Wednesday, April 10, 2013

Interest rate graphs

Where are interest rates going? Here are two fun graphs I made, for a talk I gave Tuesday at Grant's spring conference, on this question. (Full slide deck here or from link on my webpage here)



Here is a graph of the recent history of interest rates. (These are constant maturity Treasury yields from the Fed)  You can see the pattern:


Early in a recession, interest rates fall, but long rates stay above short rates. These are great times for holders of long-term bonds. They get higher yields, but prices also rise as rates fall, so they make money both ways. But you also see the see-saws. Interpretation: long-term bond holders are getting a premium for holding interest rate risk at a time that nobody wants to hold risks.

Then there is the flat part at the bottom of the recession. Now long-term bond holders get the yield, but interest rates don't change. Still, they're making money.

Then comes the interest rate rise, when long-term bond holders lose money. Obviously, you want to get out before interest rates start rising. But it's not easy. Nobody knows for sure how long recessions will last. (That seems to be the lesson of  more serious work too.) Look at all the fits and starts, all the zig zags in long interest rates. You don't want to be caught napping like in 1994. But if you, like me, thought last year or the year before looked like 1994, you got out too early. Welcome to risk and return. Notice in 2003 that long rates started rising long before the Fed did anything.


As I look at the fundamentals, current rates look pretty low. Will inflation really average less than 3% for the next 30 years, so you just break even on 30 year bonds?  But the criticism, "if we're in such trouble, why don't markets see it coming?" is still troublesome. So let's look at the actual market forecast


The solid blue line and red line are today's yield curve and forward curve. (This is the G├╝rkaynak, Sack, and Wright data). The blue forward curve is the market expectation of where interest rates will go in the future. You can lock in these rates today, so if you really know something different is going to happen, you can make a fortune. (This is why I'm not persuaded by arguments that the Fed is driving down rates below market expectations.) We can interpret this blue forward curve by the "consensus forecast." The economy slowly recovers, interest rates slowly rise back to normal levels (4%) consistent with 2% inflation and 2% real rates. The fall back to 3% rates at the long end of the curve seems a bit low, but that's the market forecast and always a good place to start prognosticating.

If the path of future interest rates follows the blue forward curve, there is no bloodbath in long term bonds: you earn this rate of return on bonds of all maturity at every date going forward. (Proving this is a good finance class problem.)

How good are market forecasts though? This may be the market's best guess, but a lot of the future is simply unknowable.  The thin blue and red lines show the forward curve and yield curve in April 2010. You can see that at the time, the consensus market forecast was for interest rates to rise starting sooner, and to rise more quickly. We all expected the recession to end quickly, as recessions usually do.

In 2010, the market forecast that today's interest rate would be 3.5%, not zero. I graphed that forecast and realization by the leftmost vertical arrow. Furthermore, the entire forward curve forecasts the entire forward curve. So, second point from the left, in 2010 the market forecast that today's one-year forward rate would be about 4.2%, not the tenth of a percent or so that we see. If the forward rate forecast is correct, today's forward rate curve should lie exactly on the 2010 forward curve. (Proving that is another nice problem set question for finance classes.)

So, from the perspective of 2010, we have seen quite a large, surprise, downward shift of the "market expectations" in the forward curve.  It has been a great few years for holders of long term bonds.

However, beware: What goes down can come up again. To those who say "interest rates are low, the market doesn't see trouble coming, why worry?" I think the graph shows the magnitude of interest rate risk. And risk goes in both directions.

So, I'm still doom and gloomy. But the danger we face is unpredictable. Large debts mean that the government is out of ammunition, didn't pay the insurance bill, the fire extinguishers are empty, we are prone to a run or a sovereign debt "bubble" bursting (I hate that word, but I think it conveys the spirit), choose your anecdote. We could have a Japanese decade. It could be February 1994, when spreads and recent history looked a lot like today's. Or we could be on the edge of Greece, whose interest rates were pretty low once upon a time as well. The market forecast interpolates between these options.

