Interesting stuff. But would it have hurt the creators of the second graph to show both series on the same axis? I'm pretty sure you'd see the same pattern, but using two axes is more confusing and looks fishy. Also (nitpicky): Why let the vertical axes go into the negatives if probabilities can't be negative?

The figure does not look fishy at all. The negative signs in the vertical axis should not hurt your eyes as long as the lines do not go below zero, which is the case. Let's try to be more constructive with our comments here.

How is this not constructive? I literally point to a concrete way in which the graph can be improved. And using two axes simply makes this graph more confusing than it needs to be: It's very natural for a human to follow the blue graph to the right, see the number next to the line and think that the most recent probability is 80%, which it's not. Also annoying: The points where the lines cross, are actually not the points in which the series have the same values. And very little is gained by using two axes: I'm pretty sure you'd see the same pattern if you use one axis. Granted: The negative value comment is a bit nitpicky, but if the figure's lowest value was zero, it would be easier to see how close the value of the blue line is to zero, which could be useful. It's not the most confusing graph I've ever seen, but it's more confusing than it needs to be.

I don't know if it is the right way to put it. The issue here is that the densities you are what we call risk-neutral densities as opposed to physical densities.

While the later describes the likelihood of different future paths of the time series, the former reweighs them using investor preferences. In other words, it's mixing preferences and expectations.

In the link to the Fed's page, they explain policy makers like to mix preferences and expectations because they like to think in terms of well being those densities happen to distort information in a way that puts more weight where gains and losses matter the most to investors.

As a last detail, it is often found in option pricing that market participants tend to put a lot of weight on larger deviations from current values of the underlying (here, CPI inflation) -- more than would be the case if you tried to estimate the probabilities of large deviations using just the time series for the underlying.

I had not noticed the scale difference. Thank you Mark Dijkstra. It looked like 80% probability of inflation exceeding 3%. That is worrisome. 40% is iffy.

Inflation options are a better measure of inflation *aversion*, not expectations, and as they are a hedging instrument they tend towards extreme values: https://www.sciencedirect.com/science/article/abs/pii/S0304405X13002274. Look at the long tails on those probability densities.

TIPS spreads are still well below 3% across the term structure, and the Cleveland Fed's inflation expectations measures (which strip out inflation and real risk premia) are under 2% across the term structure. 1.5% for 3- and 5-year.

Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.

Interesting stuff. But would it have hurt the creators of the second graph to show both series on the same axis? I'm pretty sure you'd see the same pattern, but using two axes is more confusing and looks fishy. Also (nitpicky): Why let the vertical axes go into the negatives if probabilities can't be negative?

ReplyDeleteThe figure does not look fishy at all. The negative signs in the vertical axis should not hurt your eyes as long as the lines do not go below zero, which is the case. Let's try to be more constructive with our comments here.

DeleteHow is this not constructive? I literally point to a concrete way in which the graph can be improved.

DeleteAnd using two axes simply makes this graph more confusing than it needs to be: It's very natural for a human to follow the blue graph to the right, see the number next to the line and think that the most recent probability is 80%, which it's not. Also annoying: The points where the lines cross, are actually not the points in which the series have the same values. And very little is gained by using two axes: I'm pretty sure you'd see the same pattern if you use one axis.

Granted: The negative value comment is a bit nitpicky, but if the figure's lowest value was zero, it would be easier to see how close the value of the blue line is to zero, which could be useful.

It's not the most confusing graph I've ever seen, but it's more confusing than it needs to be.

Yes, but as you have said often, markets are terrible at predicting the future paths of both inflation and nominal interest rates!

ReplyDeleteI don't know if it is the right way to put it. The issue here is that the densities you are what we call risk-neutral densities as opposed to physical densities.

DeleteWhile the later describes the likelihood of different future paths of the time series, the former reweighs them using investor preferences. In other words, it's mixing preferences and expectations.

In the link to the Fed's page, they explain policy makers like to mix preferences and expectations because they like to think in terms of well being those densities happen to distort information in a way that puts more weight where gains and losses matter the most to investors.

As a last detail, it is often found in option pricing that market participants tend to put a lot of weight on larger deviations from current values of the underlying (here, CPI inflation) -- more than would be the case if you tried to estimate the probabilities of large deviations using just the time series for the underlying.

The CPI data today seems to indicate that markets are not too far off. Cumulative CPI is 2.7%, annualized is 6.5%. This is serious.

DeleteI had not noticed the scale difference. Thank you Mark Dijkstra. It looked like 80% probability of inflation exceeding 3%. That is worrisome. 40% is iffy.

ReplyDeleteInflation options are a better measure of inflation *aversion*, not expectations, and as they are a hedging instrument they tend towards extreme values: https://www.sciencedirect.com/science/article/abs/pii/S0304405X13002274. Look at the long tails on those probability densities.

ReplyDeleteTIPS spreads are still well below 3% across the term structure, and the Cleveland Fed's inflation expectations measures (which strip out inflation and real risk premia) are under 2% across the term structure. 1.5% for 3- and 5-year.

https://www.clevelandfed.org/our-research/indicators-and-data/inflation-expectations.aspx