*The analysis of this post has been updated on June 22, 2023*

Duration volatility risk premium means compensation for bearing return volatility risk of an interest rate swap (IRS) contract. It is the scaled difference between swaption-implied and realized volatility of swap rates’ changes. Historically, these premia have been stationary around positive long-term averages, with episodes of negative values. Unlike in equity, simple duration volatility risk premia have not been significant predictors of subsequent IRS returns. However, they have helped predict idiosyncratic IRS returns in non-USD markets.

Moreover, two derived concepts of volatility risk premia hold promise for trading strategies. [1] Term spreads are the differences between volatility risk premia for longer-maturity and shorter-maturity IRS contracts and are related to the credibility of a monetary policy regime. Historically, term spreads have been significant predictors of returns on curve positions. [2] Maturity spreads are the differences between volatility risk premia of longer- and shorter-maturity options and should be indicative of a fear of risk escalation, which affects mainly fixed receivers. Indeed, maturity spreads have been positively and significantly related to subsequent fixed-rate receiver returns. These premia are best combined with fundamental indicators of the related risks to give valid signals for fixed-income positions.

The below post is based on proprietary research of the Macrosynergy team and is related to several past articles, which are linked below.

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.

Also, there is an academic research support program that sponsors data sets for relevant projects.

This post ties in with this site’s summary on implicit subsidies.

### The basics of the volatility risk premium

The volatility risk premium is __compensation for exposure to the return volatility of a financial contract__. Specifically, it is the premium for holding a short volatility position, which incurs losses if volatility turns out higher than expected. The volatility risk premium is calculated as the __difference between the option-implied (risk-neutral) annualized standard deviation of a contract’s return and its expected realized standard deviation over the life of the option__. The difference is scaled by dividing through the expected realized standard deviation.

The volatility risk premium depends on investors’ attitude towards volatility risk, being high in times of elevated volatility risk aversion and low when investors are less interested in protection. The premium can be negative if investors prefer being short the volatility of an asset, which is possible if an asset’s volatility is negatively correlated with the performance of a representative market portfolio. This can sometimes apply to safe-haven assets.

__For most assets and periods, option-implied volatility exceeds realized volatility of the same underlying asset__. This has been documented in academic research, particularly for equity (view post here), commodity derivatives (view post here), and foreign exchange markets (view post here). This suggests that in these markets investors are willing to pay a premium for options to protect them against a rise in volatility.

Indeed, for these markets published __research often points to a positive relation between estimated volatility risk premia and subsequent returns__. More specific analyses suggest that equity markets mainly pay over the odds for downside risk in mark-to-market variations while accepting a discount for upside risk. The highest premium is paid for downside skewness risk, i.e. exposure of a position to the negative skewness of an asset. This is also sometimes called “blow-up risk”. Various specific forms of variance risk premia have been significant predictors of U.S. equity returns. (view post here)

There has been __less focus on volatility risk premia in interest rate swap contracts __(or high-grade bonds for this matter). This may partly reflect __uncertainty as to how such a premium would actually affect the return of the underlying__. In contrast to equity markets, it is less clear to what extent the volatility risk aversion of the fixed-rate receiver dominates the aversion of the fixed-rate payer. Moreover, as both returns and volatility of fixed-rate receiver positions can be negatively correlated with their counterparts in the equity market it is also uncertain if related premia are reliably positive.

## A simple estimation of duration volatility risk premia

For the present purpose __duration volatility risk premium means compensation for bearing the return volatility risk of an interest rate swap contract__. In particular, the duration volatility risk premium is calculated as the difference between swaption-implied and realized volatility of forward-starting swap rates’ changes divided by the realized volatility of these rate changes. The volatility risk premium metrics are unitless and refer to a fractional deviation.

- Implied volatility is the parameter that yields the market price of a swaption when substituted into the option pricing formula under the assumption of an arithmetic Brownian motion.
- Realised volatility is the standard deviation of an exponential moving average of daily forward starting IRS yield changes with a half-life of 11 days, a convention frequently used for risk management. Note that for the calculation of duration volatility risk premia the use of IRS yields and returns is equivalent.

The data for volatility risk premia have been taken from JPMaQS (J.P. Morgan Macrosynergy Quantamental System) based on underlying J.P. Morgan market maker quotes. The premia are available for underlying IRS tenors of 2, 3, and 5 years, and swaption maturities of 3, 6, and 12 months, for 12 countries, albeit with great differences in length of history, with the U.S. starting in 1992 and Japan only in 2017. For more information view the documentation here.