The first principle of portfolio maximization is risk management, not prognostication. There remains a lot of risk.

26 comments:

  1. The forward curve incorporates both expectations and a risk premium. How do you know the "high" 2010 interest rate forecasts weren't a risk premium rather than market expecations?

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    1. I don't. Neither do the "rates are low, don't worry, borrow like mad and blow it on stimulus" critics. This is the risk-neutral forecast, and if you know enough to ask the question, you know the answer. One could go down the line of "markets are expecting a calamity but there is a huge negative risk premium," but that seems pretty ephemeral. And I was trying to keep it simple for a blog post. As we both know, modeling risk premiums is really hard. But the evidence (Fama - Bliss) is that expectations works decently well, on average, for horizons over a few years.

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    2. Thanks. I wasn't trying to be snarky! I thought maybe you had a method for teasing out those two effects, or, more likely, evidence that risk premium effects are very small in situations like these. The evidence on expectations sounds interesting... my impression was that market expectations derived from forward curves were very inaccurate (failure of uncovered IRP etc) but sounds like I might be mistaken about that.

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  2. What strikes me looking at the first graph is the compression and expansion of the yields of the 10YR vs the 3MO seen during the cycles. Try plotting (WGS10YR - WTB3MS) on FRED. The spread hits zero right before a recession and hits about 3-4% when the economy exits recession. The pattern seems to work for the entire data series.

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  3. Addendum: I was using the weekly data.

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  4. re: "The fall back to 3% rates at the long end of the curve seems a bit low, but that's the market forecast and always a good place to start prognosticating"

    Forecasting any dip in treasury rates in the long run after they rise seems questionable unless there is real reason to believe the government will get its financial situation under control. Rising debt levels and eventually even potential credit downgrades seem like they will eventually impact interest rates, at a minimum preventing them from going down.

    Unless there are major changes there is a chance entitlement spending alone may be more than federal revenue within the next decade or two. That is based on an GAO's longterm forceast, and an update of GAO's longterm forecast from December with the "high cost" scenario for medicare (in addition to the "alternative medicare" forecast the GAO adds for its "current policy" scenario). Even just using the standard GAO forecast entitlements will eventually top revenue, meaning there is nothing left over to pay for interest costs or any other spending.

    More info here on the updated forecast (including an interactive graph, and links to papers on the potential for interest rates to rise as national debt levels rise):

    http://www.politicsdebunked.com/article-list/budget-lottery

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  5. My qualm with this article is that you don't address that interest rates today have been artificially depressed by government interaction and do not reflect true market forces or investor sentiment. Investors are desperate and searching for yield. Mindless capital is being allocated inappropriately. (ie. Japanese investors piling money into European sovereign's in search of yield).

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    1. "My qualm with this article is that you don't address that interest rates today have been artificially depressed by government interaction"

      The Fed may have had some impact on interest rates but the ten year rate is consistent with the long term trend so it is doubtful that the Fed has had much impact on long rates. The move by the Fed to buying MBS may be aimed more at perceived market failures than at long rates per se.

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    2. If the Fed's policies didn't have much impact on long term rates it implies that reversal of their policies shouldn't either. Do you really believe that? I don't think you'll find many people willing to stand in front of that train.


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    3. "Do you really believe that?"

      The general answer is yes. The details depend on which Fed policy you are talking about. Stopping QE might have some small impact and raise long rates. On the other hand, raising short term rates in the absence of healthy growth might well actually reduce the long term rate.

      But what do I know - when long term rates hit 4.3% I thought it was stupid low and sold all of my long (over twenty year) bonds.

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  6. John, interesting slides. I think some light can be shed on why rates are so "low" by looking at long-term safe sovereign yields across the globe. There we see a similar pattern of long-term yields falling. They all start falling at the time at the beginning of the crisis and have yet to let up. My view is that (1) the disappearance of many private safe assets during the crisis and (2) the spate of bad economic developments since then has elevated and subsequently sustained the demand for safe sovereigns.

