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:

22 comments:

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.

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

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 worlds 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?

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:

www.spindices.com/documents/index-policies/methodology-index-math.pdf

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.

I dont know what you mean by units, (this concept doesnt appear in the S&P methodology document), and I dont understand what part of the methodology you think is fuzzy.

If you are referring to the divisor, you are correct that it hasnt 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:

https://www.researchaffiliates.com/Production%20content%20library/FAJ-2003-Two-Percent-Dilution.pdf

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 dont 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 doesnt 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 cant really treat them as equivalent to dividends in a calculation like this.

At least thats how it looks to me, unless Im 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.

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 dont know and I dont think the analysts themselves are clear. That is why I offer the alternative of using the fundamental growth rate.

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

Im 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 havent 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 youd 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.

Professor,

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

Thanks

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.