.78%) is too low (high), you are telling me that you think stock prices are too high (low). 

One reason that I posit that I am not a market timer is because I struggle with this question and there are two simple comparisons that I use for comfort. One is to compare the ERP today to implied quit risk premiums in previous years to see how it measures up to historic norms. The figure below summarizes implied equity risk premiums from 1960 to 2014:
My estimates of ERP at the end of every year from 1960 to 2014
Looking at the historical numbers, the current ERP looks high, not low; it is close to the norm if you use only the post-2008 time period. It is this argument that I used to contest the notion that the market was in a bubble in June 2014.

The other is to compare the equity risk premium to risk premiums in other asset markets. In the bond market, for instance, the default spread for corporate bonds is a measure of the risk premium and the figure below compares the equity risk premium to the Baa default spreads each year from 1960 to 2014:
Baa rates from the Federal Reserve data site (FRED) and Baa default spread computed relative to US 10-year T.Bond rate in that year.
Again, if history is any indication, equity risk premiums do not look inflated, relative to Baa default spread, though it is entirely possible that both spreads are too low. (You can download the data and check for yourself.)

We are and will continue to be inundated by experts, sages and market prognosticators, each wielding their preferred market measures, trying to convince us that markets are under or over valued. In this New York Times article from December 31, 2014, looking at where the market stands going into 2015,  the writer pointed to two widely followed statistics, the Shiller PE, a measure of how stocks are priced relative to inflation-adjusted earnings, and the Buffett ratio, relating the market cap of US stocks to the US GDP, and suggested that both pointed to an over valued markets. Both Robert Shiller and Warren Buffett are illustrious figures, but I think that both statistics are flawed, the Shiller PE, because it does not control for low interest rates, and the Buffett ratio, because of its failure to factor in the globalization of US companies. On market timing, I prefer to set my own course and am not going to be swayed by celebrity name-power in making my judgments.

The Weakest Links
If you believe at this point that I am sanguine about what stocks will do next year, you would be wrong. The nature of equity investing is that it is always coupled with worries and that the best laid plans can be destroyed by events out of your control. The notion that stocks always win in the long term is misplaced and there is a reason why we earn a risk premium for investing in equities. Looking at 2015, these are the three biggest dangers that I see:

1. An Earnings Shock? While current stock prices can be justified based on current cash flows, the cash flows to equity investors in 2014, from dividends and buybacks, represented an unusually high percentage of earnings, which, in turn, were at a high watermark, relative to history.
Based on aggregate numbers for S&P 500
Note that US companies paid out 87.58% of earnings to investors, below the 2007 & 2008 levels, but still well above the historical average (73.68%), and the profit margin of 9.84% in 2014  is the highest in the 2001-2014 time period. Both aggregate earnings and the payout ratio will be tested in the year to come. With aggregate earnings, the first test will be in the near term as the dramatic drop in oil prices in 2014 will play havoc with earnings at oil companies. As I noted in my earlier post on oil prices, lower oil prices may create a net positive benefit for the economy, but the immediate earnings benefit to the rest of the market will be modest. The second test may come from slower economic growth. While the US economy looks like it is on the mend, earnings at US companies are increasingly global, and a slowing down of the Chinese economic machine coupled with more stagnation in Europe, may net out to lower earnings. With the payout ratio, the challenge will be to deliver the earnings growth that investors are expecting, while paying out the high percentage of earnings that they are right now.

2. Fear the Fed? I have made this point before in my posts, but it is worth making again. While the equity risk premium has gone up significantly since the pre-2008 crisis, all of the increase in the risk premium has come from the risk free rate dropping and not from expected returns on stocks increasing.

If the US 10-year T.Bond rate were at 4%, closer to pre-2008 levels, right now, the equity risk premium would be only 3.95%.

3. Crisis, contagion and collapse? If we learned nothing else from 2008, it should be this. We are all part of a global economy, connected at the hip, and while that can yield benefits, the contagion risk has increased, where a crisis in one part of the world spills over into the rest of it. Again drawing on my post on oil, one danger of the sudden collapse in oil prices is that it has not only increased uncertainty about economic growth in the next year but also increased the risk of large, levered oil companies defaulting and sending shockwaves through the rest of the economy.

