Author Archives: Yichuan Wang

Can the Shanghai Stock Connect Help Chinese Investors Diversify?

Yes, but not as much if it were to allow the trading of exchange traded funds. The recent opening of the Shanghai direct stock connect has had many effects — a primary one being that now retail investors in the mainland and Hong Kong are able to buy stocks from each other’s markets. This point about retail is key. Past programs such as the Qualified Foreign Institutional Investor program have allowed institutional investors from outside China to invest in Chinese stocks in controlled amounts. So it’s no surprise to see in the WSJ article that there has been little increase in institutional demand as a result of the stock connect. The real change that we see in the Shanghai stock connect is that there is now a more liberalized attitude towards retail investors in China owning foreign stocks.

Chinese retail investors benefit the most because the addition of Hong Kong stocks to their stock portfolio allows for a dramatic increase in diversification. In effect, retail investors have now gone from a one country world to a two country world. On the other hand, Hong Kong investors could have already invested abroad, so their welfare gains are smaller. And given how much people invest in houses in China, it’s clear that households are looking for other investment outlets through which to channel their savings. Hong Kong stocks can now be one of those channels.

Even if it seems complicated for retail investors to go invest in Hong Kong, now that the connect is open Chinese mutual funds will soon have the ability to go invest in Hong Kong for their clients. In doing so they can build up a diversified basket of constituent stocks in the Hong Kong indices and sell those mutual fund shares to clients.

However, retail investors would be able to circumvent this if only they were allowed to trade exchange traded funds on the Hong Kong stock exchange. This way the retail investors would be able to directly buy diversified holdings of Hong Kong stocks, thus allowing them to capture the diversification benefits of overseas holdings without the costs of using a highly technical stock connect.

Another future benefit of trading exchange traded funds is that it lays the groundwork for Chinese investors to invest in global equities. Imagine a firm like Vanguard offering a cheap ETF on the Hong Kong market that was a Hong Kong dollar denominated fund that bought the SP500 market ETF and some diversified basket of other developed market funds. Then this would fully unleash the ability of Chinese retail investors to diversify internationally and therefore better save for retirement.

Why Don’t People Invest Abroad More?

Recent WSJ articles on whether investors should increase their foreign stock exposure or currency hedge their investments side step the more general point that households invest far too little in foreign stocks.

What is the risk in foreign stocks? First, consider the possibility that foreign stocks have lower expected returns than US stocks. But by conventional finance theory, lower excess returns are a sign that the asset provides some kind of insurance against bad events — think long term bonds that protect against recession risk earning less return than common stock. Hence if it really were the case that foreign stocks had lower expected return, that really would be a sign that somebody felt that those stocks were safer than U.S. stocks.

Now, the above story presupposed that investors have rational expectations about stock returns. What if people are just overly optimistic about foreign stocks and so they’re willing to buy them even though they earn lower expected returns? This story is at odds with the “home bias in equities“, i.e. the phenomenon that household investors have holdings of foreign stocks around 1/2 of the relative market cap of foreign stocks in the global stock portfolio. If investors in the U.S. were really excessively optimistic about foreign stocks, then they would overweight them in their portfolio — which they most certainly are not.

So if expected returns are a wash, then what about variance? Foreign stocks do tend to be more volatile, so maybe that’s what makes them risky. But that again shouldn’t really matter because if you have a big portfolio of US stocks, then adding more US stocks is actually riskier than adding a little more of foreign stocks. This is because the foreign stocks don’t move 1 for 1 with the US stocks, so by buying stocks abroad you actually reduce the variance of your portfolio. This argument is made even stronger if you suppose that your earnings in the US are strongly tied with the state of the US economy, and so holding foreign stocks would not only diversify your stock holdings but also your human capital holdings.

The point of the arguments above is that when deciding how much to invest abroad, the relevant question should not be about expected returns or just the raw amount of variability you see in returns from year to year, but rather whether you think foreign stocks will tend to do poorly when you fall on hard times. In other words, what is the covariance of foreign stock returns with how well you are doing in terms of income and consumption. Unfortunately, most retirement advice on foreign stocks focus on the higher variance and volatility, which should not be of first order concern when deciding whether to increase foreign stock exposure on the margin.

