Modigliani-Miller theorem repealed, reports PBS

Link here. 

In case you don't get it, see previous posts on buybacks here and here, that explain how buybacks do not affect share prices, and certainly cannot cause the rise since 2008.

Thanks to a correspondent for the pointer.

Nobel Symposium on Money and Banking Day 2

Day 2 of the Nobel Symposium on Money and Banking focused on monetary policy. (My last post covered Day 1 on banking.)

Bernanke

Sadly Ben Bernanke's video and slides are not up on the website. Ben showed some very interesting evidence that the crisis was an unpredictable run, rather than the usual story about predictable defaults resulting from too much credit. Things really did get suddenly a lot worse in September and October 2008. Yes, it's easy to say this is defense against the charge that he should have done more ahead of time. But evidence is evidence, and I find it quite plausible that the relatively small losses in subprime need not have caused such a massive crisis and recession absent a run. Ben says the material is part of a paper he will release soon, so look for it. One can understand that Bernanke is careful about releasing less than perfect drafts of papers and videos.

History

Barry Eichengreen gave a scholarly account of why history matters, especially the great depression, and we should pay more attention to it. (Paper, video.) He aimed squarely at typical economists whose knowledge stopped at Friedman and Schwartz, or perhaps Ben Bernanke's famous non-monetary channels paper, in which bank failures propagated the depression. He emphasized the role of the gold standard and international cooperation or non-cooperation, and warned against facile comparisons of the gold standard experience to today's events and the euro in particular.

Randy Kroszner has a great set of slides and an engaging presentation. He also started on parallels with the great depression, and told well the story of the US default on gold clauses. He closed with a warning about fighting the last war -- particularly apt given the exclusive focus of most of this conference on the events of 2008 -- and on how to start a crisis. In his view when Bank of England Gov Mervyn King said: “We will support Northern Rock." People hear "Northern Rock's in trouble? Run!" Likewise, in my view, speeches by President Bush and Treasury Secretary Paulson did a lot to spark the run in the US.

DSGE

A highlight for me, was the session on DSGE models.

Marty Eichenbaum (video, slides, subsequent paper) gave a nice review of the current status of new Keynesian DSGE models, and how they are developing in reaction to the financial crisis and recession, and the zero bound episode.

Harald Uhlig

Critiques, or more precisely lists of outstanding puzzles and challenges, are often more memorable and novel than positive summaries, and Harald Uhlig delivered a clear and memorable one. (Video, Slides)

Asset prices are a longstanding problem in DSGE models. In typical linearized form, the quantity dynamics are governed by intertemporal substitution, and the asset prices by risk aversion, and neither has much influence on the other. (I learned this from Tom Tallarini.) Rather obviously, our recent recession was all about risk aversion -- people stopped consuming and investing, and tried to move from private to government bonds because they were scared to death, not a sudden attack of thriftiness. There is a lot of current work going on to try to repair this deficiency, but it still lives in the land of extensions of the model rather than the mainstream. Harald also points out a frequently ignored implication of Epstein-Zin utility, the utility index reflects all consumption and anything that enters utility

Financial frictions are blossoming in DSGE models, in two forms: First, HANK or "heterogenous agent" models, which add things like borrowing constraints and uninsurable risks so that the distribution of income matters, and in an eternal quest to make the models work more like static ISLM. Second, in response to the financial crisis (see first day!) stylized models of banking and intermediary finance are showing up. I'm still a little puzzled that the more standard time-varying risk aversion part of macro-finance got ignored, (a plea here) but that is indeed what's going on.

The conundrum, here as elsewhere in DSGE, is that the more people play with the models, the further they get from their founding philosophy: macro models that do talk about monetary policy, (now) financial crises, but that obey the Lucas rules: Optimization, budget constraints, markets, or, more deeply, structures that have some hope of being policy invariant and therefore predictions that will survive the Lucas critique. Already, many ingredients such as Calvo pricing are convenient parables, but questionably realistic as policy-invariant.

Harald points out that since most of the frictions are imposed in a rather ad-hoc manner, neither will they be policy-invariant. This is a deeper and more realistic point than commonly realized. Every time market participants hit a "friction," they tend to innovate a way around that friction so it doesn't hurt them next time. Regulation Q on interest rates was once a "friction," and then the money market fund was invented. The result is too often "chicken papers:"

The understandable trouble is, if you try to microfound every single friction from Deep Theory -- just why it is that credit card companies put a limit on how much you can borrow, in terms of asymmetric information, moral hazard, and so forth -- the audience will be asleep long before you get to the data. Also, as we saw in day 1, there is (to put it charitably) a lot of uncertainty in just how contract or banking theory maps to actual frictions. I think we're stuck with ad-hoc frictions, if you want to go that route.

Harald's next point is, I think, his most devastating, as it describes a huge hole in current models that is not (unlike the last two) a point of immense current research effort. The Phillips curve and inflation are the central point of the New Keynesian DSGE model -- and a disaster. 

The Phillips curve is central. The point of the model is for monetary policy to have output effects. Money itself has (rightly) disappeared in the model, so the only channel for monetary policy to work is via the Phillips curve. Interest rates change inflation, and inflation causes output changes. No surprise, it is very hard for that model to produce anything like the last recession out of small changes in inflation. (I have to agree here with the premise of the financial frictions view -- if you want your model to produce the last recession, other than by one huge shock, the model needs something like a financial crisis.)

The Phillips curve in the data is well known

Less well known, but worth lots of attention, is how the now standard DSGE models completely fail to capture inflation. Harald's slide:

The point of the slide, in simpler form: The standard Phillips curve is

inflation today = beta x expected inflation next year + kappa x output gap  + shock

Essentially all inflation is accounted for by the shock. The model is basically silent about the source of inflation. Looking at the model as a whole, not just one equation, Neither monetary policy shocks nor changes in rules accounts for any significant amount of inflation. 

I made a similar graph recently. Use the standard three equation model

Now, use actual data on output y, inflation pi, and interest rate i, to back out the shocks v. Turn off the monetary policy shock vi = 0. Solve the model and plot the data -- what would have happened if the Fed had exactly followed the Taylor rule? 

Answer: Inflation and output would have been virtually the same. The inflation of the 1970s and its conquest in the 1980s had nothing to do with monetary policy mistakes. It is entirely the fault, and then fortunate consequence, of "marginal cost" shocks that come from out of the model. This is a pretty uncomfortable prediction of a model designed to be about monetary policy! Or, as Harald put it

• Data: no Phillips-Curve tradeoff.
• QDSGE: don’t account for inflation with monetary policy shocks.
• The NK / Phillips-Curve-based NK QDSGE models may thus provide a poor guide for monetary policy.

Wait, you ask, what about Marty Eichenbaum's pretty graphs, such as this one, showing the effects of a monetary policy shock?

The answer: After a lot of work, the effects of a monetary policy shock look (at last) about like what Milton Friedman said they should look like in 1968. But monetary policy shocks don't account for any but a tiny part of output and inflation variation, quite contra Friedman (and Taylor, and many others') view.

Last, standard new Keyensian DSGE models have strong "Fisherian" properties. In response to long lasting or expected interest rate rises, inflation goes up. More on this later.

