There is a very good staff working paper published by the Bank of Canada, by Jean-Sébastien Fontaine and Guillaume Nolin titled Measuring Limits of Arbitrage in Fixed-Income Markets:
We use relative value to measure limits to arbitrage in fixed-income markets. Relative value captures apparent deviations from no-arbitrage relationships. It is simple, intuitive and can be computed model-free for any bond. A pseudo-trading strategy based on relative value generates higher returns than one based on the well-known noise measure. The relative value is therefore a better proxy for limits to arbitrage. We construct relative value indices for the US, UK, Japan, Germany, Italy, France, Switzerland and Canada. Limits to arbitrage increase with the scarcity of capital: we find that each index is correlated with local volatility and funding costs. Limits to arbitrage also exhibit strong commonality across countries, consistent with the international mobility of capital. The relative value indices are updated regularly and available publicly.
…
Using a static parametric yield curve, Hu, Pan and Wang (2013) (HPW thereafter) show that an index of fitting errors—the “noise” measure—is priced in the cross-section of returns from hedge funds and carry trades. In other words, aggregating these deviations tends to reveal an important financial risk factor.
Measuring fitting errors against a parametric curve is a component of HIMIPref™ I dub “disparity”. The BoC paper then states:
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.
So it’s a tightly constrained yield maximizer, also a component of HIMIPref™.
Extending the analysis to several other countries, we find that the relative value index is correlated with local equity market volatility indices and domestic interbank lending market conditions. In addition, the relative value indices exhibit a large degree of commonality across countries. These relative value indices are available publicly and will be regularly updated. We hope that these indices will help to answer a number of research questions. In addition, future research could apply our methodology to create relative value indices for supranational, sub-national or corporate bond markets.
I have a number of technical quibbles about their methodology, but it’s a worthy effort. The two problems that come immediately to mind are first, the quality of the market data (I haven’t seen a bond database yet that hasn’t been riddled with errors) and the fact that there’s no allowance for the cost of shorting. I found in the Treasury Market in the ’90’s that there were a lot of unusually rich issues (particularly in the short end) … and that almost every one of those had ‘gone special’ in the loans market, meaning they were expensive to short. And just try getting data for THAT!
But, I will admit, the part I like best about this paper is that it provides third party validation of my investing style … which is always a useful thing to have on hand when marketing one’s services!
| HIMIPref™ Preferred Indices These values reflect the December 2008 revision of the HIMIPref™ Indices Values are provisional and are finalized monthly |
|||||||
| Index | Mean Current Yield (at bid) |
Median YTW |
Median Average Trading Value |
Median Mod Dur (YTW) |
Issues | Day’s Perf. | Index Value |
| Ratchet | 0.00 % | 0.00 % | 0 | 0.00 | 0 | 0.1857 % | 2,420.4 |
| FixedFloater | 0.00 % | 0.00 % | 0 | 0.00 | 0 | 0.1857 % | 4,441.3 |
| Floater | 3.77 % | 3.93 % | 30,155 | 17.60 | 4 | 0.1857 % | 2,559.6 |