Now, in the stories above I assumed that households are failing to optimize, and therefore I am in a position to give advice on why they should increase foreign stock holdings. For example, Heathcote and Perri write in a 2007 working paper that “Home bias arises because endogenous international relative price fluctuations make domestic stocks a good hedge against non-diversifiable labor income risk.” But it seems highly unlikely to me that households are making complicated calculations about human capital risk and global relative price fluctuations — I certainly know of no financial planners that offer this service. As such I find stories of behavioral biases against foreign stocks to be a much more likely cause of the relatively small share that U.S. investors put into foreign stocks.

Low Rates are a Sign that Monetary Policy Has Been Too Tight

A recent commentary by Stanley Druckenmiller, one of Soros’ deputies behind the famed British pound short, touches on several fallacies made by many financial commentators about interest rates, financial stability, and monetary policy. While he has many valuable insights about behavioral errors people make in markets and the pressures facing fund managers that may induce irrationality, I think he is dead wrong about the causal analysis of why long term interest rates are so low.

The basic trope is to point out that long term interest rates are very low on a historical basis, point out that the Federal Reserve has been very aggressive in keeping short term interest rates low, and then blame the Federal reserve for causing a bubble in bonds and other financial assets. According to these narratives, the Fed should sell its holdings of long term bonds and instead let long term interest rates rise.

But what happens to long term interest rates when the central bank does not ease policy aggressively? In reality, the biggest cause of low long term interest rates is when monetary policy has not been aggressive enough. Recent economic history is littered with examples:

1. Contrast US and German long term bond yields. Ironically enough, even though the ECB has been much less aggressive with its unconventional monetary policy, it’s in Europe that long term interest rates are so low. Admittedly, this is not causal evidence because it could still be the case that Fed actions are keeping long term interest rates lower than they would otherwise have been. But this is nonetheless evidence that the direct effect of larger central bank holdings on long term bonds is minimal.



2. Europe also has lots of examples of what happens when central banks try to raise short term rates too early. The central bank’s mandate is to make sure the nominal economy is healthy (growth + inflation are not too low). As such if the central bank tightens before the rest of the economy can support it, the ultimate result is that the central bank has to ease again. If the goal is to get higher interest rates in the long run, the irony is that the best policy is to keep rates low now until other signals such as inflation or unemployment sound the alarm to tighten.


Now, Stanley does make a great point that most bubbles would not be possible if long term interest rates were at 4 to 6 percent. But that’s a general phenomenon of low discount rates. When investors are patient (or less risk averse), that naturally means events in the future start to matter a lot more, and therefore it becomes possible for companies who aren’t earning any current revenue to get funding for future projects. But this structural feature of financial markets is not a reason for the Fed to prematurely tighten.

An Exercise with the Normal Distribution — The Case of Pension Fund Returns

The normal distribution is very useful when one wants to model phenomenon that are general to all kind of random variables, but in a way that you can actually do the math. One illustration of this is to look at how we can start with a model of normal log returns and think about how this math can illustrate some of the calculations showing the severity of the pension underfunding problem. While there may have been a recent controversy over how pension funds are overpaying in fees, this underfunding issue may present an even deeper problem.

Suppose one year log returns are independent each year with a mean of 6% and a standard deviation of 16%. Then the log return over a horizon of 100 years has a mean of 800% and a standard deviation of 160%. This result holds without making any distributional assumptions — the return can have any random variable’s distribution. But suppose we’re not interested in the log return, but rather the gross return — the number that answers “how many times larger is my wealth after 100 years”. We would need to take an exponential. What’s the expectation of that random variable?

The exponential function is convex — it increases at an increasing rate as the input of the function. So if the log return over 100 years is centered around 800% but with positive variance, then the gross return for 100 years should be larger than the exponential of 800%, as the random histories in which the log return was slightly above 800% will contribute more than the histories in which the log return was slightly below 800%. This result is known as Jensen’s inequality, and is illustrated in the diagram below. The average of the horizontal position of the three dots is at mu, but the average of the vertical positions is above V(mu) because the function is convex.

Ok, so in general we know this quantity is larger, but by how much? Fortunately, in the case of a normal distribution we have closed form solutions for the expectation and the median of an exponential of a normal random variable. It turns out that for a normal random variable with mean M and a variance V, the exponential has a mean of exp(M + 0.5 * V), and the median will just be exp(M). This is a calculation that can be worked out by hand, and very cleanly illustrates the idea that variation + a convex function means you get much higher expectations even though percentiles like the median don’t change.

