Monday 31 August 2015

Why Shares are too Expensive. And, while we're at it, is the idea that shares always out-perform partly just a historical anomaly?

To start, a disclaimer... this is not a suggestion to trade, merely an observation on the economy and what it should mean for share prices. There is a reasonable chance that I am wrong; I invite you to look at the arguments and decide. And even were I correct that prices are too high, it does not mean that they will come down. In fact they can get a lot higher because, to paraphrase the great economist Hyman Minsky, whenever the market is too high, people are prone to get a little over-excited.

People have been arguing for a while now that shares are too expensive against their historical valuations. Various metrics are used to define this. For example, the CAPE Shiller ratio looks at the price of shares against 10 year trailing earnings. Historically US shares have traded at a median of 16 times earnings. In the past valuations have reverted to a multiple 16, but it is difficult to time this; in the dot com boom it reached almost 45. At the moment the multiple is roughly 25. This suggests that the market would need to drop by almost 40% in order to be fairly valued.

Nonsense, the bulls say. This model is irrelevant. Have you not seen what has happened to government bond yields? A thirty year US treasury now only pays you around 3% per year. The short term bonds pay almost zero. Stocks are cheap because there is nowhere else to get a good return. Central bank action will always support asset prices and they'll just keep printing more money. Even a mediocre return is better than nothing, and stock prices reflect this.

I believe that shares are substantially overpriced based on any normal return expectation. There is an idea that shares always perform well in the long term; this may be true in the very long term but a period of very high growth followed by a series of one-off changes have led to large rises in share values over the past 80 years and these are unrepeatable. I will discuss all this in the rest of the post.

First, the share valuation model. For those unfamiliar with corporate finance models, a share can be valued by taking the sum of all of its future dividends and discounting them to the present. This means that if you will expect to receive £100 in dividends next year, you will value it slightly less than if you had £100 now.

There are two components of this discount. The first is for the interest you could receive if you invested in a risk-free (in most cases) government bond. This means that you need to receive at least the rate of interest you could have got for no risk. The second component of this discount rate is called a 'risk premium'. It is the extra return that you need to receive for taking risk with your money. If one only receives the same as the government interest rate, why would anyone make risky investments? In the recent past the risk premium for U.S. stocks could be reasonably said to be around 4%. So people invest in stocks with the expectation of receiving the risk free interest rate plus a risk premium.

As I show here, in relation to the UK, the total amount of debt has skyrocketed over the past 45 years.  This means that the total gross wealth in financial assets (not including property) has gone up from around 4x GDP to around 13x GDP in the UK (these are approximations). Similar trends are observed internationally. There are therefore a lot more savings than there were before. A savings glut, in fact (which is the same as a debt glut but viewed from the other side). For this reason, I would argue that the risk premium should reasonably be a lot lower than it has been in the past - maybe 2%. This would mean that share prices should be a lot higher than they would be with a 4% risk premium. I am taking this into account and I say that, even despite this, equities are now too expensive.

From here on, I will be looking at the US stock market, specifically the S&P 500 index; the most traded share index in the world.

Since 1945 share prices have been in one long bull market. They have been going up almost relentlessly. This leads to the idea that shares always out-perform bonds or cash in the long term. As I say, this may be true, but in the time period we have seen a number of important changes that have led to one-off increases in share prices.

  1. The reduction in government bond yields - 25 years ago a 30 year government bond paid 8%. Now it is closer to 3%. 
  2. The reduction of risk premium required - in 1990 I calculate the implied risk premium using my dividend valuation model to have been around 2%. Now I calculate it to be 0%
  3. Corporate profits as a share of GDP are at a high since 1945. In fact, the share has more than doubled since 1990. This would mean, all things being equal, a doubling in the fair value of shares.
These three effects would account for approximately a 20 fold increase in the value of shares since 1990. In fact the rise has been only around 6 fold.  As of 1990, the  S&P 500 was trading at around 350; at the time of writing (Aug 15) it is around the 2000 level.

Had these three one-time changes to risk preference and corporate rent-seeking ability not occurred then the stock market would actually have gone down considerably since 1990. 

