2019-03-15Macro `n Cheese

# Stop being so sensitive!

You’d be forgiven for thinking the title refers to financial prima donnas, when in fact I’m reflecting on something that has populated a fair share of my conversations with clients – the looks and moves of the yield curve.

Today, I thought we could take a deeper look into how short- and long-term interest rates move over different frequencies in (some) accordance with a really interesting and recently updated staff-paper from FED NY. In that paper, the authors found a statistical break point in yield curve behavior around the turn of the millennium, which they suggest is primarily related to lower beta of short- and long-term real rates. Since 2000, the low-frequency co-movement has receded quite dramatically, which would suggest, among other things, that we might be prone to over-interpret event shocks such as the introduction of QE or that the risk-taking channel of monetary policy is perhaps less pronounced than previously assumed. A more hands-on observation is that it could also be interpreted as investors becoming more yield-oriented post 2000, and whence the yield reaches a certain level they pour into the (government) bond market.

## Easier said than done

Most financial analysts agree that the short-end of the yield curve is largely a reflection of the monetary policy stance. On the longer end of the yield curve, there may be agreement in theory, but less so in practice. The instinctive, and theoretically appealing, answer most analysts would conjure to explain long rates would be some variation of the so-called Expectations Hypothesis: Long-term interest reflect investors’ expectations on future short-term interest rates. When the expectations on future short rates deviate from the observed long rate, arbitrage trading will eventually bring them in line. The problem is that the expectations theory has been rejected in almost all empirical studies. The reason is of course that it is void of many inherent and changing uncertainties – risks – when estimated[1]. For government bonds, one such risk is the changing “term premia”; the compensation investors demand to hold a long-term bond outright instead of rolling over investments in a sequence of short-term bonds.

[1] Chief among these the fact that the willingness to bear risk changes over time and for a host of reasons.

## Co-movements of rates depend on the horizon

To study how the sensitivity of long-term interest rates to short-term interest rates varies over different frequencies I have simply regressed changes in 10-year government bond yields (“long rates”) on changes in 1-year yields (“short rates”) over different frequencies (change over 1 day, over 1 month, over 2 months, over 3 months etc.). The sample is divided in two periods, “pre-2000” and “post-2000” in accordance to the FRBNY-findings mentioned above.

Note: The chart plots the estimated regression coefficients (‘β’) against the horizon (‘h’) in the two samples (pre and post year 2000) according to: ${y}_{t+h}^{10}-{y}_{t}^{10}={\alpha }_{h}+{\beta }_{h}\left({y}_{t+h}^{1}-{y}_{t}^{1}\right)+{\in }_{t+h}$  ; where the dependent is the h-month (absolute) change in the 10-year nominal yield (in bps) and the dependent is the h-month (absolute) change in the 1-year nominal yield (in bps).

Before the turn of the millennium, a one percentage point change in short-term rates over different frequencies yielded a very stable change in long-term rates of between 0.5 and 0.6 percentage points. After 2000, however, the sensitivity of long-term rates to short-term rates become considerably more dependent on, and declining with, the horizon. The sensitivity – the beta – on high frequencies is considerably higher post-2000 with the beta exceeding 0.8 on daily changes and almost touching below 0.3 on 12-month changes.

Ok, so “short term” (or, rather, high frequency) co-movements in short and long-term rates are very strong, while “long term” (or, rather, low frequency) co-movements in short and long-term rates have almost disappeared. Now, what does this mean?

– First of all, and in line with previous studies, both samples suggest positive co-movement of short and long-term interest rates. This, in turn, contradicts the expectations hypothesis, at least as long as we assume that long-run inflation expectations are well-anchored. In particular, the earlier sample period (pre-2000) does raise some questions on the stability of long-run inflation expectations as a high beta is visible over all frequencies.

In the latter sample period (post-2000), the high sensitivity to short-term rates is only present at high frequencies and decreases dramatically at lower frequencies. This pattern probably stems from the observation that over the past couple of decades, increases in short rates have predicted (a flattening of the yield curve and) a subsequent decline of long rates. Since 2000, thus, the term premia has infallibly risen, albeit only temporarily, following increases in short rates.

## Concluding discussion

From our discussion above and looking closer at the graph, it doesn’t seem overly speculative to blame the high and stable “pre-2000” sensitivity of long-term rates on shocks to (primarily long-term) inflation expectations. The low “post-2000” sensitivity of long-term rates, at least at lower frequencies, goes hand in hand in hand with more stable inflation expectations after the “great moderation”. So why is the post-2000-sensitivity even stronger at higher frequencies? – Possibly, investors have become more yield oriented, targeting a certain portfolio yield that when reached make them pile into bonds. Related, it can be that bond demand falls relative bond supply when (short term) rates initially increase and rebounds as (long-term) yields become attractive again. This would result in higher long-term rate sensitivity at higher frequencies (relative lower frequencies).

Under any circumstances, the new pattern identified post-2000 nonetheless implies that a lot of the event-studies we have relied on (using high-frequency changes of long-term yields) to, i.a., identify the effects of unconventional monetary policy (UMP) measures are exaggerating the impact of UMP-measures as effects on long-rate seem to peter out over time. It also implies that empirically calibrated monetary policy models may exaggerate the risk-taking channel as the previously more or less permanent effect on term premia (from changes to short-term rates) has become more transitory to its nature.

But, la pièce de résistance, which I have not touched much upon here, is perhaps that bond markets have become more and more predictable, which – in turn – should be possible to explore. At least for a while.

P.S. If you use the change region function in the MB-application, you can see if your favorite economy demonstrates the same pattern as the US economy. Below are a few such examples – If you want help, ask your friendly, local MB representative:

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