This can have real policy implications in the case of pensions. What I showed above is that in the case of normal one year log returns, then over time the gross returns will have an average return that is exp(0.5V) times larger than median return. Let’s calibrate this to annual stock returns with a mean of 7.5% and a standard deviation of 13%. Then at a horizon of 100 years, the mean (average) return will be 2.3 times larger than the median! (For the math nerds, the ratio is exp(0.5 * (0.13^2) * 100). This is bad bad news for pension funds that look at gross returns and think that they can expect to meet their obligations. Even if the future looks just like the past, and even if the world is well behaved and returns are normally distributed, there is a fifty percent chance that their nest eggs will be worth less than 43% of what they expected!

Intuitively, the math here is pointing out that while the average returns are very high, the average return is high because of a few worlds in which the stocks do incredibly well. But those worlds are not the relevant ones when deciding whether the pension fund will grow large enough to cover the costs of the pensions, and as such pensions may be severely underfunded relative to what expected gross returns might have you believe.

Now, this started as an exercise in the normal distribution — how would one get around that distributional assumption? In principle one could bootstrap histories of returns and run the calculations above by simulation, but this is a much more complicated topic that I will address in a future post.


Why It’s OK to be Normal

The normal distribution gets an unnecessarily bad rap.

I’m not saying that the random variables that make up the world are well approximated by normal distributions. Financial returns aren’t normally distributed. “100 year storms” in the financial world seem to come every 10 or so years. Wealth is not normally distributed. The top 1% of the US by wealth holds around 40% of the total wealth, making the distribution look more like a sharp, long tailed “power law” rather than a smooth hump like a normal distribution. Taleb’s book The Black Swan is filled with examples in which approximating a non-normal world with a normal distribution leads to disaster.

But just because the world is not well approximated with normal distributions does not mean that all analyses of risk premia have to center in on non-normality.

For example, consider David Beckworth’s explanation of the declining term premium in long term bonds. Beckworth’s argument is that because central banks have gotten better at controlling inflation, there’s less uncertainty over whether inflation will cause the real value of long term bonds to decline. This reduces risk premia on long term bonds.

I extended this argument in a blog post, pointing out the story isn’t just about lower uncertainty per se, but rather that better monetary policy means 1970’s style stagflations are going to be unlikely in the future. When the probability of stagflation declines, there is a lower chance that long term bonds and the economy do poorly at the same time. Because the nightmare scenario in which both long term bonds decline in value and the economy does poorly is less likely, then long term bonds are seen as less risky and so the risk premium declines.

In this very standard finance theory story, risk premia on an asset are not defined by the variance in the price of an asset, but rather whether that asset does poorly when people are hurting from recessions. Note that there’s no distributional assumption about whether future shocks look normal or not.

But now relative to this story about how central banking has changed the co-movement between the strength of the economy and long term bond prices, in comes Isabella Kaminska discussing non-normality. She points out that the declining bond risk term premium does not make sense because economies are becoming increasingly interconnected, and as such the distribution of future economic outcomes will look increasingly non-normal and extreme.

This is an important observation with regards to Beckworth’s risk premium theory because it may explain why markets would be wrong to overlook risk premiums. Boom and bust cycles, in terms of risk, are something of an irrelevance. In this new system of systems structure, the type of risk that matters most is system-destroying risk that threatens the entire interwoven web of systems.

But here we see a case in which concern about non-normality detracts from the fundamental story about why risk premia on long term bonds has fallen. The key factor driving risk premia is how assets pays off in bad times, not just how uncertain the payoff is. In fact, in times of crisis the prices of long term bond prices tend to spike up as people flee to safety. Therefore if the world looks increasingly non-normal with more and more financial crises, then it should be the case that the risk premia decline even further because it’s more likely that long term bonds pay off well when the rest of the economy is faltering.

The core of the message is that much of finance theory can be done in a distribution free manner, and that the relevant variable most of the time is now just how uncertain an asset’s price is, but rather how it will likely co-move with other economic variables in the future. In a future post, I will go on the offensive and show why the normal distribution is still very useful in spite of its poor fit to most economic events.

Conflicting Views on Inequality and Growth

A quote from a recent interview with Dani Rodrik helps shed light on some of the conflicting arguments surrounding the effects of income inequality on the political system and economic growth. In particular he points out that unless policies can mitigate the human costs of economic inequalities, the kinds of unpopular policies that promote productivity growth may not be possible.

Rodrik’s two arguments are:

1. Inequality causes politics to be much more sensitive to the needs of the rich, thereby creating a disconnect between the government and most of the population.