The perfect storm, of course, would be for all three phenomenon to occur together: a drop in earnings and an increase in interest rates, with an overlay of a global crisis, with catastrophic consequences of stocks. I think that the odds of this happening are low, because the circumstances that cause an earnings collapse are the ones that would keep interest rates low, but I may be missing something. If you disagree, you could take the safe route and hold cash, but unless your probability assessments of a crash are high and a crash is imminent, that does not strike me as prudent. (I have reattached the spreadsheet that I developed for my post on bubbles that you can use to make your own assessment.) 

Bottom line
Like every other year in my investing memory, I start this year both hopeful and fearful, hopeful that financial markets will navigate through whatever the new year will throw at them and fearful that there will be something that will rock them. Given what I know now, I don't see any reason to dramatically alter my exposure to stocks, bonds or real assets, and I will continue to look for stocks that I think are under priced. I wish you the very best in your investment choices this year as well and I hope that no matter what happens to your portfolio, you are healthy and happy!

Attachments: Data Sets
  1. Historical Returns for US stocks, T.Bonds and T.Bills: 1928-2014
  2. Implied Equity Risk Premiums for S&P 500: 1960-2014
  3. ERP, Baa Yields and Real Estate Cap Rates: 1960-2014


3rdMoment said...

I have a question. It appears that you are using analyst forecasts of per-share index earnings to get expected earnings growth. It seems to me that by using the per-share numbers, and also counting buybacks as part of the cash flows to shareholders, you would in effect double-count the effect of buybacks, since the buybacks themselves are a necessary part of achieving the projected per-share earnings growth.

In other words: the cash spent on buybacks is not available to shareholders directly, but instead rewards them through faster per-share earnings growth. So it seems wrong to count them as if they were equivalent to dividends AND in addition count their contribution to per-share earnings/dividend growth. I would think you would either need to use a measure of total earnings growth (rather than per share), or if you want to use per-share earnings growth you would need to remove buybacks from the cash-flows available to shareholders.

Am I missing something here?

Also, it appears that you may be using gross buybacks instead of net buybacks. Is that right?

Anonymous said...

Thanks for a great post, I really like your approach to estimate the ERP. I did however stumbled on you thoughts of the Buffet-estimate. What if using the estimate but consider world gdp growth combined with US gdp? Where "world gdp growth" for eg is defined by US top export countries and weight to US current account... / mr. p

Aswath Damodaran said...

It is precisely to avoid the double counting that I use the top-down estimates. These are estimates of aggregate earnings for the S&P 500, rather than the one obtained by adding up individual per share growth growth rates. That would have yielded a growth rate of 11.50%.
On the GDP question, you could look at world capitalization as a percent of world GDP, but I am not sure what you would read into it. Much of the world's businesses were private until a few years ago and you would expect the ratio to increase over time.

Anonymous said...

Why do you compare ERP to Baa rated bonds alone & not to the 'average' bond since you are deriving ERP from an average equity i.e., S&P 500? Also why do you compare the ERP/Default Spread ratio and not the difference?

3rdMoment said...

Thanks for the reply, but it still appears that even the top-down estimates are estimates of *per-share* earnings (i.e. per index share) which reflects the changes in the index divisor, which itself reflects the effect of buybacks.

For example, in your spreadsheet you list an earnings forecasts 135.83 for 2015. Looking at the spreadsheet "sp-500-eps-est.xlsk" from the S&P website, the 135.83 figure is in cell M76, which is clearly labeled as a forecast of "12 MONTH EARNINGS PER-SHARE." Both the top-down, bottom up, and realized values in this spreadsheet are all presented as values per-share (i.e. per "share" of the index).

The realized value for this number will be the total aggregate operating earnings for the index firms, divided by the index divisor. The index divisor will be adjusted to already reflect the reduced share counts that come from any (net) buybacks that occur.