Ellen McGrattan

Ellen stole the show. (Slides.) Take a break, and watch the video. She manages to be hilarious and incisive. And unlike the rest of us, she didn't try to sheohorn a two hour lecture into her 15 minutes.

Her central points. First, like Harald, she points out that the models are driven by large shocks with less and less plausible structural interpretation, and thus further from the Lucas critique solution than once appeared to be the case. The shocks are really "wedges," deviations from equilibrium conditions of the model with unknown sources

What to do? Focus on rules and institutions. This is a deep point. Even DSGE modelers, in the desire to speak to policy makers, often adopt the static ISLM presumption that policy is about actions, about decisions, whether to raise or lower the funds rate. The other big Lucas point is that we should think about policy in terms of rules and institutions, not just actions.

Monetary policy and ELB

Stephanie Schmitt-Grohé (slides, video)  talked about the Fisherian possibility -- that raising interest rates raises inflation. New-Keynesian DSGE models, with rational expectations, have this property, especially for permanent or preannounced interest rate increases, and when at zero interest rates or otherwise in a passive regime where interest rates do not react more than one for one with inflation. She and Martin Uribe have been advocating this possibility as a serious proposal for Europe and Japan that want to raise inflation.

She presented some nice evidence that permanent increases in interest rates do increase inflation -- and right away, not just in the long run.

Mike Woodford. (slides, video)  gave a dense talk (37 slides, 20 minutes) on policy at the lower bound. During the ELB, central banks moved from interest rates to asset purchases and forward guidance. Mike asks,

To what extent does this mean that the entire conceptual framework of monetary stabilization policy needs to be reconsidered, for a world in which ELB might well continue periodically to bind? 

In classic form, Mike sets the question up as a Ramsey problem. Given a DSGE model, what is the optimal policy, given that interest rates are occasionally constrained? He derives from that problem a price level target. The price level target works, intuitively, by committing the central bank to a period of extra inflation after the zero bound ends. It is a popular form of forward guidance. The innovation here is to derive that formally as an optimal policy problem.

Mike's price level target is stochastic, changing optimally over time to respond to shocks. I'm a little skeptical that the central bank can observe and understand such shocks, especially given the above Uhlig-McGrattan discussion about the nature of shocks. Also, as I emphasize in comments, I'm dubious about the great power of promises of what the central bank will do in the far future to stimulate output today. I'm a fan of price level targets, but on both sides, not just as stimulus, but for utterly different reasons.

Mike takes on rather skeptically the common alternative -- quantitative easing, asset purchases during the time of the bound. He points out that to work, people have to believe that the increase in money is permanent, and won't be quickly withdrawn when the zero bound is over. As evidence, he points to Japan:

Similarly, he likes the price level target over forward guidance -- speeches in place of action -- as it is a more credible commitment to do things ex-post that the bank may not wish to do ex-post.

Finally, he addresses the puzzles of new Keynesian models at the zero bound -- forward guidance has stronger effects the further in the future is the promise; effects get larger as prices get less sticky, and so on. He argues that models should replace rational expectations with a complex k-step iterated expectations rule.

Me.

Video, slides from Sweden, slides from my webpage, written version. I covered this in a previous blog post, so won't repeat it all. I put a lot of effort in to it, and it summarizes a lot of what I've been doing in 15 minutes flat, so I recommend it (of course). It also offers more perspective on above points by Mike and Stephanie. My favorite line, referring to Mike's push for irrational expectations is something close to

"I never thought we would come to Sweden, that I would be defending the basic new-Keynesian program, and that Mike Woodford would be trying to tear it down. Yet here we are. Promote the fiscal equation from the footnotes and you can save the rest." 

Emi Nakamura

Poor Emi had to go last in an exhausting conference of jet-lagged participants. She did a great job (video, slides) covering a century of monetary history and monetary ideas clearly and transparently. These are great slides to use for an undergraduate or MBA class on monetary policy, as well. An abbreviated list:

• Gold standard
• Seasonal variation in interest rates under the gold standard; money demand shocks
• Money demand shocks in the 1980s -- how the supposedly "stable" V in MV=PY fell apart when the Fed pushed on M.
  
  
  
• Theoretical instability / indeterminacy of interest rate targets
• The switch to interest rate targets and corridors in operating procedures
• The (near-miraculous) success of inflation targets
  
• Taylor rules and other theory of determinate inflation under interest rate targets
• How is it "monetary economics" without money?
• Why did immense QE not cause inflation? 

The overarching theme is the grand story of a move, intellectual and practical, from money supply targets (of which gold is one) to interest rate targets.

Postlude

Monday featured two panels, Macroeconomic research and the financial crisis: A critical assessment, with Annette Vissing-Jørgensen, Luigi Zingales, Nancy Stokey, and  Robert Barro ; and Banking and finance research and the financial crisis: A critical assessment with Kristin Forbes, Ricardo Reis, Amir Sufi, and Antoinette Schoar.

Perhaps it's in the nature of panels, but I found these a disappointment, especially compared to the stellar presentations in the main conference. Also I think it would have been better to allow more (any, really) audience questions; the whole conference was a bit disappointing for lack of general discussion, especially with such a stellar group.

In particular, Luigi led by excoriating the profession for not paying attention to housing problems and financial crises. I thought this a bit unfair and simultaneously short-sighted. He singled out monetary economics textbooks, including Mike Woodford's, for omitting financial crises. Well, Mike omitted asteroid impacts too. It isn't a book about financial crises. And, after lamabasting all of us, he said not one word about events since 2009. What are we missing now? I had to stand up and ask that rude question, again suggesting that perhaps we are all not listening to Ken Rogoff this time. Annette went on to ask something like "don't you Chicago people believe in any regulation at all," and the respondents were too polite to say what an unproductive question that is and just move on.

Again, I offer apologies to authors and discussants I didn't get to. The whole thing was memorable, but there is only so much I can blog! Do go to the site and look at the other sessions, according to your interests.

Nobel Symposium on Money and Banking Day 1

I attended the Nobel Symposium on Money and Banking in May, hosted by the Swedish House of Finance and Stockholm School of Economics.   It was a very interesting event. Follow the link for all the presentations and videos. (Click on "program." )

This review is  idiosyncratic, focusing on presentations that blog readers might find interesting. My apologies to authors I leave out or treat briefly -- all the presentations were action-packed and even my verbose blogging style can't cover everything.

"Nobel" in the title has a great convening power! The list of famous economists attending is impressive. And each presenter put great effort into explaining what they were doing, in part on wise invitation from the organizers to keep it accessible.  As a result I  understood far more than I do from usual 20 minute conference presentations and 15 minute discussions.

The first day was really "banking day," giving a whirlwind tour of the financial economics of banking.

Trading liquidity

Darrell Duffie gave (as always) a super presentation on the effects regulation is having on arbitrage in markets. (Slides, video)

Summer School Suggestion

The Asset Pricing online class is back, now hosted on Canvas. This is a first-year PhD level course in asset pricing. Advanced undergraduates and MBAs with some economics and basic calculus can take it too.  I mention it again as it is well suited as a summer school project, and I realized in talking to colleagues that not everyone who knew about the original class knows it's alive again.  Go here to sign up.