Since 1990, owning the shares in the S&P 500 would not have been better than owning a portfolio of 30 year bonds. This is despite the doubling of corporate profit share to GDP and reduction in risk premium. This really highlights how poor equities’ performance has been since 1990 (relative to bonds) - and how the great fall in bond yields has managed to disguise this. Perhaps this has convinced investors that equities have a natural right to perform well in the long term.

The reason for this relative under-performance of the S&P 500 has been the performance of nominal GDP.

If the proportion of corporate profit to GDP remains the same, then corporate profit can only grow with nominal GDP. This is an extremely important point that many analysts appear to miss when making earnings growth projections.

Between 1945 and 1990 nominal GDP growth averaged around 8% per year. This means that total profits could be expected to grow by around 8% per year. In this period, there would be every reason to think that shares would keep increasing in value. However, between 1990 and today, GDP growth is closer to 4.6% PA. And in the current period of secular stagnation we may only be able to expect around 3.5%. In fact since 2008, we have averaged 2.7%.

Taken in conjunction, the change in the expected nominal GDP growth from 8% to 4.6%, along with points 1-3 above can account for the change in value of the S&P 500 since 1990.

Since 1-3 are one-off events, I would argue that there has actually been no evidence since 1990 that stocks are better than bonds in the long term, despite the apparent 6 fold increase in price.

So going forward, will shares outperform? I use the discounted dividend model above with the following parameters:

o Nominal GDP growth prediction of 3.5% per year
o Disruption rate set at 2%
o Dividend growth, g = Nominal GDP minus disruption
o Discount rate, r, of the US treasury 30 year yield (approx. 3%) plus 2% risk premium, giving r = 5%

By ‘disruption’ I mean that if one held a portfolio of all the stocks in the S&P 500, each year, 2% of profits will go to new companies that we did not already own shares in. In other words, if one bought the whole S&P 500 index today and held the shares for 30 years, one would only have shares in 55% of the S&P index at that future time. The index rebalances for new participants, but there is friction as it does so.  We assume that corporate profit share does not increase from this post-war high level, and that risk premiums and risk free rates do not decrease further from these all-time lows.

How realistic is this pricing model? Looking at the actual  performance of dividends against nominal GDP we can find the following. Given a) the increase in nominal GDP between 1990 and today and b) the share of corporate profit rising from 4.2% to 10.1% of GDP in the same time period, then we would expect dividends to rise by around 8.5% per year. In fact they rose by about 6.5% per year which accounts for the 2%  'disruption' discussed above. This means that a nominal GDP model for modelling dividend returns is not unreasonable empirically (as well as it being an economic identity).

So this pricing methodology has held well in the past. Now, it is dependent on the assumptions put in of course. All of these assumptions can be changed and all affect prices considerably. Maybe nominal GDP will be higher than 3.5%, maybe lower. Maybe corporate profit share will go up, maybe down. This is why evaluation of fair value is so difficult.

However, using what I consider to be the reasonable assumptions above, the only way that I can get that shares are fairly priced is by assuming almost a zero risk premium. This is absurd and can not continue indefinitely. 

With a risk premium of just 2%, I get that fair value is 40% lower than the current price. Or the S&P at around 1200. This actually broadly agrees with CAPE Shiller.

This is not to say that prices will definitely go down. They could just stay roughly where they are for many years before fair value catches up. But the market tends not to work like that and this is why I believe that, despite central bank intervention to support share prices, we will still see a large correction.

According to this model, calculated using a 2% risk premium, share prices have been overpriced since 1990 (with the exception of a short period in 2008-09).  The worst period was at the height of the 2000 dot com bubble where they were 300% overvalued. Stocks have kept going up despite this over-pricing, because of falling bond yields.  If bond yields stop falling then we may have reached the point where gravity takes its toll.  With so many central banks at the lower bound it is arguable that they cannot repeat their asset inflation success of the last 30 years.

My conclusion is that risk free bonds are a better investment than shares at this time in the long term. For those that worry about a large printing of money to stave off disaster, and the subsequent inflationary impacts, I would suggest that inflation linked bonds may be suitable, certainly on a risk-return basis. But as mentioned before, I am not giving investment advice and caution strongly against listening to me about anything.

I believe that low interest rates have driven shares to irrationally high levels and that ultimately they should either fall by a lot, or have a long time waiting for fundamental value to catch up with the current price. We will see if I am correct.