So it still seems to me that by using forecasts of per-index-share earnings, you are in effect double counting buybacks.

More on the methodology for index calculations including the divisor and index EPS can be found here:

Aswath Damodaran said...

3rd Moment,
The way in which S&P calculates units is fuzzy. In fact, the number of units used by S&P has remained remarkably stable, which is surprising given the volume of buybacks over the last decade. One possibility was that stock issues had offset buybacks and it is to check this that I did my post on buybacks, where I also looked at aggregate stock issues each year. In fact, if the unit number reflects buybacks, it should have dropped by about 15% in the last 5 years and it has not.
One solution is to bypass the index entirely and work with overall market cap, earnings, dividends and buybacks. That is easy to do, but getting a growth rate in these earnings is close to impossible. In my spreadsheet, I do offer the choice of a fundamental growth rate which should not have any double-counting effect in it.

3rdMoment said...

I don't know what you mean by "units," (this concept doesn't appear in the S&P methodology document), and I don't understand what part of the methodology you think is fuzzy.

If you are referring to the divisor, you are correct that it hasn't fallen as much as you would expect if buybacks were the only factor (and even then, you need to be careful to use net rather than gross buybacks). This is because the divisor is also adjusted for certain other things like when firms are added/dropped from the index and for mergers or spin-offs. This captures the effect of the "dilution" that Bernstein and Arnott write about here:

It is true that all these factors taken together have resulted in only a small decrease the divisor in recent years. But this is in contrast to some earlier periods where the divisor grew substantially.

In any case, the divisor (and the per-share earning numbers that it is used to calculate) *entirely* reflects the benefit that share buybacks provide to shareholders. So I still don't see how you can justify using per-share forecasts AND counting buybacks as if they were dividends.

The way I think of it, whatever earnings the firm doesn't pay out in dividends, it retains to invest to generate earnings growth. It can do this the traditional way by making real investments, or it can do share repurchases to reduce share count and generate per-share earnings growth that way. So while I agree that buybacks are a form of "payout", you can't really treat them as equivalent to dividends in a calculation like this.

At least that's how it looks to me, unless I'm missing something important.

Anonymous said...

Should historical growth in earnings for 10-year period be 5.42% instead of 4.14%? It looks like you have taken 9-year period growth.

Aswath Damodaran said...

3rd Moment,
While you are right to be cautious about the possibility of double counting of growth, I think that you and I have to disagree on the treatment of buybacks as cash flows and here is why. Assume that you own all of the equity in the S&P 500 and that you are looking at your IRR, based on future cash flows. Both dividends and stock buybacks go to you (since you are the only owner) and they will look exactly equivalent to you. It is true, though, that if companies return the cash to you, they cannot reinvest it, and that is why the growth rate in your earnings will be lower. My fundamental growth rate is based on the much lower reinvestment that companies are making.

On the S&P divisor, here is what I mean by fuzzy. I In 2014, buybacks were about six times larger than buybacks and if there had been no changes to the index, the divisor should have decreased by about 2-3%. The divisor barely changed. If the changes to the index explain it, then I am afraid the divisor becomes an almost meaningless number to track.

Finally, on growth, I am constantly looking for ways to avoid double counting growth. Clearly, bottom up estimates are off the table, since they are based on per share earnings in individual companies. With aggregate earnings in the S&P 500, it is unclear what analysts are forecasting. If they are forecasting collective earnings at the existing companies in the index, then there is no problem using the estimate. If they are doing something more complex, I might be. I don't know and I don't think the analysts themselves are clear. That is why I offer the alternative of using the fundamental growth rate.

3rdMoment said...

Thanks for the discussion, and yes it appears we will have to disagree.

I'm not sure why you are so skeptical about the divisor. A few years ago I also had some questions/concerns about the index earnings calculations, but when I sat down with the methodology document I convinced myself that it appears to be very well designed. The goal would be to get an accurate measure of returns to an investor who holds a cap-weighted basket of stocks in the 500 largest firms. This basket is constantly changing as firms shrink and grow, merge and split, and as new firms appear and others go out of business completely. And of course you also need to account for stock issues and repurchases. All this stuff is covered in the methodology document in what looks to me like the correct way.

