Real government bond yields are indicators of standard market risk premia and implicit subsidies. They can be estimated by subtracting an estimate of inflation expectations from standard yields. And for credible monetary policy regimes, inflation expectations can be estimated based on concurrent information on recent CPI trends and the future inflation target. For a data panel of developed markets since 2000, real yields have displayed strong predictive power for subsequent monthly and quarterly government bond returns. Simple real yield-based strategies have added material economic value in 2000-2023 by guiding both intertemporal and cross-country risk allocation.

The below post is based on proprietary research of Macrosynergy.

A Jupyter notebook for audit and replication of the research results can be downloaded here. The notebook operation requires access to J.P. Morgan DataQuery to download data from JPMaQS, a premium service of quantamental indicators. J.P. Morgan offers free trials for institutional clients.

This post ties in with this site’s summary of implicit subsidies in financial markets.

## Why real yields are indicative of risk premia and implicit subsidies

Real government bond yields are annualized yields to maturity minus estimates for expected annualized inflation from today to maturity. Technically, they are estimates and not directly observable, but reasonable inflation models can be constructed based on common sense and macro-quantamental data (see below). Real yields are plausible indicators of both standard risk premia and implicit subsidies in bond markets:

**Standard risk premia**are__compensation for exposure to uncertainty that clears an efficient market__. They arise from the uncertainty of payoffs and depend on the correlation structure contract returns and agents’ aversion toward risks. All other things equal increases in risk premia charged by investors in bond markets manifest as increases in real bond yields.**Implicit subsidies**are expected returns over and above the risk-free rate and conventional risk premia (view summary here). They arise from large transactions or other types of market interventions with motives other than conventional portfolio optimization. Such motives include government policy agendas, convenience yields (non-standard benefits of owning an asset), and behavioral biases, such as salience bias and loss aversion. Implicit subsidies are akin to__fees for services__. In government bond markets, these subsidies, or conversely charges, often arise through monetary policy, financial regulation, and tax laws. For example, under non-conventional monetary policy, central banks reduced real yields and expected returns through duration extraction, i.e., shifting bonds and duration risk onto their balance sheets (view post here). This policy and its market impact were not motivated by financial risk-return optimization.

Tracking a reasonable estimate of real interest rates incurs only modest information cost. However, related returns are not altogether a “free lunch”. Conventional risk premia are fair payments for uncertainty. Implicit subsidies have their own drawback: ultimately, they attract crowds and, like all crowded trades, incur the risk of sudden outsized drawdowns when conditions change. This is a form of “setback risk” or “endogenous market risk” (view summary here).

## How to calculate generic real government bond yields

This analysis uses generic government bond yields and inflation expectation metrics of the J.P. Morgan Macrosynergy Quantamental System (“JPMaQS”). The daily time series of the system are generally point-in-time information: they represent what the market knew about the variable at the end of a day. This “timestamping” and use of “vintages” does not matter much for market data, which are not revised or released with lags. However, quantamental data are a more reliable way to incorporate macroeconomic data, such as inflation, for the purpose of backtesting.

__Government bond yields on JPMaQS are taken from zero-coupon yield curves calculated based on J.P. Morgan price data using interpolation__ for the maturities between the liquidly traded contract prices (view documentation). Yield data of this quality are available for nine developed markets: Australia (AUD), Germany (DEM), Spain (ESP), France (FRF), the UK (GBP), Italy (ITL), Japan (JPY), New Zealand (NZD), and the U.S. (USD). This analysis focuses on 5-year yields, albeit the analysis can be extended to other maturities such as 2-years and 10-years in the attached notebook. The starting point of the data is different across countries, and only the U.S. series goes back to 2000.