  1. Nice post. I have similar misgivings about stock prices given the lousy debt-soaked economic setting we've created , because , in the final analysis , you're going to need a functioning economy to sustain stock prices long-term.

    A little off-topic ( not entirely ) , I have an idea I want to run by you later regarding how to plausibly generate a model incorporating debt in a "quantity theory" manner , that results in a velocity very near one , over the long haul ( using U.S. data ).


    1. Interesting. Would love to hear about it.

    2. OK , Ari , here’s what I’ve been thinking : We aren’t measuring our economy correctly to do any sort of “quantity theory of debt” analysis . Steve Keen is on the right track by suggesting that “asset turnover” or some variant thereof must be tallied along with gdp. My take is that the metric of choice has to be net worth , in line with the old Haig-Simons concept of income. People strive to create either income or wealth , or both. You can see specific efforts at net worth creation in examples like the homeowner who takes out a loan to put in a $15k kitchen upgrade before marketing his home for sale , hoping to get $25k , $35k , or more in a higher sales price. You can see it in execs who direct their companies to borrow and then buy back shares mainly to enrich themselves , or in the Fed buying junk MBS paper at inflated prices to generate a “wealth effect” , using monetary base “credit”.

      So , my focus is on a gross domestic INCOME version of the economy ( call it cGDI , for consolidated GDI ), consisting of gdp(=gdi) + net worth changes.

      Here’s net worth as a ratio to gdp , using the correct sum of household and gov’t net worth ( in the U.S. data , all business net worth is aggregated to households ):

      Notice that over the 60-plus year period , the NW/gdp ratio never falls below 3.3. This is an important fact for this exercise. My contention here is that a relatively constant and large majority share of net worth is endogenous to the gdp machine , like it’s welded to the side , flowing and growing and shrinking with and just like gdp , and requiring no financial support from outside gdp ( similar to the p/e ratio of the bluest blue chip ). I think that it’s likely that this ( market-determined) share is at or around that 3.3x figure we see evidenced above ( which amounts to ~85-90% of total net worth up to the ~mid-90s , and still ~75% or so thereafter ) , so in this next graph I’ve subtracted 3.3 from the ratio , and then added a second series for debt/gdp.

      Next , I’m assuming that the debt velocity for gdp is exactly 1.0 ( not an important or necessary assumption , as we'll see ), so I subtract 1 gdp from the debt/gdp ratio to leave the share of debt that has to cover the NW that's not wedded to gdp :

      Even in this quick and dirty exercise , you can see that the leftover debt/gdp matches reasonably with the leftover NW/gdp. The gap from ~83-95 may be partially explained by the S&L bust , and I suspect that some or most of the ~$5 trillion in "missing U.S. wealth" that Zucman claims is likely parked offshore came out during this period. Splitting the bubbles about in the middle seems a reasonable performance , and the post-2008 period represents a major data-break , what with QE and such , such that I'm inclined to ignore that part , for now. Note that I have included the monetary base with the nonfinancial debt measure. The effect of doing that is negligible before 2008 , but I think it has to be included from then on , so best to go with it from the start.

      This graph shows a standard velocity ratio , using the full measure of debt divided by gdp + non-gdp-linked NW :

      The trend line at $1.07 is just eyeballed , to give some sense of the +/- fluctuations.

      Considering the possibility of looted "missing wealth" and such , I think it's possible that the velocity may be near one for both wealth and gdp pretty much throughout the timeline. The important takeaway to this model , however ( if it's right ) , is that $1 of debt directed to gdp growth gets you $1 of gdp plus $3.30 of NW , while $1 of debt directed specifically toward wealth-building gets you only $1 in NW.

      Up till the mid 1990’s we did more of the former and less of the latter. With QE , it was the worst - we were literally picking up pennies in front of steamrollers.


    3. This is a weird coincidence - I was surfing Mark Thoma's site and came across this Fed paper on monetary policy and house prices :

      ..... which had this tidbit :

      "...Two years after a 1 percentage point increase in the short-term interest rate, real house prices are estimated to decline by over 6%, while real GDP per capita declines by nearly 2%. This implies a ratio of 3.3 in terms of the decline in house prices for a 1% decline in the level of output after two years. Looking at a longer time horizon of three or four years (not shown in the figure), the ratio rises to about 3½. "

      That's close enough to be scary.......