Faculty can also assign it or parts of it, and using the canvas system find out if students have taken the quizzes. This makes it a useful summer school prerequisite for fall classses, or you can use it or parts of it in a flipped classrom -- have the students do an online unit, take the quiz, and then show up to class prepared for more advanced discussion.

More information here on my webpage, along with all the videos and notes, and lots of extra material. If you don't want to take the quizzes, you can see the videos and notes without taking the course.

DB warns of US debt crisis.

"A coming debt crisis in the US?" warns a Deutsche Bank report* by Quinn Brody and Torsten Slok.

Source: DB

This graph is gorgeous. US deficits have, historically, been driven overwhelmingly by the state of the business cycle, and have very little to do with tax policies and spending decisions that dominate press coverage. In booms, income rises, so tax rate times income rises. In busts, the opposite, plus "automatic stabilizer" spending kicks in.

Until now.

There is a good reason past deficits did not really spook markets. They understood the deficit was a temporary phenomenon, due to temporary poor demand-side economic performance. We do not have that excuse now.

In case you thought this was some alarmist crank sheet, the report starts by quoting the latest CBO
report:

the CBO argues that, assuming current policies and trends are not changed, “the likelihood of a fiscal crisis in the United States would increase. There would be a greater risk that investors would become unwilling to finance the government’s borrowing unless they were compensated with very high interest rates.” 

Conference on the cross section of returns.

The Fama-Miller Center at Chicago Booth jointly with EDHEC and the Review of Financial Studies will host a conference on September 27–28, 2018 in Chicago, on the theme “New Methods for the Cross Section of Returns.” Conference announcement here and call for papers here.

Papers are invited for submission on this broad theme, including:

• Which characteristics provide incremental information for expected returns?
• How can we tame the factor zoo?
• What are the key factors explaining cross-sectional variation in expected returns?
• How many factors do we need to explain the cross section?
• How can we distinguish between competing factor models?
• Do anomaly returns correspond to new factors?  

Why a blog post for this among the hundreds of interesting conferences? Naked self-interest. I agreed to give the keynote talk, so the better the conference papers, the more fun I have! 

This is, I think, a hot topic, and lots of people are making good progress on it. It's a great time for a conference, and I look forward to catching up and trying to integrate what has been done and were we have to go. 

My sense of the topic and the challenge: (Some of this reprises points in "Discount rates," but not all) 

Both expected returns and covariances seem to be stable functions of characteristics, like size and book/market ratio. The expected return and covariance of an individual stock seems to vary a lot over time. So we need to build ER(characteristics) and then see if it lines up with covariance(R, factors | characteristics), where factors are also portfolios formed on the basis of characteristics. 

Buybacks redux

Two more points occur to me regarding share buybacks. 1)When buybacks increase share prices, and management makes money on that, it's a good thing. The common complaint that buybacks are just a way for managers to enrich themselves is exactly wrong. 2) Maybe it's not so good that banks are buying back shares.  3) The tax bill actually gives incentives against buybacks. What's going on is despite, not because.

Recall the example. A company has $100 in cash, and $100 profitable factory. It has two shares outstanding, each worth $100. The company uses the cash to buy back one share. Now it has one share outstanding, worth $100, and assets of one factory. The shareholders are no wealthier. They used to have $200 in stock. Now they have $100 in stock and $100 in cash. It's a wash.

Why do share prices sometimes go up when companies announce buybacks? Well, as before, suppose that management had some zany idea of what to do with the cash that would turn the $100 cash into $80 of value. ("Let's invest in a fleet of corporate Ferraris"). Then the stock would only be worth $180 total, or $90 per share. Buying one share back, even overpaying at $100, raises the other share value from $90 to $100.

That was the big point. Share buybacks are a good way to get money out of firms with no ideas, into firms with good ideas. We want firms to invest, but we don't necessarily want every individual firm to invest. That's the classic fallacy that I think it turning Washington on its head. Best of all we want money going from cash rich old companies to cash starved new companies. Buybacks do that.

1) Management getting rich on buybacks is good.

OK, on to management. Management, buyback critics point out, often has compensation linked to the stock price. They might own stock or own stock options. So when the buyback boosts the stock price, then management gets rich too. Aha! The evil (or so they are portrayed) managers are just doing financial shenanigans to enrich themselves!

The fallacy here, is not stopping to think why the buyback raises the share price in the first place. If it is the main reason given in the finance literature, that this rescues cash that was otherwise going to be mal-invested, then you see the great wisdom of giving management stock options and encouraging them to get rich with buybacks.

Fama Portfolio

The Fama Portfolio, is a new book from the University of Chicago Press. This is a collection of Gene Fama's papers, edited by Toby Moskowitz and me. It includes introductory essays by a group of Gene's distinguished colleagues, Ken French, Bill Schwert, René Stulz, Cliff Asness, John Liew, Campbell Harvey, Jan Liu, Amit Seru, and Amir Sufi.

The essays explain the ideas in modern terms, tell you why the papers are important, explain how the papers influenced subsequent thinking, update you on where our understanding on each point is today, and speculate about where new ideas may go. The continuing vitality of this work, even parts decades old, is impressive.

The task was hard. Which Fama papers should one read? Well, all of them! but we nonetheless had to pick. We typically chose a famous one from early in one of Gene's many research programs, and then a less known later one that really sums it up clearly. Gene's ideas get clearer over time, just like the rest of ours do.

The press lets us post our essays.  Here are mine (most joint with Toby):

1. Preface;
2. Efficient Markets and Empirical Finance; 
3. Luck vs. Skill;
4. Risk and Return; 
5. Return Forecasts and Time Varying Risk Premiums; 
6. Our Colleague.

Other authors may post their essays on their webpages. Otherwise, you'll just have to buy the book!

The contents:

Buybacks

A short oped for the Wall Street Journal here  on stock buybacks. As usual, they ask me not to post the whole thing for 30 days though you can find it ungated if you search. An excerpt:

... Buybacks do not automatically make shareholders wealthier. Suppose Company A has $100 cash and a factory worth $100. It has issued two shares, each worth $100. The company’s shareholders have $200 in wealth.  Imagine the company uses its $100 in cash to buy back one share. Now its shareholders have one share worth $100, and $100 in cash. Their wealth remains the same.

Wouldn’t it be better if the company invested the extra cash? Wasn’t that the point of the tax cut? Perhaps. But maybe this company doesn’t have any ideas worth investing in. Not every company needs to expand at any given moment.

Now suppose Company B has an idea for a profitable new venture that will cost $100 to get going. The most natural move for investors is to invest their $100 in Company B by buying its stock or bonds. With the infusion of cash, Company B can now fund its venture.

Tremors

A debt crisis does not come slowly and predictably. This year's short term bond holders, a very risk averse lot, are mostly interested in whether next year, new bondholders will show up, to lend the government money to pay this year's bondholders back. Bondholders can run on small jitters over that expectation.

When bondholders get nervous, they demand higher interest rates. More than higher interest rates, they diversify their portfolios, or just refuse. Debt gets "hard to sell" at any price. A different class of bondholders, willing to take risks for better rates, must come in to replace the safety-oriented clientele that currently holds short-term government debt.