To calculate real 5-year bond yields, __we subtract 5-years ahead inflation expectations according to the Macrosynergy method__ (view documentation). The estimate assumes that market participants form their __inflation expectations based on the recent inflation rate (adjusted for jumps and outliers) and the effective inflation target__. For recent inflation, this metric uses an average of headline and core inflation. For the 5-year forward horizon, the weight of recent inflation to the effective target is 1/5 to 4/5. This implicitly assumes a linear convergence of inflation to its target. The effective inflation target is the mean of the target range announced or implied by the authorities plus an adjustment for past “target misses”, which is the last 3 years’ average gap between actual inflation and the target mean (view documentation). Altogether, this is a one-size-fits-all generic and formulaic way to estimate inflation expectations for all countries with inflation-focused monetary policy regimes.

For some analyses, we want to __distinguish between credit risk premia and other components of the real yield__, such as interest rate risk and implicit subsidies. Therefore, we also calculate credit spread-adjusted real yields by subtracting 5-year sovereign credit default swap (CDS) spreads where available. Again, these spreads have been taken from J.P. Morgan trading data (view documentation here).

Real yields are considered predictors for subsequent monthly or quarterly government bond returns. The target returns are also taken from JPMaQS and represent generic zero-coupon bond cash returns at the 5-year maturity and are based on interpolated zero-coupon yield curves (view documentation).

## Evidence of highly significant predictive power

Panel analysis shows a very strong predictive relation between real bond yields and subsequent cash returns for the available data set since 2000. The below graph displays a panel scatter plot of quarter-end real 5-year government bond yields and subsequent quarterly returns. There has been a strong and highly significant positive relationship. __Pearson correlation between period-end yield and next-period return has been over 40% at the quarterly frequency and 26% at the monthly frequency__. Non-parametric correlation (Kendall tau) has been slightly lower at 29% and 18% but still sizable. The monthly balanced accuracy, i.e., average correct prediction of the sign of subsequent monthly returns, has been over 56%, even though the real yield signal had a slight short bias (44% positive signals) and returns had been mostly positive (61% of all months).

__The positive predictive relation is statistically highly significant, with a near 100% probability of being non-accidental__ according to various tests. Most importantly, this significance has been ascertained by using the Macrosynergy panel test (view post). This test recognizes that country experiences are not independent and subject to common factors. Simply stacking data can lead to “pseudo-replication” and overestimated significance of correlation. A better method is to check significance through panel regression models with period-specific random effects. This technique adjusts targets and features of the predictive regression for common (global) influences. The stronger these global effects, the greater the weight of deviations from the period-mean in the regression. Simply put, __the combination of intertemporal and cross-country relations of real yields and subsequent returns confirms the positive predictive power__.

The predictive power of relative cross-country real yield differences is shown below. The isolated intertemporal predictive power can be verified by using the U.S. data set. Using the U.S. time series alone, the quarterly correlation coefficient of real yields and subsequent returns remains 25% and is highly significant.

__If one subtracts CDS spreads, real yields retain highly significant predictive power,__ even though some of the risk premia are disregarded by this metric and prediction performance statistics are somewhat lower. Correlation coefficients of period-end adjusted real yields and subsequent 5-year government bond returns have been 33% at quarterly frequency and 20% at monthly frequency. The balanced accuracy of CDS-adjusted returns has been over 56%, as high as for regular real yields.

We __estimate the economic value of real yields as government bond allocation signal by calculating standard naïve PnLs in accordance with a generic procedure__ used in many previous Macrosynergy research posts. A naive PnL is calculated for signals that depend on the real bond yield at the end of each month and that serve as the basis for the positions of the next month and under consideration of a 1-day slippage for trading. We derive two standard types of signals that determine the size (USD value) of the bond positions in each market:

- A
**proportionate signal**is simply a normalized value of the real yield (using panel standard deviations up to the date of the signal). Signals are capped at 2 standard deviations in either direction for each currency area as a reasonable risk limit. - A
**binary signal**simply takes a unit long or short position in each bond market in accordance with the sign of the real yield.

__These signals are not optimized. They are merely the simplest versions of their kind__ and are designed to test proofs of concept. Also, the naïve PnL does not consider transaction costs or compounding, as these depend on institutional circumstances and can interfere with assessing the “pure” value generation of the signal. Finally, for the chart below, the PnL has been scaled to an annualized volatility of 10%. This does not simulate proper volatility targeting but is merely a transformation for easier graphical representation.