The estimates for expected realized volatility follow the simplest convention for transparency, simplicity, and to reduce the scope for data mining. In practice, using recent realized volatility as a proxy is typically not optimal. Oftentimes, a more realistic estimate can be constructed by considering the trade-off between the timeliness and noise ratio of recent price changes and the long-term mean reversion of volatility (view post here).

## Stylized features of simple duration volatility risk premia

### Average premia and time-series patterns

The average volatility risk premium here is based on the arithmetic average of the premium for the three underlying IRS tenors (2, 3, and 5 years) and the three option maturities (3, 6, and 12 months). Also, to smooth the fairly high volatility of the daily series we focus on 5-day rolling moving averages in the empirical analysis below.

__Volatility risk premia across the available sample periods have posted positive long-term averages for all currency areas__. The highest premia have been charged in Switzerland and Israel, the lowest in the U.S. and South Korea. In all countries, the premia have at least temporarily been negative.

The above currency symbols are BRL (Brazilean real), CHF (Swiss franc), EUR (euro), GBP (British pound), HKD (Hong Kong dollar), HUF (Hungarian forint), ILS (Israeli shekel), JPY (Japanese yen), KRW (Korean won), NOK (Norwegian krone), USD (U.S. dollar), ZAR (South African rand).

Over time the premia have been stationarity with sustained periods of months or years above average and occasional episodes below average or in negative territory. Beyond, there has been ample short-term volatility, even after taking 5-day rolling moving averages. U.S. data are now available for three decades and reveal pronounced and sustained phases of negative and positive premia.

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Volatility risk premia have been positively correlated across all markets, based on the longest common samples. This suggests that they reflect common global factors.

### Relation to subsequent swap returns

The simplest hypothesis is that a higher volatility risk premium indicates a higher aversion to bearing longer-term rate uncertainty. From a bond investor and fixed receiver position, this should translate into higher premia charged and higher average returns. Of course, debtors and fixed payers could charge similar premia and offset that relation. Thus, unlike equity risk, the structural long in duration risk may be more tenuous.

Indeed, __based on correlation and accuracy statistics there has been no clear relation between the duration volatility risk premia and subsequent IRS fixed receiver returns__ on either the weekly or monthly frequency. Higher premia on volatility risk have not translated into higher returns on outright duration exposure of investors.

Looking at the relation across currencies, the USD market experienced on balance negative relation between volatility risk premia and subsequent duration returns, albeit not a very significant one. By contrast, __the correlation of volatility risk premia in non-U.S. markets with subsequent IRS receiver returns relative to the U.S. has been positive with modest significance__. This suggests that premia are charged for idiosyncratic volatility risk and predictive for idiosyncratic returns in non-USD currency areas.

Indeed, __non-USD volatility risk premia have been a valuable and fairly reliable signal for positions in non-USD fixed-rate receivers__ relative to the U.S. market. For example, the balanced accuracy of weekly signals, i.e. the average of the ratios of correctly detected positive returns and correctly detected negative returns, has been 51.2% and has been over 50% for around 70% of all countries and around 70% of all calendar years since 2000.

A naïve trading strategy, rebalancing longs and shorts in relative IRS positions would have produced a Sharpe ratio of 0.6 since 2000, before transactions. In the 2000s the performance mainly owed to a successful timing of fixed receiver and payer positions. In the 2010s the performance was carried mainly by the bias towards fixed receivers.

### Term spreads of premia

#### Average premia and time-series patterns

Here __we define term spreads of volatility risk premia as the differences between premia for 5-year interest rate swaps and premia for 2-year interest rate swaps__. Conceptually they are surcharge premia for volatility risk on longer-duration swaps versus shorter duration rates exposure. In a well-anchored monetary policy regime with a credible long-term inflation target, longer duration volatility should be a lesser concern than shorter-duration volatility. A central bank that is committed to long-term price stability will do what it takes in the short run to honor its commitment. Under conventional monetary policy, this means that short-term interest rates will have to absorb a greater part of the pressure that arises from economic shocks.

Term spreads have been deeply negative in some low-inflation or deflation countries, particularly Switzerland and Israel.

Over time, the spreads have displayed trends, cycles, and ample short-term volatility.

Unlike volatility risk premia, term spreads have not been all positively correlated across currency areas.