As interest rates rise, interest costs on the debt rise. At $20 trillion of debt, when interest rates rise to 5%, interest costs rise to $1 trillion dollars, essentially doubling the deficit. That makes markets more nervous, they demand even higher interest rates, and when that spiral continues, you have a full blown debt crisis on your hands.

Short term debt compounds the problem. Since the US has borrowed very short term, interest increases make their way to the budget more quickly. If the US had borrowed everything in 30 year bonds, the spiral mechanism from higher rates to higher deficits would be cut off.

The crisis typically comes in bad times -- when in a war, recession, or financial crisis, the government suddenly needs to borrow a lot more and markets doubt its ability to repay.

But there is a case for a crisis to happen in good times as well. We have known for decades that the fundamental US problem is promised entitlement spending far beyond what our current tax system can fund. Markets have, sensibly I think, presumed that the US would fix this problem sooner or later. It's not that hard as a matter of economics. Well, say markets in 2005, OK for now, you have a war on terror and a war in Iraq on your hands, we'll trust you to fix entitlements later. Well, say markets in 2012, OK for now, you're recovering from a massive financial panic and great recession. We'll trust you to fix entitlements later, and we'll even lend you another $10 trillion dollars. But what's our excuse now? At 4% unemployment, after 8 years of uninterrupted growth, if we can't sit down now and solve the problem, when will we? Markets have a right to think perhaps America is so fractured we won't be able to fix this in time. Or, more accurately, markets have a right to worry that next year's markets will have that worry, and get out now.

All this is well known, and most commenters including me think that day is in the future. But the future comes often quicker than we think.

With that prelude, two pieces of news strike me as distant early warning signs. Here, from Torsten Sløk's excellent email distribution are two graphs of the bid-to-cover ratio in Treasury auctions.

Torsten's interpretation:

The first chart below shows that the bid-to-cover ratio at 4-week T-bill auctions is currently at the lowest level in almost ten years.... demand is also structurally weaker when you look at 10-year auctions, see the second chart. The main risk with issuing a lot of short-dated paper such as 4-week T-bills is that in 4 weeks it all needs to be rolled over and added to new issuance in the pipeline. In other words, the more short-dated paper is issued, the bigger the snowball in front of the US Treasury gets. 

Things are so far looking ok, but the risks are rising that the US could have a full-blown EM-style fiscal crisis with insufficient demand for US government debt, and such a loss of confidence in US Treasury markets would obviously be very negative for the US dollar and US stocks and US credit. The fact that this is happening with a backdrop of rising inflation is not helpful. Investors in all asset classes need to watch very carefully how US Treasury auctions go for any signs of weaker demand.

The last part is the mechanism I described above. As an ivory tower economist, I tend to overlook such technical issues. If the bid to cover ratio is low, well, then that just means we need higher rates. But higher rates aren't a panacea as above, since higher rates make paying it back harder still. As I look at debt crises, also, it isn't just a matter of higher rates. There comes a point that the usual people aren't buying at all.

Again, we're not there yet, and I think we have a long way to go. But this is a little rumble.

The second tremor is Why International Investors Aren’t Buying U.S. Debt in the Wall Street Journal.  The overall message is also that international investors are getting nervous.

US 10 year yields are 2.9% already. German yields are 0.68%. Why aren't people buying our debt? Well, number one, they are worrying a further slide in the dollar. Which comes when next year's international bond holders really don't want to hold US debt.

Most of the article is.. well, difficult for this former finance professor to follow. The article claims that one used to be able to lock in the difference, "Last year, buying Treasurys and swapping the proceeds back into euros provided European investors with a higher return than buying German sovereign bonds."[my emphasis] This sounds like arbitrage, "covered interest parity violations." That arbitrage is not perfect, but my impression is that it's not whole percentage points either. And you really can't lock in 10 years of funding. Besides which, someone else is on the risk-taking side of the swap. So the interviewed traders must be only partially hedging the difference. Perhaps it's really "uncovered interest parity," where you borrow Europe 0.68% invest in the US 2.9% and pray or only partially hedge the exchange rate risk. (On that, "The New Fama Puzzle by Matthieu Bussiere, Menzie D. Chinn, Laurent Ferrara, Jonas Heipertz, blog post at econbrowser documents that uncovered interest parity, where you invest in the high yield currency and take the risk, is losing its profitability. Interest spreads seem to correspond to future exchange rate changes after all.)

All to follow up on for another day. Mostly, it rang a bell as a little tremor that people who answer WSJ reporter's phone calls are expressing nervousness about US debt.

Again, these are little rumbles. I still think that a full blown crisis will come only amid a large international crisis, featuring some big country defaults (Italy?), big financial trouble in China, perhaps a war, state and local pension failures, and the US comes to markets with unresolved entitlements and asks for another $10 trillion. But I could be wrong. We live on an earthquake fault of debt, and the one thing I know from my own past forecasting ability (I have lived through 1987, the dot com boom and bust, 2008, the recent boom, and more, and saw none of them coming in real time) that I will not see it coming either.

Update:  Reply to Benjamin Cole, below. The US has never spent less on defense, as a fraction of GDP or of the federal budget, than it is doing today, since the 1930s. Here is defense / GDP. Defense / federal budget is even less, as the budget has expanded as a share of GDP.

Stock Gyrations

Is this 1929, the beginning of the end? Or 2007? Is it 1974, annus horribilis in which the stock market drifted down 40% having something to do with stagflation, and did not recover until the 1980s? Is it 1987, a quick dip followed by recovery in a year? Or just an extended version of the flash crash, when the market went down 10% in a few hours, and bounced back by the end of the day? Are we in a "bubble" that's about to burst? How much does this have to do with the Fed? Of course I don't know the answer, but we can think through the logical possibilities.

(Note: This post has equations, graphs and quotes that tend to get mangled when it gets picked up. If it's mangled, come back to the original here.)

Why do prices fall?

Stock prices fall when there is bad news about future profits, or when the discount rate rises.

The discount rate is the rate investors require, looking forward, to get them to buy stocks. If people require a better rate of return, with no change in their expected cashflows, prices drop.

Stop and think about that a second, as it's counterintuitive. Yes, the only way to get a better return out of the same profits or dividends is for today's price to drop.

Another way to think about it: Suppose all of a sudden there are good profitable opportunities for your money -- bond interest rates rise, or it's a good time to take money out of markets and invest in your company. Well, people will try to move money to those alternatives. But the stock market is a hot potato; someone has to hold the stocks. So stock prices must decline until the rate of return going forward matches the other attractions on a risk-adjusted basis. Good news about returns going forward is bad news about a downward jump in stock prices.

Bad news about cashflows is, well, bad news. The dashed line shifts down. Your stocks are not going to pay off as well as before. Higher required returns are neutral, really, for long-term investors. The price drops today, but the higher returns mean the price will slowly recover, just as long-term government bonds do.

So is this a moment of bad cashflow news or higher discount rate?  Most commentary suggests it's not bad news about cashflows. The economy seems finally to be growing, and there isn't anything like a brewing subprime or other problem, as there was in 2007. Maybe we don't know about it, but one certainly doesn't read about it.

