PERSPECTIVE3-5 min to read

Treasury yields: what will happen to risk premia as the Fed reverses QE?

We estimate that a gradual unwind of the Fed’s Balance sheet could push Treasury yields higher – but by how much? This paper sets out our calculations and methodology.

12-12-2022
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Authors

Robert Scott
Official Institutions, Strategic Client Group

We estimate that a gradual unwind of the Fed’s Balance sheet could push Treasury yields higher. If the Fed’s projections for the unwind are achieved, official sector holdings of Treasuries will fall from 35% to 20% of the total amount outstanding. This will push the 10-year risk premium up by an expected 130 basis points (bps) – although it could be as little as 35bps and as high as 215bps over the next 30 months.

This is based on an analysis of the relationship between official sector holdings of Treasuries and the term or risk premium derived from the yield curve using an affine term structure model. This rise in the risk premium is independent of the outlook for inflation and real rates.

This paper sets out our forecast and methodology in more detail.

In recent months, market observers have focused on the implications of the coming unwind of the Fed’s balance sheet and the potential impact on the US Treasury bond market. This is almost unprecedented in modern financial markets and there is little historical data to guide us on what the impact might be on yields. We cannot assume yields will just rise to pre-QE levels, since the level of inflation and the structure of the economy today is very different to how things were before the global financial crisis.

We are, of course, referring to central banks, particularly the Federal Reserve and large foreign exchange reserve-holding central banks around the world.

Since 2008, with quantitative easing, the Federal Reserve has accumulated a large holding of US Treasuries with the express aim of pushing longer-term yields lower and therefore stimulating investment in the economy. This was motivated largely by the global financial crisis and the more recent Covid pandemic. These purchases were made regardless of the yield and expected return on Treasuries.

Low yielding Treasuries pushed many marginal investors into other markets around the world in search of better returns. These capital flows threatened to overwhelm exchange rates of exporting emerging economies who chose, instead, to stabilise their exchange rates, preserve their exporting industries and accumulate reserves by holding US Treasuries as well. This was also a rational act that manifests as risk-agnostic behaviour, even though there are perfectly reasonable objectives that are achieved by central banks holding Treasuries.

The result of this cumulative behaviour is where we are today. Central banks now hold around 33% of US Treasuries outstanding, and the risk premium received by investors in US Treasuries has been negative for the better part of a decade (although it does depend on which measure you use). Of interest is the strong relationship between the portion of Treasuries outstanding held by central banks (the return-agnostic investors) and the compensation paid to investors for bearing duration and inflation risk. Observation of this relationship gives an interesting opportunity to hypothesize as to the impact of an unwind of at least a portion of these holdings on the yield level and returns in the Treasury market going forward.

Risk premia exist because most investors are risk-averse and require a premium to assume investment risks. In capital markets theory, this explains why the capital market line in CAPM (capital asset pricing model) is upward-sloping. In the US Treasury market, it explains why the yield curve is on average upward-sloping and why forward rates tend to overpredict future realised spot rates[i]. For Treasuries, expected returns and yields are neatly described by former Federal Reserve Chairman Ben Bernanke:

“It is useful to decompose longer-term yields into three components: one reflecting expected inflation over the term of the security; another capturing the expected path of short-term real, or inflation-adjusted, interest rates; and a residual component known as the ‘term premium’. Of course, none of these three components is observed directly, but there are standard ways of estimating them.”[ii]

The estimation of the risk premium is usually produced with what is known as an affine term-structure model. This is an elaborate statistical model that imputes, through analysis of the variation across the yield curve and across time, what the essential components are. The key benefit from this approach to modelling the yield curve as compared to splines and principal component analysis is that one is able to derive an estimate of the risk premium paid to investors to bear risk in the market.

The downside of course is that this family of models is among the most complex available in empirical finance. Rather than building our own model we have adopted the estimates from two popularly used models, one from the Federal Reserve[iii] and the second from the Bank for International Settlements[iv]. Chart 1 shows the long-term history of these two measures on the term premium of the 10-year Treasury yield.

606728_Webcharts_01

In normal circumstances, the risk premium is positive and reflects the marginal degree of risk aversion in the market, or the extra return demanded by investors to be indifferent to holding a long maturity note or bond versus a strategy of rolling over a succession of short-term investments like t-bills. Usually, the investor prefers the short-term strategy over the longer-term holding because they are averse to inflation surprises, which are asymmetrically risky in the upward direction.

Starting during the global financial crisis, the Federal Reserve in pursuit of quantitative easing and other central banks through the accumulation of foreign exchange reserves, bought Treasuries at any price, regardless of the expected return or yield.[i] At the same time, however, the US government has greatly increased the amount of debt outstanding. If the government simply borrows from the Federal reserve, there is less of a likelihood of an effect on the market, and so we have measured this anomaly as central bank holdings (including the Fed) as a percentage of total outstanding debt. In addition, and this might be a presumptuous leap, we have measured non-US central bank holdings of US Treasuries as official sector holdings of US Treasuries as reported in the US Treasury TIC data. This data also includes holdings from sovereign wealth funds and other government agencies. It could be argued that SWF holdings of Treasuries arise from the same balance of payment issues that can lead to accumulation of central bank reserves. It is not always the case, but as the data seems to indicate, it’s a pretty good corollary.