2. It causes a closing of society towards liberal reforms such as openness to trade and immigration.

The first argument is a very common one. This view embodies the apocalyptic vision of corporate lobbyists paying people to stand in line for congressional hearings in their place, thereby shutting out activists who might otherwise want to attend such hearings.

But the second argument describes how inequality can exert negative effects on growth by hurting the popularity of liberalizing reforms. The story here is that most policies that promote general productivity growth have the effect of causing a concentrated mass of losers while only having a diffuse benefit. If the U.S. government were to lower tariffs on Brazilian sugarcane, that would mean cheaper sugar for everybody in the United States. That’s certainly very, well, sweet, but on the other hand that would mean a great loss of wealth and employment for those who are currently in the sugar industry.

If there is a strong social safety net to mollify the effects of suddenly becoming very poor, then there might be less of an incentive to fight back against growth boosting reforms that have large diffuse benefits but small yet concentrated costs. This seems particularly relevant for an issue such as immigration. If there are social services to make relative poverty less likely, then there is less likely to be grumbling about “job stealing immigrants“. When unskilled workers are earning very low wages in the U.S., they’re going to complain if you let a lot more unskilled workers move into the U.S. But if conditions at the bottom of the economic ladder aren’t too bad, then natives might be willing to accept that immigrants aren’t just lumps of labor, and that their inflow will mean “there are more jobs building apartments, selling food, giving haircuts and dispatching the trucks that move those phones.” This might cause some relative gains and losses among natives, but because conditions don’t get too bad the natives won’t mind as much.

Another story along these lines is that higher inequality encourages higher levels of capital taxation. It’s generally agreed that taxing stocks of factories, houses, and other forms of productive capital is bad for long term growth because it discourages in productive investments in the future. However, if there is extreme inequality in wealth in society, then there will be populist pressures to raise capital taxes, thereby hurting long term growth. This in fact was the prediction of one of Rodrik’s own models with Alberto Alesnia, “Distributive Politics and Economic Growth“.

I find these two stories about immigration and capital taxation interesting because they point out that part of the problem behind economic inequality is the populism that it might engender. To avoid this populism, redistribution to the poor may be a second best solution. So even though a politician might want to pursue pro market policies such as opening the borders or lowering capital taxes, she might find it useful to also champion the existing welfare state as a means to mitigate the inequalities that those policies cause.

These stories also point out that sometimes, relative inequality does matter. Even though the American poor are very rich on global standards, if we are worried about the potential effect of economic inequality in the US on growth, it might well make sense to look at relative inequalities.


How Much is Bad Investing Costing You?

Investing advice tends to have lots qualitative suggestions but little quantitative measure of how important those suggestions are. As a result, advice ends up just telling people how important doing everything is, but there’s no transparent metric of how important each piece of advice is. This is a severe problem for investment advice, as when there are so many issues to think about it’s important to have some way to prioritize.

As a short list of issues to think about:

  1. How much am I paying in taxes? If I hold bonds in a regular IRA, the coupon payments will get taxed at a lower capital gains rate instead of my regular income tax rate. If I hold stocks in a Roth IRA, that means I get to pay significantly less for the larger capital gains in the future. So if some accounts get taxed more heavily than others, how should I optimally allocate assets across accounts?
  2. On the topic of asset allocation, do I have the right mix of stocks and bonds? I know that stocks tend to go up in the long run, but some simulations I read on the internet made me concerned. Even though stocks tend to go up in the long run, I can still manage to lose a lot of money over a long period of time. So how risky are my asset holdings really? And just because I get a few tenths of a percentage point of extra returns, how much should that be worth to me?
  3. Am I properly diversified internationally? One of the biggest questions in international finance is why portfolios are home biased. Why do people in the US buy US stocks while Europeans buy mostly European stocks? It can’t just be a story of the US stock market just earning higher returns or having lower risks, because if that were the case then Europeans would come flood the US market. So if there isn’t a big return gap, then a failure to diversify internationally must mean that I would be taking on too much risk. Instead of putting all their nest eggs in the US stock basket, I would be better off splitting their money between Europe and the US.
  4. How does my job figure into all of this? If I work at an auto company, I probably shouldn’t own my company’s stock because if the company goes down, so goes my job. That would also be a failure to diversify. Also, that means that if I live in the US, I should invest more abroad so that if the economy does poorly at home, perhaps I can capture the higher returns from investing abroad.
  5. How much am I losing to transaction costs and fees? If my employer offers me poor plans, is it still worth it to save in my 401K if I get matching contributions? And if not, how much is it costing me to buy high cost mutual funds? Would it be worth it for me to complain?