So let's think about discount rates. Why might investors require a higher return on stocks? Is it interest rates, a risk premium, and is the Fed behind it all?

Where are we? 

Are we  in a "bubble'' that is about to pop? Let's start by reviewing some facts. Here is the cumulative return on the NYSE since 1990. (This is the CRSP NYSE. Sadly the data stops 12/31/2017 so I don't show the recent drop. The larger index including NASDAQ shows a larger rise and fall in the tech boom and bust, but is otherwise about the same.)

Cumulative return NYSE since 1990. Source CRSP

This graph does not show anything terribly unusual about the recent period. Stocks drift up during expansions, and take a beating in recessions. There are also little blips like the Krugman election panic of November 2016. (Sorry, I couldn't resist.)  Why have stocks gone up so much? Well, mostly because the expansion has gone on so long. The recent period is also notable in that the little wiggles are much smaller -- less volatility. That ended last week too.

Update: Thanks to Torsten Slok at DB the last year follows. His point, it's sharp but not all that big.

Next, look at the price-dividend ratio. (For a variety of reasons this is a better valuation measure than the commonly used price earnings ratio. This (CRSP) measure of dividends includes all cash payment to shareholders. No, repurchases don't cause a problem.)

Price / dividend ratio, NYSE. Source CRSP

You can see prices were high relative to dividends in the booming 1960s; they really rose in the late 1990s before the big 2000 bust. Then you see the 2008 crisis and recovery, and more recent wiggles. You can see prices fall in recessions, even relative to dividends which also fall in recessions.

Where is the booming stock market? Stock prices relative to dividends have not grown at all since the end of the recession.  Well, evidently, dividends have been rising just as fast as prices in the current expansion -- which again weren't rising all that fast anyway. So the main reason stock prices are high is that dividends are high, and people expect that slow growth to continue.

So here we were before the recent drop. Are prices too high? Well, not as much as in 1999 for sure! But P/D is a lot higher than historical norms.  Is this the beginning of a drop back to historic levels like 30, or even 20? Or is this a new normal? There is way too much commentary lately that whatever we remember from 20 years ago was "normal" and that things have to go back to that. Not without a reason.

Interest rates and stock prices 

To think about this question we need some basics of what determines price-dividend ratios. Over long time periods, the return you get on stocks is the dividend yield -- how many dividends they pay per dollar invested plus the growth in dividends. Over short time periods you also get price appreciation per dividend, but over long time periods, the ratio of price to dividends comes back and price growth is the same as dividend growth.  In sum,

return = dividend yield + growth rate

\[ r = \frac{D}{P} + g \]This is also where price comes from. The price you're willing to pay depends on the expected return going forward, and expected  dividend growth (Prices are high relative to current dividends if people expect a lot more dividends in the future.)\[  \frac{D}{P}  = r - g = r^l + r^e - g \]\[  \frac{P}{D}  =\frac{1}{r - g} =\frac{1}{ r^l + r^e - g}  \] Here I broke apart the expected return into components. First, the expected return on stocks is equal to the long-term real risk-free rate \(r^l\) plus the risk premium \(r^e\). This is just a definition -- the risk premium is \(r^e=r-r^l\).

So, looked at either as D/P or P/D, we now have the tools to think about what pushes stock prices around.

(There is nothing inherently ``rational'' or ``efficient markets'' about this. Behavioral finance just says the expectations are wrong, for example that people think \(g\) is big when in fact \(r\) is small.)

Stock prices are very sensitive to real interest rates, risk premiums, and growth expectations. At our current P/D of 40, for example, this means \(r-g=1/40=0.025\) or 2.5%. Just half a percent change  in expected return or growth rate, \(r-g=0.02\) would mean \(P/D=1/0.02=50\), a 25% rise in stock prices. Conversely, a half percent rise in real interest rates would mean \(r-g=0.03\), a decline to \(P/D=33\) a 16.7% fall.  No wonder stocks are (usually) volatile!

Now, to what's going on? If we take growth rate expectations off the table, then stock prices are moving because of changes in interest rates. And small interest rate changes do indeed imply big stock valuation changes -- though, again, take heart because it means the rate of return is higher, as in the first picture.

Does this relationship hold historically? Here is the D/P ratio (P/D upside down) and a measure of long-term real interest rates.

NYSE D/P, Cleveland Fed 10 Year real rate, and 10 year TIPS

(The problem with 10 year real rates is knowing what 10 year expected inflation is, given that we did not have TIPS. There are lots of other problems too, such as unwinding the liquidity premium in government bonds. Here I used the Cleveland Fed's real rate model, which is in part based on survey expectations. I added the 10 year TIPS yield where we have it to confirm the general pattern of the Cleveland Fed's calculation.)

This is a remarkable graph: The entire rise in valuations from 1980 to 2008 corresponds exactly to the decline in real interest rates.

By this measure, the decline in real rates was huge, from 7% to essentially 0%. Plug that in to \(P/D=1/(r-g)\) and we're done. Stock prices are exactly where they should be.

In fact, by this measure, stock prices are too low. In 2008, real rates kept right on trundling down another two percentage points, but the dividend yield stabilized.

Well, I was careful to say "corresponds to" not "caused by" for a reason. The risk premium and growth expectations changed as well. Arguably the move to a low-growth economy starting in 2000, cutting one to two percentage points off \(g\), offset the decline in real rate. Or perhaps the risk premium isn't as low as we think it is. This isn't just waffling -- the relationship is basically an identity. One of those options must be true. If the dividend yield is 2.5%, and the real interest rate is 0%, then \(r^e-g\) is 2.5%, and has grown since 2000. Either the risk premium has grown 2.5% -- so much for the ``low risk premium'' -- or growth expectations have fallen 2.5%. Or the long-term real rate is profoundly mismeasured here.

More on all this in a minute. But the graph reminds us 1) Real rates have come down a lot, and 2) persistent changes in real rates really are an important part of stock market valuations. Oh, and they have nothing to do with ``risk appetite'' and all that other blather. Stocks are valued like bonds plus risk. We are noticing here that the bond-like component got much more valuable. That alone, not the risk component or the growth component, accounts for two decades of huge price rises.

This actually updates significantly some of my own work, and the asset pricing consensus. The great question why do price-dividend ratios vary so much occupied us a lot in the late 1980s and early 1990s, including myself, John Campbell, Bob Shiller, Gene Fama and Ken French. The rough answer we came to -- pretty much all variation in D/P or P/D comes down to variation in risk premiums, the \(r^e=r-r^l\) term. The underlying fact is that times of high P/D are not reliably followed by higher dividend growth (Shiller), and they are reliably followed by low  excess returns (Fama and French). If you add it up, the risk premium effect neatly accounts for all the variation in P/D (Campbell and Shiller, me).

Well, in the data up to 1990, we didn't see much persistent variation in real rates of interest, and what we did see was not correlated well with stock prices. Well, that was 1990, and now is now. This graph suggests that in fact a lot of the recent variation in P/D corresponds to lower real interest rates.  Also, it's the low frequency, decade to decade movement in P/D that is not well accounted for by any models. An academic version of this observation needs to be written.