I admit I haven't tried to get the compustat data and recreate the calculation myself...that might be an interesting exercise. My confidence in the index calculation is bolstered by the fact that realized returns to investors in S&P500 index funds closely track the numbers reported by S&P. But if you have some specific idea of how they are doing it wrong, I think a lot of people would be very interested in that.

In any case, I think we can agree that it is VERY important to be clear on what you are forecasting. If you are forecasting earnings-per-index-share, then it is double counting to include buybacks as cashflows to shareholders. Since buyback yield is over 2%, this makes a very important difference in your overall return forecast.

Your point about not knowing what analysts are really doing is a valid one, I suppose, as is your skepticism about bottom-up forecasts. But it seems like a weak defense to me. The forecasts aggregated by S&P are labeled as "per-share", and they are measured in units that can only be interpreted as per-share, so it seems most reasonable to assume that (to the extent they have any value at all) they should be taken as forecasts of per-share earnings.

Also note that if you were to try instead to focus on collective total earnings instead of per-share earnings, you would need to account for the fact that the index is constantly changing, and the net effect is the "dilution" that I referenced in an earlier comment. So you'd need a growth rate somewhat smaller than the overall growth rate of total earnings in the economy.

The reason that this is important is that I believe that your forecast of 8% nominal returns (implying something like 6% real returns) going forward is unrealistically high, due to the double-counting issue, and also the fact that you appear to be using gross rather than net buybacks (as far as I can tell). This problem is partly ameliorated by the fact that your terminal growth rate might well be too low if you were to take it as a measure of per-share growth. If we were to instead look at earnings yields directly, and how they have historically related to real fundamental returns, I believe we would get a lower forecast.

Thanks again, I enjoy the blog.

Anonymous said...


Could you explain how did you obtain the long term growth rate of 5.58% on 01/01/2015?


Kaiserina said...

Hi Aswath! Been reading you for years -- fantastic stuff!

I am an armchair economist, i.e. not an economist at all, but I understand a lot.

You wrote that the following would be disastrous:"a drop in earnings and an increase in interest rates, with an overlay of a global crisis..."

How likely do you think that will happen in the Canadian economy? I can see it happening very clearly. If the market flattens and Canada is "forced" to raise rates (the OECD has been on their butt to do that for years), and oil prices remain low, in a country as highly levered as Canada (our average level of debt is quite high because of the overheated housing market), what result do you think that would have?

Thanks very much!

Ben said...


Can you explain where "r = Implied Expected Return on Stocks" is derived from in your calculations? I did not see that mentioned anywhere.

Eric T. said...

Hello. It is incorrect to include buybacks in deriving the implied equity discount rate. Just look at how the dividend discount model is calculated. And a buyback is not a dividend; it alters the number of shares outstanding, so we are mixing apples and potatoes. If you are valuing a house, you can use the rents (yield) you will get into perpetuity; it is wrong to use the proceeds of the sale of rooms to figure out that yield because we are mixing returns with the asset we are valuing. If you exclude that you will find that the implied equity risk premium is much lower than what you are suggesting - as it should be in a low interest rate environment. Thank you.

Anonymous said...

"Risk premiums are mostly nonsense. The world isn't calculating risk premiums." -- Warren Buffett (2005)

Aswath Damodaran said...

I have to disagree with you. Assume that you own all of the equity in the S&P 500 companies. Both dividends and buybacks come to you, right? Thus, you collect both as cash flows. It is true that using per share growth rates can lead to an inconsistency and that was the basis for my prior exchange with 3rd Moment, but to argue that buybacks are not cash flows to equity investors is to miss a large portion of the cash flows to equity investors collectively today.

Aswath Damodaran said...

I have never subscribed to the notion that if Buffett says it, it must be true. You are free to make your own judgment.

Eric T. said...