    4. Marko, I don't fully understand but will try to think it through ( I like your use of FRED by the way) ...

      I'm assuming that net worth is total assets minus debt. As debt goes up there is no reason that net wealth should go up but it does because debt creates gross wealth and gross wealth needs to invest in something. Therefore all asset prices rise as debt rises. This relationship between net worth and increased debt is not surprising therefore.

      This part is important though, because it shows the relationship between asset prices and debt and it backs up the idea that we have had a one-time rise in asset prices I discuss above.

      I am a bit confused about the part where you say this though:

      The important takeaway to this model , however ( if it's right ) , is that $1 of debt directed to gdp growth gets you $1 of gdp plus $3.30 of NW , while $1 of debt directed specifically toward wealth-building gets you only $1 in NW.

      Also the next part about house prices and GDP - I don't quite get how it fits in. Could you explain a bit further?

    5. Thanks for the questions , Ari. I tend to assume that others have been spending all their time looking into the exact same issues as I have , so I don't explain things as well as I should.

      The part about the differential outcomes of a debt dollar is in many ways analogous to the way stocks are valued. If a company borrows and then spends $1 million jazzing up the executive suites , it might , if they do a nice job , increase the net worth of the company via the market value added to the building in excess of the $1 million.
      However , if they took that $1 million and somehow increased earnings per share by a $1 - or even a fraction of that - and their p/e ratio was 15 or 20 , the shareholder net worth increase would end up being multiples over that achieved in the first example.
      Richard Werner talks a lot about this idea when he distinguishes debt that goes into gdp vs debt that is used for speculation or other uses not contributing to gdp , i.e. productive vs non-productive debt.

      Here's gdp vs net worth on a log scale ( I used a multiplier of 3.4 -instead of 3.3 as above - just to tighten up the fit ):

      It's tempting and understandable to look at the time around 2010 and think that gdp will be pulled up to reestablish the baseline relationship with net worth - sort of like Friedman's "plucking" process , but with net worth setting the trend for - and attracting - gdp, from above. In fact , if you plug in variable "b" , potential gdp , for variable "a" in the formula for that graph , you'll see that the baseline does , in fact , rise up to a more "normal" level.

      As I see it ,however , that's a cargo cult mentality and one that we need to disparage and try to dislodge at every opportunity , as it just encourages speculation and coddling of the rich. Ultimately , the net worth of a country is a function of that country's gdp , which is in turn a function of fundamental attributes like good institutions , educated workforce/citizens , rule of law, etc. The NW/gdp ratio can change over time , as Piketty demonstrates , but what doesn't change is that absent a productive economy , wealth tends to evaporate.

      As to the article cited , on re-reading the snip I posted , I think I'll have to go re-read that article. What I thought it indicated was that they saw about the same relationship between house prices and gdp as I saw between what I define as gdp-linked net worth and gdp , i.e. about 3.3x. They show ~3-4x multiple in the >percentage< change differentials between house prices ( which I assume as a proxy for NW ) and gdp.

      However , my model predicts that - on a percentage basis - this baseline NW will move in step with gdp over the long haul. So if gdp rises by 1% , baseline NW will rise by 1% ( but , on a dollar basis , it will rise $3.30 per $ of gdp rise ).


    6. I thought I'd add a note about the "potential gdp" graph variation I suggested above. Since it's using potgdp , you can extend the timeline into the future , thus allowing some predictions :

      My prediction ( to ~ 2025 , the last date shown ) and comments :

      The potential gdp curve (blue) might change compared to the curve as shown , but the relationship of the net worth curve (green) to the potential gdp curve will continue as in the past , i.e. limited excursions north of the baseline , always returning to baseline.

      If you want to blow a bubble , better to blow one using equity , as in 2000 , rather than debt , as in the housing bubble , because you can maintain a stable debt/gdp ratio in the former , and probably won't in the latter.

      Nice NW "head-and-shoulders" formation developing......


    7. So if I have this right, net worth needs to fall by 25% to be in line with GDP. Which is similar to what happened in 2008 on your graph.

      Maybe interesting times ahead.

      One can definitely see how GDP growth has stagnated and I think that the lack of productive investment on the one side and lack of demand on the other have something to do with it.

      I would probably assign the divergence between the two to the effect of so much debt in the system causing the savings glut. And all of these savings are just cycling through asset prices and causing them to rise due to the reduction in risk premiums talked about above.