We test the economic value of the real yield signal in two ways.

- First, for unbiased or balanced signals, as described above, we check for consistent long-term PnL generation without a systematic long bias.
- Second, we calculate related long-biased signals by adding one standard deviation to the balanced signals and compare the related PnLs to a long-only portfolio.

Finally, note that all the below PnLs are based on uneven panels, i.e., countries could only be considered for a specific month if feature and target data were available.

The naive PnLs of strategies based on __balanced real yield signals have produced material economic value without long-term bond market correlation__. The average Sharpe ratios since 2000 have been 1.1 for both the proportionate and binary signals. Seasonality has been modest. The proportionate signal had only one longer period (2019-2022) of failure to generate PnL.

Moreover, __the long-biased strategies have materially outperformed a long-only book of equal long positions in all 9 markets__, as illustrated in the graph below. The long-only book has had a good performance in its own right since 2000, with a long-term Sharpe of 1.0. However, the overlay of the real-yield signal for intertemporal and cross-sectional allocation would have lifted the ratio to 1.5 both for the proportionate and binary versions of the signal.

## Evidence for real yields as predictors of relative bond returns

Further, it can be shown that __also relative real yields have been highly significant predictors and material PnL generators__. To show this, we calculate real yields as relative yields of one country versus all the other available ones for each period. Due to a lack of non-U.S. data for the early years of the data panel, this exercise can only start in 2004, and the full set of 9 countries’ data is only available for the 2010s.

Notwithstanding the data limitations, the predictive relation between relative real yields and subsequent relative returns looks strong and highly significant, according to the standard Pearson statistic and the Macrosynergy panel test. The quarterly correlation coefficient has been 35% for standard yields and 27% for real yields adjusted for CDS spreads.

In fact, the __balanced accuracy of monthly return predictions has been 61%, higher for the relative yield signal than for the absolute real yield signal__. This plausibly reflects that the “neutral” level of the real yield is plausibly close to zero, while for absolute yields, that neutral level may depend on the economic situation and would typically require estimation. It is also striking that accuracy has been above 50% consistently for all yields since 2004, with only two years (2008 and 2010) posting lower values. Since the complete set of 9 countries has been available from 2012, monthly accuracy has been above 50% for every year.

The naïve PnL for standard binary and proportionate relative real yield signals with monthly rebalancing points to material value generation, particularly since all 9 countries have been available. The long-term Sharpe ratio of the proportionate and binary signal has been 0.7 and 0.9, respectively, with a negative average correlation to the 10-year U.S. treasure return. The relatively low returns of the 2000s mainly reflect the low number of countries and positions at the time.

## Why formulaic real yields trump breakeven real yields

Some countries have reasonably liquid inflation-linked government bond markets: Australia, the UK, Japan, and the United States. From these inflation linkers, one can back out breakeven inflation rates for the 5-year maturity and related real yields (view documentation). This is a valid alternative to the above formulaic inflation expectations.

However, the use of market-implied inflation expectations, as opposed to quantamental inflation expectations, suffers from several shortcomings:

- Most importantly, market-implied inflation rates are
__only available for a small subset of markets,__and meaningful price history is even more limited than for good quality formulaic real yields. __Since breakeven inflation is a price, it is naturally affected by risk premia and market dislocation__. For example, if inflation risk premia are high, maybe because their correlation with equity markets is elevated, one would subtract this risk premium from the real bond yield and thereby understate the overall premium offered by the bond. Indeed, there is reason and evidence for the time variance of inflation risk premia. At times, they can even become negative (view post).- Finally, comparing the predictive power of real yields for formulaic and breakeven inflation, we find that the
__formulaic real yields produce better statistics, even for the small set of four countries that provide breakeven yields__. Pearson correlation of formulaic real yields is 40% (quarterly) and 24% (monthly) versus 33% and 21% for the breakeven real yield.