Practical bottom line: The stories that the recent stock price decline comes from rising long-term real interest rates make sense. They might be wrong, but they make sense. That's saying a lot more than most of the other stories being bandied around right now.

Interest rates, growth,  stock prices, and the Fed. 

The story is not that easy however. We have to think about real interest rates \(r\) and growth \(g\) together. And there is this puzzle to answer -- how can it be that good news about the economy sends the market down? If \(P/D=1/(r-g)\) more \(g\) should raise \(P\), no? It should shift up the dashed line in my first graph?

No. We have to think about where real interest rates come from. One of the most basic relationships in economics is that higher growth means higher real interest rates.  If everyone will be richer in the future -- growth -- they need an incentive to save and not blow it all today. And growth means a higher marginal product of capital, and hence higher interest rates. As a simple equation, \[ \text{real rate} = \gamma g \]where \(\gamma\) is a parameter, usually between about 1/2 and 2, and get ready for a bar fight at the AEA convention over just what value to use. 1% higher growth means about a half percent to two percent higher real interest rate.

(There is a second term too, important in understanding things like the financial crisis. More uncertainty means lower interest rates. Not today.)

If \(\gamma=1\), if one percent growth means one percent higher real interest rates, then higher growth has no effect at all on stock prices or price dividend ratios. (\(D/P = r^l + r^e - g.\) Raise \(r^l\) and \(g\) by the same amount.) If, as I think is more likely right in this case, \(\gamma>1\), then higher growth lowers stock prices. Yes. Higher growth means a higher discount rate as well as more dividends. The discount rate effect can overwhelm the cashflow effect.

This has nothing to do with the Fed. There is a natural human tendency to look for Agency, for some man or woman behind the curtain pulling all the strings, and these days that means the Fed. For example, the WSJ Editorial on stocks:

"The paradox of the equity-market correction is that it’s taking place even as the real economy looks stronger than it’s been since at least 2005 and maybe 1999. "

"So why are stocks falling amid all the good news? The best answer we’ve heard is that stocks are reflecting a return to volatility and risk after years of the Fed’s financial repression. With its quantitative easing bond purchases, the Fed has for a decade suppressed market price signals in bonds."

"Investors may finally be figuring out that the global quantitative-easing monetary party is ending."

Look back at my graph. Real interest rates have been on a slow downward trend since 1980. That trend is unbroken since 2008. There is not a whiff that QE or anything else has budged that trend. (Lots of good graphs on this point in 8 heresies of monetary policy here. ) If the Fed has anything to do with it, it is the slow victory over inflation expectations, not QE and a lot of talk.

Yes, the papers like to say that higher growth will induce the Fed to raise rates. The Fed can put a finger in this dike for a bit if they want to, but even the Fed cannot long fight the positive or negative relationship between real growth and real interest rates.

So it makes perfect sense, at least as a logical possibility, that more growth lowers stock prices! Again, this is like my lower line in the first picture -- and actually a bit better because we also raise the terminal point. If this is what happened, well, regret that you didn't see it happening and stay out during the dip, but be reassured the market will make it back.

Risk premiums 

What about the ``unusually low risk premium''? Aren't the Fed's ``massive QE and abnormally low interest rates distorting risk premiums and causing asset price bubbles?'' (The best definition of ``bubble'' I can muster is a risk premium that is too low, distorted somehow.)

Here is the contrary view. We are at the late summer of the business cycle. The economy is relatively healthy, at least if you're a stock market investor. (Many of these own companies.) Economic volatility is still at an all time low. Bonds are still giving pretty atrocious real returns. Yeah, stocks look pretty healthily priced -- as you contemplate your \(P/D = 1/(r^l + r^e - g)\) it looks like the extra return from stocks \(r^e\) is pretty low. But what else are you going to do with the money? You can afford a little risk. Contrariwise, the same investors in the bottom of the great recession, with very low \( P/D\) signaling a high risk premium \(r^e\), said to themselves or their brokers, yes, this is a buying opportunity, stocks will likely bounce back. But my business is in danger of closing, my house might get foreclosed, I just can't take any risk right now.

In short, it is perfectly rational for investors to be more risk-averse, and demand a higher risk premium \(r^e\) in the bottom of recessions, and to hold stocks despite a low risk premium in quiet good times like right now. And this has nothing to do with the Fed, QE, or anything else.

John Campbell and I wrote a simple model of this phenomenon a long time ago, and I've reviewed it several times since, most recently here. Sorry for flogging the same ideas, but this possibility still hasn't made it to, say, the Fed-obsessed WSJ editorial pages, to say nothing of the Trump-obsessed pages at other outlets.

John and I tied risk aversion to consumption trends. If consumption is high relative to the recent past, in good times, you more willing to hold risk. If consumption is declining relative to the recent past, you get more scared. Lots of other mechanisms, including debt, work much the same way. If you don't like the precise model, consumption relative to recent past is a good general business cycle indicator.

Let's look historically. Here is consumption less a moving average (I used \(x_t = \sum_{j=0}^\infty 0.9^j c_{t-j})\), plotted with the log of the price/dividend ratio. The two series have different scales. The point is to see the correlation.

Consumption minus a moving average, and log P/D on NYSE. 

The pattern is longstanding. In good times, when consumption rises relative to recent past, stock valuations go up. In bad times, such as the great recession, consumption falls and so do stock valuations. People are scared. The same pattern happens regularly in the past.

The two lines drift apart, but as we saw above real interest rates account for that. Then the business-cycle related risk premium here accounts for the rises and dips.

And, if I may belabor the point, there was no QE, zero interest rates, and so forth going on in all these past instances when we see exactly the same pattern. Higher real interest rates are a regular, simple, utterly normal part of expansions, and lower risk premiums are a regular, simple, utterly normal part of expansions. 

I was interested to read Tyler Cowen at Bloomberg back in to this view, based entirely on intuition:

In a volatile and uncertain time politically, we have observed sky-high prices for blue-chip U.S. equities. Other asset prices also seem to be remarkably high: home values and rentals in many of the world’s top-tier cities, negative real rates and sometimes negative nominal rates on the safest government securities, and the formerly skyrocketing and still quite high price of Bitcoin and other crypto-assets.

Might all of those somewhat unusual asset prices be part of a common pattern? Consider that over the past few decades there has been a remarkable increase of wealth in the world, most of all in the emerging economies. Say you hold enough wealth to invest: What are your options?

In relative terms, the high-quality, highly liquid blue-chip assets will become expensive. So we end up with especially high price-to-earnings ratios and consistently negative real yields on safe government securities. Those price patterns don’t have to be bubbles. If this state of affairs persists, with a shortage of safe investment opportunities, those prices can stay high for a long time. They may go up further yet.

These high asset prices do reflect a reality of wealth creation. They are broadly bullish at the global scale, but they don’t have to demonstrate much if any good news about those assets per se. Rather there is an imbalance between world wealth and safe ways of transferring that wealth into the future

To sum this all up in a single nerdy finance sentence, in a world where wealth creation has outraced the evolution of good institutions, the risk premium may be more important than you think.