#### Relation to subsequent swap returns

The simplest hypothesis would be that a more positive term spread indicates that fixed receivers of longer duration swaps will – on a volatility parity basis – pay higher risk premia and, hence, be indicative of positive returns on volatility-neutral curve-flattener positions.

Historically __correlation between term spreads and subsequent returns on the volatility-neutral curve-flattener positions has been positive and highly significant__, both at a weekly and monthly frequency.

As a weekly trading signal term spreads have displayed balanced accuracy of 50.3% at a weekly frequency without bias for either the 5-year or the 2-year leg of the relative position. The accuracy is not very high but in conjunction with the low correlation of signals across countries and the good correlation of returns it has been powerful enough to make a difference: a simple naïve strategy with weekly rebalancing would have produced a Sharpe ratio of 0.61 since 2000 (without consideration of transaction costs).

### Maturity spreads of premia

#### Average premia and time-series patterns

Here we define maturity spreads of volatility risk premia as the differences between premia for options with a 1-year maturity and premia for options with a 3-month maturity. Conceptually these are __surcharge premia for bearing volatility risk in the swaption market over a longer horizon__. On this conceptual basis the premia should be positive if uncertainty is expected to increase. If the market is already experiencing high volatility this would be a premium for crisis escalation. If the market is in a placid state, it would be a premium for the end of that placid state. Since rising uncertainty and particularly crisis escalation is usually associated with higher rather than lower rates, due to the zero bound, it should weigh disproportionately on fixed receiver positions.

Maturity spreads have on average been negative in almost all countries. Variations have displayed very different amplitudes, with larger countries posting smaller fluctuations.

The time series of maturity spreads have been stationary with pronounced cycles around a negative mean, as exemplified by the U.S. history in the graph below.

The correlations of maturity spreads across currency areas has been diverse. The correlations of most developed countries with the U.S. and the euro area have been positive. Japan and emerging markets have displayed more idiosyncratic dynamics. Thus, trading strategies on maturity spreads would imply considerable relative exposure across countries.

#### Relation to subsequent swap returns

The simplest hypothesis is that a positive maturity spread indicates the prevalence of inflation and interest rate risk escalation concerns and, hence, gives rise to a positive premium charged on fixed-rate receivers. Thus, one should expect a positive relationship between the maturity spread and subsequent swap returns.

Indeed, the __correlation of the average maturity spread with subsequent 5-year IRS receiver returns has been positive and highly significant__ at both a weekly and monthly frequency.

Balanced accuracy at a weekly frequency has been 51.1% across the panel and above 50% for over two-thirds of all markets. This suggests that the maturity spread helps predict the direction of IRS returns.

Alas, a simple strategy that uses only the maturity spread (z-score around zero) as a signal for receiver versus payer position would not have created much positive PnL over the past 22 years. This is due mainly to its strong short-duration bias. Since, in stable monetary regimes, there is not much “escalation risk premium” on offer, the signal would have been negative in almost 70% of all weeks across all countries. The signal would have implied a massive short duration risk bias.

This illustrates that __positive correlation and predictive power alone are not enough to make a good directional positioning signal__. The signal must also set the right long-term bias and gather a critical mass of explanatory power for all the premia charged on a contract. The maturity spread, which reflects a single type of risk premium, cannot provide that. As with many short risk-bias strategies, its own overall performance as a trading signal is not impressive. However, it is a valid contributor to signal for directional exposure to duration risk.

### The link to fundamentals

Duration volatility risk and related __premia are valid indicators of the prices that the market is charging for various types of risk. __Term spreads are related to the risk of a monetary policy becoming unanchored, with rates and inflation becoming non-stationary and drifting in one direction for a prolonged period. Maturity spreads are related to deteriorating market uncertainty over the horizon of a year or so.

However, by themselves, these premia only indicate whether the price for such risk is positive or negative and whether it is high by historical standards. __They do not provide much judgment on whether the price of the risk is justified given the fundamental position of the economy__, outside the proposition of mean reversion. For example, high risk of inflation and interest rates becoming unanchored might be well justified in an economy where the central bank pays little heed to its inflation target and where there is rampant money and credit growth. And the risk of escalation of turbulences is greater when leading economic indicators point to inflation or currency devaluation risk.

Therefore, composite signals that combine volatility risk premia and derived concepts with data on the fundamental position of the economy are likely to be more reliable predictors and better long-term signals for trading strategies. Put simply, __mean reversion of premia is a more sensible approach if one takes care of estimating what the mean actually is, conditional on the macroeconomic environment__.