We have chosen to focus on the risk premium as measured by the BIS model[ii], which is based on the methodology developed in Hoerdahl and Tristani (2014). The differences in term premia at the 10-year maturity is largely due to differing assumptions in the models used to estimate them. For a detailed description of the various models used to estimate term premia, the reader is encouraged to consult Cohen, and Xia (2018)[iii] While the trends and dynamics are similar for both models, the magnitude of shift and correlations are much stronger for the BIS model as we shall see shortly.

Risk premia in the 1990s were in a much healthier and positive range than the current environment. Chart 2 shows the long-term history of our chosen proxy for the term premium overlaid with the percentage of holdings of US Treasuries by the official sector. Hopefully for most viewers, the relationship should be apparent. We have tested the two series to determine if there is a strong statistical relationship, in econometric circles, known as “cointegration”, and the results are strong in favour of this. What this means is that although both series are not mean-reverting, there is a strong tendency to revert towards each other. Or, more accurately, the risk premium tends to drift in the direction implied by official sector holdings. This is strong evidence that there is some basis for inferring a causal or structural relationship between the two.[iv] It also gives us a strong basis to make inferences about a change in Federal Reserve holdings and the impact on the risk premium in the future. In the next section we will estimate what a likely reduction in Federal Reserve holdings will mean for the 10-year term premium.

606728_Webcharts_02

Unwind of QE and the rise in the term premium

Given the strong statistical relationship between official holdings and the term premium, we have estimated the likely impact of an unwind of a portion of the Federal Reserve’s holdings of Treasuries over the two and a half years (until end 2025). Chart 3 shows the modelled relationship and the estimated change for such an unwind.

606728_Webcharts_03

The Federal Reserve has been more explicit in recent months as to the extent and pace of the reduction in its balance sheet. We have used a simple assumption of USD 60 billion decline per month for the estimation period. This is in line with the Federal Reserve’s latest projections, although it is only meant as a rough estimate since the Fed will always maintain some flexibility to react to current circumstances and there are many potential mark-to-market effects that are difficult to predict.

There is also the issue of market efficiency. Any relationship between a market price, like a risk premium, and publicly available information, cannot be relied upon to evolve slowly over time. Information could in principle be priced in very quickly and so our simulation should not be considered reliable from a temporal perspective. There is nothing to stop this adjustment from moving faster than the pace of the Fed’s unwind, as appears to be the case in 2013/14 where expectations for Fed unwind of QE moved very quickly (the so-called “taper tantrum”). Recent market volatility suggests that some of this may have already been priced in.

The reduction in the Federal Reserve’s balance sheet over the next two and a half years, assuming central bank reserve levels remain constant, results in a reduction of the official holdings as a percentage of Treasuries outstanding to 20% and implies a rise in the risk premium from around zero currently to plus 122 basis points. Given the standard error of the estimate, there is a 95% chance that the rise in the term premium will be between +36 basis points and +215 basis points. This is independent of what happens to monetary policy, inflation and growth. Given the current yield of 2.77% and unchanged real and inflation rates, this could amount to a loss of 2.89% on the 10-year on a one-year horizon and -3% over the next three years[i].

While investors are very focused on this new economic environment we find ourselves in, it is important to keep in mind that getting growth, inflation and the monetary policy response correct, may not be enough to get the bond market right this time around.

Term premia could be the big surprise that upsets the Fed-watchers this cycle. Investors should also be cognisant of how a 100 bp rise in 10 year yields might affect the Fed’s reaction function: it could potentially become less willing to tighten further. “Quantitative tightening” could feed into the broader policy decision through its effect on financial conditions, further complicating the bond market reaction.

It should be reinforced here that these returns are not forecasts per se but are simulations based on risk premia rising to their modelled levels and rely on the assumptions that no other factors impact yields, central banks continue to hold treasuries at the same level they currently hold and that the Federal Reserve reduces its balance sheet along the lines of what has already been announced. The standard errors and resulting large range of plausible forecasts should also be noted.

[i] For example, see Fama, Eugene F. “Forward rates as predictors of future spot rates,” Journal of Financial Economics, 3 (1976), pp. 361-377

[ii] Bernanke, Ben S., Long-Term Interest Rates, At the Annual Monetary/Macroeconomics Conference: The Past and Future of Monetary Policy, sponsored by Federal Reserve Bank of San Francisco, San Francisco, California, March 01, 2013, https://www.federalreserve.gov/newsevents/speech/bernanke20130301a.htm

[iii] Tobias Adrian, Richard K. Crump, and Emanuel Moench, "Pricing the Term Structure with Linear Regressions," Journal of Financial Economics 110, no. 1 (October 2013): 110-138.

[iv] P Hördahl and O Tristani, “Inflation risk premia in the euro area and the United States”, International Journal of Central Banking, September 2014

[i] It should be noted here that expected return and yield are not the same thing, but they should be similar in magnitude.

[ii] P Hördahl and O Tristani, “Inflation risk premia in the euro area and the United States”, International Journal of Central Banking, September 2014

[iii] https://www.bis.org/publ/qtrpdf/r_qt1809h.pdf

[iv] An Augmented Dickey-Fuller test confirms that the residuals of the regression between the two series do not have a unit root (are mean reverting).

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Authors

Robert Scott
Official Institutions, Strategic Client Group

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