    Bernanke recently had a great speech on this development. Here was my response to it:
    http://macromarketmusings.blogspot.com/2013/03/bernankes-friday-night-special-part-i.html

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  7. John,

    This is what one would expect as the twin laws of information, Moore's law and Metcalf's law, are applied and the most important factor of production, information, makes capital less and less valuable.

    We have not reached a point of a negative feedback loop. We know that information is making capital less valuable in the future, so it has less value now.

    People are just happy that we don't have Kimball's electronic money.

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  8. How can the Fed expect any sort of real recovery with near zero interest rates? Who wants to lend at that rate?

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    1. The banks have excess reserves. We have a shortage of borrowers, not a shortage of lenders.

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  9. Just one devastating comment. The curves you show mean nothing (or very little) without error bars attached to them. Try to estimate the errors (not easy), which should increase with time, and the curves will acquire some meaning. Forecast curves like those above should never, never be published without error bars.

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    1. These are pure data, not estimates.

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    2. Forward and yield curves for 2040? Pure data?

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    3. Rafal,

      Read the link that John provides:

      http://www.federalreserve.gov/pubs/feds/2008/200805/200805pap.pdf

      "Rather than fitting a spline-based, nonparametric curve, we impose some structure on the shape by imposing a parametric form that fits the TIPS yields remarkably well. The benefit of the parametric approach is that it smoothes through the idiosyncratic movements in yields of individual securities and accurately represents the underlying shape of the (real) discount function. The yield curves that we fit assume that the instantaneous forward rates (whether real or nominal) follow the functional form..."

      Basically what they are doing is taking the individual data points, formulating a best fit curve for those data points, and extrapolating that data forward in time.

      So your suspicions are correct. This is not "pure data".

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    4. No, it's not "forward in time" it is fit "across maturities." This is not a forecast, it is an interpolated and smoothed version of today's prices (y axis) plotted against maturity (x axis).

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    5. John,

      I thought we were discussing the forward curve, not the market yield curve. It is unclear from the graph what m-year forward rates beginning n-years hence are being represented.

      Are we looking at a 1 year projection from now where the entire yield curve will be or are we looking at a projection of where 1 year rates will be 1 to 29 years from now?

      Are we looking a a forecast for Fed policy (short term interest rates) or are we looking at a forecast for fiscal policy (maturity spectrum) ?

      "The yield curves that we fit assume that the instantaneous forward rates (whether real or nominal) follow the functional form..."

      Anytime someone uses the word assume, I get wary.

      Have you given any more thought to government equity?

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  10. The way I see it as a simple minded investor is that long term bonds are at an all time high. They have a lot more room to go down, than they have to go up. I am staying in cash until the market returns to something resembling historic averages where there is more room on the upside.

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  11. That's right, but they are not forecast curves. The forward and yield curve represent prices today.

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    1. "The blue forward curve is the market expectation of where interest rates will go in the future."

      Here is what forward interest rates really are:

      "An alternative way of describing the yield curve is in
      terms of forward rates. We can solve for continuously-compounded instantaneous forward rates at all horizons. Or we can solve for m-year forward rates beginning n-years
      hence."

      You can solve for m-year forward rates beginning n-years hence as long as m + n < duration of longest security sold. For instance, you can solve for 5-year securities 10 years from now by looking at the price of existing securities that have 15 years of remaining maturity.

      Trying to forecast the price of 20 year securities 20 years from now is just a guess because those securities don't exist yet.


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  12. I made a handy animation of the LIBOR/Swap curve a few weeks ago. Fun to watch, especially as it heads into 2006-2008.

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    1. Very cool visual that is particularly helpful to demonstrate fixed income risk to less sophistocated (or even all) investors.

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