Except for this business about "shortage of safe assets," that's pretty much the intuition. (Tyler: all assets are in fixed supply in the short run. Prices adjust. This isn't really a ``shortage.'') The point that high valuations extend to homes, bonds, bitcoins, and global stocks is a good indicator that the phenomenon is generalized risk aversion rather than something specific to one market or economy. 

This view should not necessarily make you sleep at night however.  It means that a downturn will be accompanied by higher risk aversion again, and not only will dividends fall, prices will fall further. Moreover, historically, asset price falls have been preceded by periods of higher volatility. Alas, many periods of higher volatility have just faded away, so it's a warning sign not a signal.  Sure, this mechanism means they will bounce back, but if you are clairvoyant enough to see it coming it will be better to avoid the fall! If not, well, be read to buy when everyone else is scared -- if you are one of the lucky few who can afford not to be scared.

The VIX, volatility, technical factors 

There is another kind of ``discount factor variation,'' including 1987 and the flash crash. Sometimes the machinery of markets gets in the way, and prices fall more than they should. They quickly bounce back. If you can buy at the bottom you can make a fortune, but the prices fell precisely because it's hard to buy.

There were scattered report on Monday of hours long delays for retail customers to trade. (Can't find link.) But I do not get a sense this was a big clog in the markets. I would be curious to hear from people closer to markets.

The bigger news is the return of volatility -- big daily changes. To put this in historical perspective, here are two plots

The surprise, really, is just how low low volatility had become. Historically the stock market index has had a volatility around 15-20% per year -- a typical year saw a 15-20% change, and a typical day saw a \(15-20 / \sqrt{250} \approx \) one percent change. But, as you see in the top graph, volatility also declines in the late summer of the business cycle. Volatility has many occasional little eruptions, typically around price drops, and then washes away. Except when volatility rises in advance of the next recession and market decline. Which is this? I wish I knew.

Volatility is not about "fear" nor is it about "uncertainty." Volatility occurs when options change quickly. Constant bad news or good news just leads to constantly low or high prices. This is a sign of a time when either a lot of real information is hitting the market, or a lot of people are trying to process what's going on ahead of everyone else.

The "VIX bust" is hot in the news. A lot of people bet that the graph you saw above would not rise. To be ``short volatility'' means basically that you write insurance to people who worry about markets going down, (volatility is a big part of the value of put options) and you write insurance to people who are worried about events like right now in which markets start to move a lot. Hello, when you write insurance, occasionally you have to pay up.

As the graphs make clear, writing volatility insurance, or betting that volatility will continue to go down,  is like writing earthquake insurance. Not much happens for many years in a row, and you can post nice profits. Then it jumps and you lose big time. Anyone who did this based just on historical returns is now crying the tears of the greedy neophyte. But they have lots of company. Back in the 1990s, Long Term Capital Management went under, basically for betting that similar looking graphs would continue to go down.

Well, if after all these years people are at it, P.T. Barnum had a good word for them. But did this have something to do with the stock market crash? How Bets Against Volatility Fed the Stock Market Rout in WSJ is an example of this train of thought.

On first glance, sure, a lot of people lost a ton of money, and then sold out other risky positions. But Econ 101: for every buyer there is a seller.  Derivatives contracts are pure cases of this fact -- the net supply really is zero, for everybody who lost a dollar shorting VIX somebody else made a dollar buying it.

To get a story like this to go you need all sorts of market discombobulations. Somehow the people who lost money must be more important to markets than the people who made money. This can happen -- if a bunch of traders in a complex obscure security all lose money, and all try to sell, there is nobody to buy. But I don't really see that case here, and stocks are not a complex obscure security.

A trader friend also tells me that he has seen lots of people stop hedging -- so sure low volatility would continue that they don't cover the downside. He said many have lost a ton, and now are frantically selling to cover their positions. Such price pressure can have short run impacts, but does not last long.

Inflation and real interest rates 

So we're back at hints of higher long-term real interest rates as the main likely culprit behind this week's decline and gyrations.

Here too most of the stories don't make much sense. Inflation per se should not make much difference. If expected inflation rises, interest rates rise, but real interest rates are unaffected. Inflation may make the Fed act more quickly, but there is not much correlation between what the Fed does with short term rates and the behavior of 10 year or more rates that matter to the stock market -- or to corporate investment.

Yes, there is some correlation -- especially at the end of expansions, short and long rates rise together. But the correlation is a whole lot less than the usual Wizard of Oz behind the curtain stories. And even the Fed cannot move real rates for very long. There is a good chicken-and-egg question whether the Fed can hold short rates down for long when long rates want to rise. The Fed pretty much has to jump in front of the parade and pretend to lead it.

Inflation does seem finally to be rising. The fact that higher rates are associated with the dollar falling suggests that a lot of the higher rates are due to inflation, and TIPs have not moved (top graph.)

So, the question before us is, are long-term real rates finally rising -- back to something like the historical norm that held for centuries, and if so why?

The good story is that we are entering a period of higher growth. Depending on your partisan tastes, point to tax cuts and deregulation, or state that Obama medicine is finally kicking in. This would raise real growth, with \(\gamma>1\) lead to a small stock price decline, but higher stock returns and bond returns going forward.

There is a bad story too. Having passed a tax cut that left untouched will lead to trillion-dollar deficits, Congressional leaders just agreed to $300 billion more spending. The Ryan plan that tax cuts would be followed by entitlement reform may be evaporating. Publicly held debt is $20 trillion. At some point bond markets say no, and real rates go up because the risk premium goes up. The US is in danger that higher interest rates mean higher interest costs on that debt, which means higher deficits, which means higher interest rates. $20 trillion times 5% interest = $1 trillion in interest costs.

The former leads to some inflation if you believe in the Phillips curve. The latter leads to stagflation in a tight fiscal moment.

Which is it? I don't know, I'm an academic not a trader.

One consolation of the stock market decline: I hope we don't have to hear how all the corporate tax cut did was to boost the stock market!

Well, two days ago this was going to be a short post responding to the WSJ's view that the Fed is behind it all, and Tyler's nice intuition. It got a bit out of hand, but I hope it's still interesting.


****

Data Update (Geeks only).

P/D isn't really "better" than P/E or other measures. A measure is what it is, you have to specify a question before there is an answer. Ideally, we want a measure that isolates expected returns, and tells us if prices are higher or lower given the level of expected dividends.  So ideally, we would account for expected future dividends and the result would be a pure measure of expected returns (rational or not). P/D works pretty well that way because dividends are not very forecastable. Price divided by this year's dividends turns out to be a decent approximation to price divided by anyone's forecast of future dividends. But not perfect. P/E is less good that way because earnings bat about a bit more than dividends. For individual companies you can't use P/D, because so many of them do not pay dividends. Following Fama and French, the ratio of market value to book value is better there, because book value is usually positive, or not so frequently zero.

I use the CRSP definitions. I start from the CRSP return with and without dividends and infer the dividend yield. ''Dividends" here includes not only cash dividends but all cash payments to shareholders. So, if your small company gets bought by Google, and the shareholders get cash, that is a "dividend" payout. I suspect this accounts for the difference noted by WC Varones below. As others point out, earnings has all sorts of measurement issues, and also does not control for leverage.