Thank you for your feedback. Since you used bonds as the starting point for your framework, for consistency then you should have included quantitative easing - which is like the government buying back its own bonds. My point is you are using the value of an asset (shares repurchased x price) to value that asset. It's the cash flows that such asset generates, in the case of equities future dividends, that give them a value. The fact that I can sell those shares to the company or anyone else is the outcome of that valuation, not the input.

Shishir said...

Dear Professor,

Thanks for this great post!.
I have a fundamental question here..when an investor is looking at equity he/she is not only looking at dividend and buybacks but also capital appreciation. How is the last element getting captured in the
ERP.Are we agreeing that the ERP computation process has some of the shortcomings like that in dividend discount model

mspacey4415 said...

I really like that last chart which shows how total required return has been rather stable the past decade, while ERM increases came mostly from rate drops

my interpretation of that chart is that ERM & rates are in a negative correlation environment, and if rates smoothly rises the next few years (controlled rise, not some crisis induced spike), then ERM will decrease. So if the world has similar growth outlooks the market P/E would be essentially the same.

would you agree with that interpretation?

Aswath Damodaran said...

If the expected return on equity stays fixed (fixed cost of equity) and earnings growth remains unchanged, the PE ratio will stay stable. And you are right. This depends on a smooth progression of rates, rather than a spike.

ryanwh said...

Professor Damadoran,

First, thank you for this great post and for all your prior research on ERP.

I have a simple question: after reviewing this post, last year's version of it, and "Equity Risk Premiums (ERP): Determinants, Estimation and Implications" at SSRN, I cannot figure out why you assume that S&P earnings growth in the second stage of the model should be equal to the risk-free rate (however defined).

It would seem to me that estimating second-stage earnings growth as the risk-free rate would work for an individual company subject to competition better than for a (proxy for) the economy as a whole. For the S&P 500, companies compete with one another, the winners win, new entrants come in with high margins, etc.

Can you elaborate on why the best assumption for second-stage earnings growth is the risk-free rate (I understand and agree that the 10-year Treasury is the best proxy for the risk-free rate, but why *any* risk-free rate)?

Thank you.

Unknown said...


In this post ( you considered not only dividends and buybacks in order to estimate cash returned to shareholders, but also shares issued by companies. Why haven´t you considered this in your calculations of ERP?

Unknown said...


No answer on that?

"In this post ( you considered not only dividends and buybacks in order to estimate cash returned to shareholders, but also shares issued by companies. Why haven´t you considered this in your calculations of ERP?"

best regards,

Unknown said...

I've spent two whole days thinking about different estimates of the ERP, and would like to do my best to try and clear up what to me seems like some confusion. Earlier you wrote:

"Assume that you own all of the equity in the S&P 500 and that you are looking at your IRR, based on future cash flows. Both dividends and stock buybacks go to you (since you are the only owner) and they will look exactly equivalent to you."

I don't think this is the case. Dividend estimates for an index are made on the basis that you continue to hold the shares. If you hold fewer shares as a result of a buyback you will receive less cash in the future as a result.

Suppose the S&P 500 has a fixed annual payout per share, c, and you start with s shares. If all payouts were dividends the cash flow would be c.s + c.s + c.s + ... On the other hand if all payouts were stock buybacks the cash flow would be c.s + c.s.(1-c/p1) + c.s.(1-c/p1-c/p2) + ... Where p1, p2 are the price levels of the index at the time of the buybacks. The cash flow reduces because you hold fewer and fewer shares as time progresses. Dividends and buybacks are not equivalent.

To compute the value of equity for an index one needs to at least notionally continue to hold the shares in the index. This means you don't get to participate in the buybacks. In short I don't think share buybacks and share issues have any effect on the calculation of the ERP based on an index. Computing the ERP using total market cap and dividends is a different story, and there the dilutive effect of such issues would need to be considered.

PM said...


I know you include buybacks/stock issuance in your calculation for ERP. In this article, Research Affiliates (Rob Arnott's firm) concludes that: "The dilution rate for the U.S. equity market in 2014 was 1.8%, equivalent to roughly $454 billion. Companies thus issued significantly more shares than they repurchased."

Any thoughts on whether there has been net buyback or dilution over the last few years?