      So yes, I suppose as you put it, people invest in existing assets rather than productive capacity. Meaning that asset values go up relative to productive capacity.

      Interesting relationship you have shown there. Maybe a good crash predictor.

    8. Yes, that's pretty much how I see it. I think the whole "wealth effect" concept has corrupted economic thought , with resultant weak economic performance.

      Raise GDP by a buck , you get >$3 in net worth increase , and GDP tends to persist , via circular flow. To get a buck of gdp by the wealth effect , you have to pump up wealth by ~$20 , whereas gov't ( or QE for the people ) could get a buck for a buck , on average.

      When you look at the dotcom and housing bubbles on that graph , you need to use a magnifying glass to detect any upward deflection of gdp induced by the wealth bubble , and any effect that is there disappears with the bubble. The only justification I can imagine for this being part of our monetary policy arsenal is that rich people think it's sweet.


    9. Just for the record , this is the correct velocity graph for the first Sept 1 post above :

      I had the inverse ratio in the first attempt. I'm used to looking at debt/gdp ratios , and I guess it's a hard habit to break. When the result is ~ 1 either way , it's easy not to pick up on a mistake like that.


  2. Interesting post. While i agree that these are conditions that put the massive rise in valuations in perspective, i don't necessarily agree that stock out-performance is a historical accident. Wouldn't the same potential conditions apply to bonds as well? For instance, declining interest rates benefits both asset classes. It is possible that the impact on shares is just more (less) pronounced. Thoughts?

  3. Maybe 'accident' is the wrong word but I am just trying to point out that the returns we have seen in US equities has been truly exceptional and we don't necessarily have the right to expect it to continue.

    The US has had a period of extraordinary growth going back 150 years. For one thing, we have to acknowledge the survivorship bias we have in looking at the US, rather than, for example, Russia where all shares became worth zero after the revolution in 1917. If we had had a basket of all major countries' shares in 1900 they would not have performed as well as a basket of US stocks.

    Looking since 1945, we can see the period to 1990 where we had around 8% nominal GDP growth per year. This is really a great period of growth and in this rapidly expanding pie everyone profited - both share and bond holders.

    But it is interesting to note that after the second world war, the US had around 40% of GDP in private sector debt. This grew to around 200% by 2008. All of this debt is wealth to the creditor who had to put their money somewhere. So the amount of money for investing got larger and consequently the returns for each unit of money had to be smaller. This led to a reduction in interest rates and, more recently also risk premia.

    This is not the only reason for the fall in interest rates, it is also the period of stability and lower inflation in 'the Great Moderation' from the mid eighties to now. The real interest rate was very high in 1990; probably from fear of another inflation.

    So the combination of high economic growth combined with rising debt levels and rising stability led to huge equity gains both from growth and declining risk premia and interest rates.

    But I believe that we must see this for what it is - a truly exceptional and largely one off event. Growth has stagnated and interest rates and risk premia have shrunk to very low levels. Similarly profits as share of GDP are very high, probably due to outsourcing and technological rent seeking. Whether this can be sustained is open to question.

    You are correct that the same applies to bonds, regarding the one-off nature of the rise. What I am suggesting here is that, even at these very high bond prices, bonds are comparatively better value than shares in the long term.

    This, in my opinion, would remain the case unless the government embarked on a very large fiscal deficit programme, that stimulated more economic growth. Maybe eventually they will realise that this is needed but it is not coming in the near future.

    1. Thank you for the thorough response and unfortunately, provided we don't have an escalation in geopolitical tensions, you may be correct that the Government isn't going to embark on such a politically unfeasible program.

  4. So if money is going to leave (or evaporate) with a downturn in US equities, where would Ari put his money? Real Estate (US real estate)? Foreign markets? Under the mattress?

    1. I really don't want to be giving investment advice (and this isn't advice), but if real estate gives a good yield and one can be pretty sure of renting it out then maybe that is good. For money to be completely safe, inflation linked bonds are good as you know you will get back more or less the same in real terms as you put in - nothing else can say that.

      I have a combination of the two. Also (as described in an earlier post) I have been short Australian dollar against Japanese Yen to benefit from the China slowdown - but trading this sort of thing is not advisable unless one knows what one is doing (and probably not even then).


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