Dividends are very seasonal, so you can't divide price by this month's dividends or you get a lot of noise. I use the last year's worth of dividends, brought forward by reinvesting them. This introduces some "return" into the dividend series. If you just sum dividends, though, identities like \(R_{t+1} = (P_{t+1}+D_{t+1})/P_t \) no longer hold in your annual data.

x = load('crsp_nyse_new_2018.txt');

caldt = x(:,1);
totval = x(:,2);
usdval  = x(:,3);
sprtrn = x(:,4);
spindx = x(:,5);
vwretd = x(:,6);
vwretx = x(:,7);

[yr,mo,day,crsp_date_number] = decode_date(caldt);

T = size(vwretd,1);
vwretda = (1+vwretd(1:T-11)).*(1+vwretd(2:T-10)).*(1+vwretd(3:T-9)).*...
          (1+vwretd(4:T-8)).*(1+vwretd(5:T-7)).*(1+vwretd(6:T-6)).*...
          (1+vwretd(7:T-5)).*(1+vwretd(8:T-4)).*(1+vwretd(9:T-3)).*...
          (1+vwretd(10:T-2)).*(1+vwretd(11:T-1)).*(1+vwretd(12:T));

vwretxa = (1+vwretx(1:T-11)).*(1+vwretx(2:T-10)).*(1+vwretx(3:T-9)).*...
          (1+vwretx(4:T-8)).*(1+vwretx(5:T-7)).*(1+vwretx(6:T-6)).*...
          (1+vwretx(7:T-5)).*(1+vwretx(8:T-4)).*(1+vwretx(9:T-3)).*...
          (1+vwretx(10:T-2)).*(1+vwretx(11:T-1)).*(1+vwretx(12:T));
   
vwdp = vwretda./vwretxa-1; %D_t+1/P_t+1 = [(P_t+1+D_t+1)/P_t] / [P_t+1/P_t] -1;
vwdda = vwdp(13:end)./vwdp(1:end-12).*vwretxa(13:end);   % D_t+1/D_t = D_t+1/P_t+1 / D_t/P_t * P_t+1/P_t
vwdda = [ones(23,1)*NaN; vwdda];
cumval = cumprod(1+vwretd);
vwdp = [ ones(11,1)*NaN; vwdp]; % keep length of series the same

I get stock data from CRSP via WRDS. This is the NYSE only. I can't post the full data, as it belongs to CRSP. Here is an excerpt that will let you calculate the last year, and check that things are right if you download the whole thing.

%crsp_nyse_new_2018.txt
%   caldt            totval                  usdval                 sprtrn         spindx        vwretd        vwretx
19260130       27624240.80       27412916.20      0.022472       12.74      0.000561     -0.001395
19260227       26752064.10       27600952.10     -0.043956       12.18     -0.033046     -0.036587
19260331       25083173.40       26683758.10     -0.059113       11.46     -0.064002     -0.070021
19260430       25886743.80       24899755.60      0.022688       11.72      0.037019      0.034031
...
20160129    17059005700.00    17976992500.00     -0.050735     1940.24     -0.050111     -0.051700
20160229    16986848800.00    17001893900.00     -0.004128     1932.23      0.005104      0.002251
20160331    18122913200.00    16951468600.00      0.065991     2059.74      0.072190      0.069562
20160429    18503144900.00    18082712100.00      0.002699     2065.30      0.023324      0.021716
20160531    18479138100.00    18410229900.00      0.015329     2096.96      0.006124      0.003392
20160630    18613173100.00    18422135300.00      0.000906     2098.86      0.011175      0.008957
20160729    19054705700.00    18557630600.00      0.035610     2173.60      0.028433      0.026872
20160831    18993464300.00    19049575300.00     -0.001219     2170.95      0.000196     -0.002532
20160930    18829544800.00    18880924600.00     -0.001234     2168.27     -0.003876     -0.005878
20161031    18404742600.00    18802632900.00     -0.019426     2126.15     -0.021331     -0.022944
20161130    19220882900.00    18383296300.00      0.034174     2198.81      0.048548      0.045701
20161230    19568491300.00    19178151000.00      0.018201     2238.83      0.021566      0.019486
20170131    19824534000.00    19526674900.00      0.017884     2278.87      0.014007      0.012623
20170228    20355248600.00    19781803200.00      0.037198     2363.64      0.031422      0.028905
20170331    20237616500.00    20334429600.00     -0.000389     2362.72     -0.003961     -0.006103
20170428    20286715000.00    20194157100.00      0.009091     2384.20      0.003950      0.002468
20170531    20299003900.00    20276905500.00      0.011576     2411.80      0.002199     -0.000507
20170630    20602218600.00    20256933000.00      0.004814     2423.41      0.018204      0.016235
20170731    20747539100.00    20488018000.00      0.019349     2470.30      0.015290      0.013394
20170831    20593088100.00    20742392900.00      0.000546     2471.65     -0.005133     -0.007874
20170929    21147810200.00    20381001300.00      0.019303     2519.36      0.030435      0.028662
20171031    21343546700.00    21130998500.00      0.022188     2575.26      0.011831      0.010360
20171130    21904734200.00    21302790800.00      0.028083     2647.58      0.030537      0.027670
20171229    22016063100.00    21683038400.00      0.009832     2673.61      0.015914      0.014117

If I screwed up, let me know and I'll fix it!

Asset Pricing Competition

John Campbell's text, "Financial Decisions and Markets" is out from Princeton University Press. With some mild chagrin, I must say it's a splendid book. (Chagrin, of course, because it's an obvious major competitor to my own effort in Asset Pricing.)

It is spare, concise, and clearly written. How can I say that of a 450 page book, with wide text and tiny margins? Well, it's the concise version of the Encyclopedia Britannica, breathtakingly comprehensive and up to date in its coverage of important research topics.

The first part is a whirlwind tour of asset pricing theory. Here, John adopts the traditional organization -- expected utility, static portfolio choice, static CAPM and APT as equilibrium relations where supply meets demand, and finally we meet the discount factor and consumption-based pricing. I chose to go the other way around, and start with the basic asset pricing equation \(p_t u'(c_t) = E_t [\beta u'(c_{t+1}) x_{t+1} ]\), following Bob Lucas' insight that asset pricing is the same as in an endowment economy, and filling out the CAPM and APT and so forth as special cases. I never even got to portfolio theory -- it's in a draft chapter for the long-delayed next version. I still think that's the right organization, but most people don't want to teach it that way. John's more conventional organization, combined with clarity and concision, may be more what you want.

Even here, John's empirical taste and contributions rings through Any textbook is in many ways a summary of its authors' research journey, and John's journey has gone far and wide. You see a preview of the style on the 6th page of chapter 2 (p. 28) where you meet approximations for log returns, and the growth-optimal portfolio on the next page. On calculating minimum-variance portfolios, on p. 37, you get  graph of time-varying return correlations from Campbell Lettau Milkier and Xu (2001), a provocative fact usually ignored. After efficiently presenting the classic CAPM, we get (p. 51) an insightful application to Harvard's endowment, highlighting the difficulties of using these oft-repeated portfolio and pricing theories in practice.