That these are only a small sample of the potential questions a person could ask is probably one of the reasons the field of “behavioral finance” exists. When these financial decisions really are so confusing, it’s important to have a model that accommodates under-optimizing behavior because it’s just too hard to optimize it all. As such, not only is it important to outline the directional arguments for investing in low cost index funds, for diversifying, for investing abroad, but there should be some source of easy quantitative reference and modeling tools to figure out how important these issues are relative to each other.

What Prediction Errors in Fed Funds Futures Tell us about Monetary Policy

The failure of fed funds futures to predict the start of the tightening cycle can be viewed through a risk neutral pricing perspective. Thinking about the risk premia embedded in Fed Funds Futures also illustrates the different risk properties of near term and long term bonds.

Fed Funds Futures are contracts that represent bets that pay off depending on where the Federal reserve sets interest rates in the future. If investors are risk neutral, then the price of a current Fed Funds future contract can be directly mapped into a probability that the Fed will tighten.

This sounds like a great idea, except for the fact that it has given horrible predictions for the past 5 years. The killer picture comes from a BofA reportshowing that although the Fed Funds futures curve has predicted rate hikes every year since 2009, interest rates have nonetheless stayed flat.

The failure of the Fed funds futures curve to predict rate hikes can be interpreted as a measure of how much market participants fear a premature rate hike. As I discussed in the context of inflation caps and floors, futures prices are a combination of the expected future price and the risk premia. The risk premia arises because market participants are scared of certain scenarios and are willing to buy insurance against them.

In this case, I conclude that the market is scared about a premature rate hike. Such a rate hike would put an end to the US economic recovery, and so the greater “pain” of this scenario gets translated into a larger contribution to the futures price. Sure, the physical expected value of the Fed funds rate in a year might be very low. But the risk neutral probability — which prioritizes painful events — of a rate hike is higher, and that is seen in the futures price. So even if those who short the Fed Funds futures consistently lose money, they’re in a trade that pays off if the Fed tightens too soon, i.e. they’re perfectly insured against a monetary policy error.

This might seem contradictory with my past analysis that, based on a similar risk premium analysis, long term bond markets seem to be expressing fear about low interest rate states of the world. In my view, this comes down to a difference of what long term and short term interest rates represent. The Fed controls the short term interest rate in the short run. Hence it is possible for Fed tightening to substantially raise short term interest rates. However, long term interest rates are related to the expected values of future short term interest rates. If the Fed tightens too much now and causes inflation to fall, then that will make long term bond yields lower.

This point about the difference between long term and short term interest rates was made forcefully by Bernanke in a recent blog post. Long term interest rates reflect primarily long term expectations. So if the Fed tightens too soon, that means we would expect both short term interest rates to rise and long term interest rates to fall. As such time variation in the risk premia of both long term interest rates and Fed Funds futures point towards market fears of the potential damage of an early exit by the Fed.

Robotic Comparative Advantage

Robots are going to take over all of our jobs. Except comparative advantage says that they probably won’t.

First, consider the stylized fact that investment in software and information technology hasn’t really grown as a share of private non-residential investment over the past decade. Sure, it had a dramatic run-up in the many decades prior to that, but it seems surprising to think that everybody is talking about how machines are going to take over everything while investment in the actual machines has been fairly low.



Ok, but let’s try and use theory to think about what might happen in the far future. The conventional view takes the set of jobs as some fixed quantity, and then argues that machines will take that fixed amount away. For a quote reflecting this view, consider a paragraph from the HBR article cited above:

And here is the even more sobering news: Arthur speculates that in a little more than ten years, 2025, this Second Economy may be as large as the original “first” economy was in 1995 – about $7.6 trillion. If the Second Economy does achieve that rate of growth, it will be replacing the work of approximately 100 million workers. To put that number in perspective, the current total employed civilian labor force today is 146 million. A sizeable fraction of those replaced jobs will be made up by new ones in the Second Economy. But not all of them. Left behind may be as many as 40 million citizens of no economic value in the U.S alone. The dislocations will be profound.

In this view, the math is obvious. There’s around 146 million workers in jobs. Machines will take away 100 million jobs. So then there are only 40 million jobs left. Throw on some people who can transition, and then the remaining 40 million will have no economic value. Take this to an extreme in which machines get even better, and even more jobs are displaced. In the limit, then there are no jobs (or perhaps only 1% of us will have jobs), and then the rest of us will be, as the HBR article describes “of no economic value”.

