Relative value can be defined as expected price convergence of contracts or portfolios with similar risk profiles. For fixed income this means similar exposure to duration, convexity and credit risk. The causes of relative value are limited arbitrage capital and aversion to the risk of persistent divergence. Relative value in the fixed income space has been pervasive and persistent. Relative value trades can be based on parametric estimation of yield curves or comparisons of individual contracts with portfolios that replicate their essential features. The latter appear to have been more profitable in the past.

*The post ties in with SRSV’s lecture on systemic value and price distortions*.

*The below are excerpts from the paper. Emphasis and cursive text have been added. *

### Causes of fixed income relative value

“Relative value captures apparent deviations from no-arbitrage relationships…[*In fixed income markets*] an expensive bond would be shorted, while a cheap bond would be purchased.”

“Bonds emitted by the same issuer with the same cash flows should have the same prices and yields. This is the law of one price. In practice, however, __deviations from the law of one price are pervasive in the bond market__…Deviations can be large—as in 2008—or they can be small—as in 2014—but they are rarely absent…For example, at the height of the global financial crisis, the difference in yields between very similar bonds issued by the US Treasury exceeded 100 basis points. Such a large difference can persist for extended periods of time, even in normal times…This __points to the existence of limits to arbitrage in fixed income markets__.”

“These persistent deviations reveal limits of arbitrage due to funding market frictions and bond market segmentations…The profit motive of arbitrageurs can reduce deviations when funding constraints are loose and when arbitrage capital is abundant, as in 2014. Conversely, __deviations [ and relative value] will be larger and more persistent when funding constraints are tight and arbitrage capital is scarce__, as in 2008.”

### Methods of fixed income relative value

“The most common strategy to exploit deviations [*of the law of one price*] is the so-called relative value trade. Relative value is based on the idea that bonds with the same risk should have the same expected returns. For instance,__ a relative value trade may involve a portfolio of bonds replicating the duration and convexity of the target bond__. This is different than replicating the cash flows, since exact replication of a coupon bond is typically much costlier.”

*Parametric models*

“Existing approaches to measure [*relative value*]…rely on parametric models, of which Hu, Pan and Wang’s (2013) noise index is arguably the most popular. __Using a static parametric yield curve, Hu, Pan and Wang show…an index of fitting errors—the ‘noise’ measure__… For this class of measures, preliminary estimates must be obtained for the parameters of a factor yield curve model to derive an index of fitting errors (relative to curve). Parameter estimation introduces a layer of complexity. It also introduces sampling uncertainty and potential model misspecification.”

*Non-parametric relative value*

“We introduce a new measure of deviations based on the relative value of bonds. This measure is model-free, bypassing the need for preliminary parameter estimation. It is intuitive and easy to compute. For any bond in our sample, __we use a small number of comparable bonds to form a replicating portfolio with the same duration and convexity__. This bond and its replicating portfolio should have the same expected return. The relative value for that bond is the difference between its yield and that of the replicating portfolio.”

### Profitability of fixed income relative value

“A measure capable of identifying deviations from limits of arbitrage should generate positive returns over time.”

“We compute [*non-parametric*] relative value and Hu, Pan and Wang’s noise measure every day and for each bond and use them as trading signals. __Once a bond’s signal exceeds a predetermined threshold, our strategy enters a convergence trade that carries no interest rate risk__. The trade is exited when the signal falls to zero or when the duration of the trade exceeds a calendar year. We aggregate profits and losses across convergence trades to compute monthly returns.”

“__U____sing [ non-parametric] relative value as a trading signal for a pseudo-trading strategy produces significant excess returns__…In the US Treasury bond market, [

*non-parametric*] relative value produces an average monthly return of 0.52% between 1988 and 2017.”

“This stands in contrast to trading measures based on __parametric yield curve models, which are shown to produce a large number of false-positive signals that generate small negative returns__… A strategy based on Hu, Pan and Wang’s measure generates significantly lower returns and signals a large number of ultimately unprofitable trades… False-positive signals are generated by fitting errors in the yield curve estimation process and are not associated with significant deviations from arbitrage relationships. Establishing a convergence trade in these cases generates small negative returns, notably because of transaction costs…The noise measure produces an average return of 0.16% [*in the U.S. market 1988-2017*]”

### Indices of fixed income relative value

“Higher returns from pseudo-trading strategies mean arbitrageurs face greater costs or greater risk when implementing these strategies.”

“__We propose an aggregate relative value index…and compute it for several large sovereign issuers__. Higher values for the index indicate that deviations from arbitrage relationships are larger on average (in absolute value). These indices are available publicly and updated regularly on the Bank of Canada’s website. __We find that the index is highly correlated with local volatility indices (such as the VIX)__. This is consistent with the mechanism whereby higher systematic volatility raises the scarcity of arbitrage capital. We also find that a country-specific relative value index is typically correlated with a local version of the spread between the overnight index swap (OIS) and the interbank lending market rates. This is consistent with the mechanism whereby higher funding costs raise limits of arbitrage.”

“The index for the US, UK, Canada, Germany and Switzerland are highly correlated. By contrast, the relative value index for the bond market in France and Italy diverged from that of other countries during the euro area sovereign crisis. The case of the bond market in Japan appears to be largely idiosyncratic.”