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2018-12-06Macro `n Cheese

Cheap or Dear

One thing Roger rarely discusses is his personal investment policy, but today he reveals that he is – fittingly, given his persona – fully invested in bonds... And why that might not be the best idea.

Stock markets have experienced a tumultuous autumn, falling by as much as 10% and erasing the accumulated gains for 2018. That said, by most measures’ equities remain expensive when looking at most fundamental measures such as Tobin’s q and Shiller’s cyclically adjusted Price-to-Earnings (P/E-) ratio, a k a Shiller CAPE.


But just how expensive are stocks in relation to other liquid assets such as bonds? If investors have no other (liquid) place to hide, how bad is it really to be invested in stock markets? – Here, we will leave Tobin’s Q behind and focus on the Shiller CAPE. The CAPE is calculated as the S&P500 price index divided by a 10-year rolling average of inflation adjusted earnings per share. This is used to smooth out short-term (cyclical) earnings fluctuations.

An old econ-hero of mine, Robert Gordon of Northwestern University and Collins & Gagnon – must-follow on Twitter – of the Peterson Institute for International Economics (PIIE) a think-tank that does “what it says on the label” have their doubts on using this measure for guidance, as the current 10-year rolling average still includes the great recession. They prefer an 8-year average instead. Others have suggested that the high CAPE is driven by the Trump tax cut, but my personal view is that it is really lower interest rate costs that have driven stronger earnings post-crisis (and why it is important to keep an eye on corporate’s real interest rate burden).

Under any circumstances, the CAPE currently stands around 31, which is well above its historical average (17) and even if some of its ascension has to do with the cyclical factors mentioned there is also a structural criticism against the CAPE measure building on the increased use of share buybacks for redistributing earnings back to shareholders. In short, the arguments go something like this: If share buybacks rise relative to dividends it may affect the growth in (real) earnings per share. Since Shiller himself has also acknowledged these shortcomings he has recently published a complementary CAPE-measure, the total return version, which corrects for this problem by reinvesting dividends and, also, scaling EPS accordingly. This critique is something that I discussed in a blog last year (I still stand by the conclusions, mind you).


As you can see, the overall picture of currently high valuations from a historical perspective doesn’t change much when looking at the total return CAPE (TR CAPE). From an allocation perspective, however, this offers little consolation as we need to take into consideration alternative investments. And the only asset class offering similar liquidity is bonds. As stocks are considered riskier than bonds, they command an excess return in comparison to bonds. This ‘excess return’ is called the equity premium (EP). The EP can be calculated using expected future returns – the ‘Ex Ante Equity Premium’ – or using past returns – the ‘Ex Post Equity Premium’. Building on the PIIE-blog post by Collins & Gagnon I thought we could have a look at whether the Ex Ante Risk Premium can be explored for forecasting the ex post excess return of equities vis-à-vis bonds.

Using mainly, but not only, the Shiller data set and utilizing the strong predictive powers of 12-month forward EPS we can prolong and update the Shiller data set to a more recent time period. Below, I have defined the Ex Ante Equity Premium as the reciprocal of CAPE, adjusted for the inflation-adjusted yield on the 10-year treasury note. The Ex Post Equity Premium is the nominal yield of holding the S&P500 and reinvesting all dividends for ten years, adjusted – again – for the yield on the (assumed zero-coupon) 10-year treasury note. Since the ex post inflation is identical, I can use data in nominal terms but since it is indeed ‘ex post’ this data stops 10 years before the latest common outcome (i.e., currently in 2008).


While the general impression is consistent with similar calculations on Shiller data only – a clear positive correlation – it seems as if ex post EP is somewhat higher when using the most recent data available. Indeed, the average ex post EP is 6.2%, and the ex ante EP is 4.7%. When comparing our data with Shiller’s, it seems as if the differences mainly emanate from updates to the long-term S&P 500 price index and the data on the nominal interest rate. For those interested, we are in the process of adding the full (and new) Shiller data-set so you can exchange the data as you please (for whatever reason).

Another thing that leaps out from the graph above is that ex post EP has very rarely been negative, i.e., the ex post excess return of holding stocks to bonds is almost always positive. In my calculations only 109 ex post observations out of 1644 (6.7%) are negative. Note, also, that negative/low ex post EP is almost always accompanied by low ex ante EP, with the possible exception of the early 20th century. Of course, this is, to some extent, the natural consequence of the movements in stock prices as it affects both measures.

Several studies, including one of my all-time favorites by Jordà et al (2017), suggest some kind of break in many economic and financial series around World War II. This is visible in our data as well when regressing the ex post EP on the ex ante EP.


In the full data set (left), a one percentage point (p.p.) higher ex ante EP is associated with a 0.6 p.p. higher ex post EP. In the post war period (right), the beta rises to 0.8 p.p..

Ideally, we should probably use an ARIMA-model (keep those support tickets coming) to explore the predictive relationship between ex ante and ex post EPs (we do use 10-yr averages) and a simple, off the cuff, OLS-regression do set off a lot of statistical alarm bells. However, following previous studies and trying different specifications, on differentiated variables as well, the results seem quite stable and passes simple tests (feel free to open the charts in Macrobond and play around with the specs). If that is not sufficient for you, my results also mirror those of Collins & Gagnon very nicely (however, I chose to exclude the MA-term as it was both insignificant and worsened all of the information criteria.


The main takeaway is of course that the ex post EP is expected to remain positive and that there seems to be no, or at least a very small, risk of lurching into negative territory. So, albeit with great hesitation to current stock market valuations, alternative investments (bonds) seem worse still. Speaking as someone almost fully invested in bonds.

– Darn it!

As to whether stocks will compensate for the risks involved, now that is a different story altogether...


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We don’t usually have views and opinions about economic and financial states of affairs, (not ones that we express publicly as a company, anyway). We do believe, however, that people can and do appreciate a variety of perspectives. What you’ve just read is the perspective of our resident chief economist. While we think he’s very smart, Macrobond Financial does not expressly endorse the views he presents here. And, as the old adage goes, you shouldn’t believe everything you read (not without finding the data, performing a few analyses and presenting it in a nice chart). We want to make it clear that we are not offering this information as investment advice. That being said, if you have the application you can easily check everything that’s mentioned here, and decide for yourself. If you don’t have the application, now you have a great reason to get it.