But this doomsday scenario is a direct contradiction of the theory of comparative advantage. Introductory economics teaches us that the relevant measure to figure out if someone can offer economic value is not the person’s absolute advantage at doing tasks, but rather their comparative advantage at doing something else. So long as not everybody’s opportunity costs are the same, then there are opportunities for trade. Sure, the U.S. has an absolute advantage at making clothes — we have fantastic factories and machinery to back them — but because we have higher value goods to produce we do not have a comparative advantage in clothes. As such we import most textiles from overseas.

In the robot scenario, there will be tasks that robots are relatively worse at, even if they can outcompete humans at most tasks. So long as there is some finite supply of silicon and metal and servers, then there will be more and less productive uses of computing power, and so there will be better and worse things that humans can do. Sure, computer vision might get really good, but are we willing to spend our computing power to make better toys relative to, say, more complex tasks in medicine? And if there is this allocation of computing power, then on the other side there must be an allocation of human power to do other jobs.

Now, we might need a sea change in the way we do regulation to make this workable. Minimum wages might need to be lowered so that it stays worthwhile to hire everybody. A stronger safety net and wage subsidies might be needed to make sure nobody falls through the cracks as overall material wealth increases. But fundamentally there’s no reason to believe trade will be impossible in a future in which most of our wealth comes from robot production.


Market-Based Probabilities: A Tool for Policymakers (Revised)

The gap between market forecasts of inflation based on securities prices and where inflation actually goes is a feature, not a bug. This gap is a risk premia that can be informative about what scenarios are worrisome to investors, and as such may be useful for policy makers deciding on how to weight the relative costs of inflation and deflation.

Justin Wolfers’ NYT article on market based inflation expectations explains how to derive inflation expectations from asset prices. In the article, he walks through an academic asset pricing paper that estimates a probability distribution for future inflation based on the prices of bets on inflation. The basic idea is that there is a betting market in which people can place bets on where they think inflation will be going. Just like how a bookie’s prices say something about the probability of certain horses winning a race, the prices on this inflation betting market make statements about the probability inflation ends up in certain zones.

Justin summarizes the findings:

While traders view inflation of roughly 2 percent as the most likely outcome, the market is also telling us the probability of other levels of inflation — or deflation. And it is saying that the risks of missing the 2 percent target are extremely unbalanced: It is twice as likely that inflation will come in below the Fed’s target as above it.

But there’s another aspect to asset prices that doesn’t show up for horse betting: risk premia. Whether inflation is high or low is related to the strength of the economy as a whole. In particular, if I were to tell you that there was going to be deflation in two years, your best bet would be that we were going through a double dip recession in which aggregate demand fell. You should then be willing to pay a premium to buy insurance against that scenario. In other words, you should be willing to pay better than fair odds that there will be deflation. Sure you might lose the bet on average, but when deflation hits and you lose your job, at least you got your racetrack winnings to cushion the blow.

Therefore the market forecast is equal to the true future expected inflation plus a risk premium that reflects whether low inflation or high inflation scenarios are scarier. If people are scared of a Japan style deflation, then the market forecast will underestimate true inflation. If on the other hand people are worried about 1970’s style stagflation, the market forecast will overestimate true inflation.

While this can be a nuisance if you want to get the best physical forecast of actual inflation, it can actually be tremendously valuable for central bankers who need to decide on whether to be more worried about the costs of high inflation or low inflation scenarios. For example, negative risk premia on inflation expectations tell policy makers that low inflation scenarios are much worse than high inflation scenarios. If this is the case, then the inflation target should be asymmetric — better to avoid scary deflation than deal with temporarily higher inflation.

Narayana Kocherlakota* made this argument in a recent macro seminar at the University of Michigan. (I’m borrowing the post title from his paper). In the context of a theoretical model he showed that the central bank’s objective function should focus on maximizing household welfare, not minimizing its own forecast errors. But based on the analysis above, the different levels of household welfare across different states of the world are embedded into the market forecast based on prices. So with some caveats about the financial constraints facing households, the central bank should try and make the market forecast equal the target.

As a more general point, this risk premium analysis shows how asset pricing is a form of quantitative psychology. Estimating risk premia helps answer the question “what do these asset prices say about the events that scare people”? And once policy makers know about these feared scenarios, they can adjust policy to make sure they don’t happen.

*As Narayana was quick to remind us, these are implications of a model from his own research, and not meant to represent the views of others in the Federal Reserve System.