| OpRet | 0.00 % | 0.00 % | 0 | 0.00 | 0 | -0.1647 % | 3,069.5 |
| SplitShare | 4.75 % | 4.87 % | 76,109 | 4.38 | 6 | -0.1647 % | 3,665.7 |
| Interest-Bearing | 0.00 % | 0.00 % | 0 | 0.00 | 0 | -0.1647 % | 2,860.1 |
| Perpetual-Premium | 5.36 % | -1.68 % | 64,217 | 0.14 | 17 | 0.1366 % | 2,820.2 |
| Perpetual-Discount | 5.35 % | 5.31 % | 61,187 | 14.94 | 19 | 0.1922 % | 2,946.5 |
| FixedReset | 4.25 % | 4.28 % | 157,571 | 4.58 | 99 | 0.1981 % | 2,474.7 |
| Deemed-Retractible | 5.08 % | 5.58 % | 101,454 | 6.01 | 30 | 0.1273 % | 2,899.9 |
| FloatingReset | 2.77 % | 2.77 % | 50,717 | 4.06 | 8 | -0.0326 % | 2,675.7 |
| Performance Highlights | |||
| Issue | Index | Change | Notes |
| HSE.PR.G | FixedReset | -2.13 % | YTW SCENARIO Maturity Type : Limit Maturity Maturity Date : 2047-10-12 Maturity Price : 23.16 Evaluated at bid price : 24.32 Bid-YTW : 5.30 % |
| PVS.PR.E | SplitShare | -1.34 % | YTW SCENARIO Maturity Type : Hard Maturity Maturity Date : 2022-10-31 Maturity Price : 25.00 Evaluated at bid price : 25.75 Bid-YTW : 4.98 % |
| MFC.PR.M | FixedReset | 1.03 % | YTW SCENARIO Maturity Type : Hard Maturity Maturity Date : 2025-01-31 Maturity Price : 25.00 Evaluated at bid price : 23.43 Bid-YTW : 5.16 % |
| MFC.PR.L | FixedReset | 1.09 % | YTW SCENARIO Maturity Type : Hard Maturity Maturity Date : 2025-01-31 Maturity Price : 25.00 Evaluated at bid price : 22.35 Bid-YTW : 5.79 % |
| SLF.PR.G | FixedReset | 1.10 % | YTW SCENARIO Maturity Type : Hard Maturity Maturity Date : 2025-01-31 Maturity Price : 25.00 Evaluated at bid price : 18.31 Bid-YTW : 7.70 % |
| HSE.PR.A | FixedReset | 1.11 % | YTW SCENARIO Maturity Type : Limit Maturity Maturity Date : 2047-10-12 Maturity Price : 17.30 Evaluated at bid price : 17.30 Bid-YTW : 4.77 % |
| RY.PR.J | FixedReset | 1.18 % | YTW SCENARIO Maturity Type : Call Maturity Date : 2020-05-24 Maturity Price : 25.00 Evaluated at bid price : 24.90 Bid-YTW : 3.97 % |
| TD.PF.A | FixedReset | 1.34 % | YTW SCENARIO Maturity Type : Limit Maturity Maturity Date : 2047-10-12 Maturity Price : 23.12 Evaluated at bid price : 23.45 Bid-YTW : 4.24 % |
| BMO.PR.Q | FixedReset | 1.43 % | YTW SCENARIO Maturity Type : Hard Maturity Maturity Date : 2022-01-31 Maturity Price : 25.00 Evaluated at bid price : 22.67 Bid-YTW : 4.39 % |
| Volume Highlights | |||
| Issue | Index | Shares Traded |
Notes |
| TRP.PR.J | FixedReset | 115,286 | YTW SCENARIO Maturity Type : Call Maturity Date : 2021-05-31 Maturity Price : 25.00 Evaluated at bid price : 26.71 Bid-YTW : 3.68 % |
| RY.PR.R | FixedReset | 113,400 | YTW SCENARIO Maturity Type : Call Maturity Date : 2021-08-24 Maturity Price : 25.00 Evaluated at bid price : 26.95 Bid-YTW : 3.55 % |
| TD.PF.D | FixedReset | 108,102 | YTW SCENARIO Maturity Type : Call Maturity Date : 2020-07-31 Maturity Price : 25.00 Evaluated at bid price : 24.57 Bid-YTW : 4.21 % |
| TD.PF.B | FixedReset | 105,581 | YTW SCENARIO Maturity Type : Limit Maturity Maturity Date : 2047-10-12 Maturity Price : 22.99 Evaluated at bid price : 23.36 Bid-YTW : 4.27 % |
| NA.PR.Q | FixedReset | 104,275 | YTW SCENARIO Maturity Type : Call Maturity Date : 2017-11-15 Maturity Price : 25.00 Evaluated at bid price : 24.97 Bid-YTW : 1.29 % |
| RY.PR.J | FixedReset | 84,784 | YTW SCENARIO Maturity Type : Call Maturity Date : 2020-05-24 Maturity Price : 25.00 Evaluated at bid price : 24.90 Bid-YTW : 3.97 % |
| There were 57 other index-included issues trading in excess of 10,000 shares. | |||
| Wide Spread Highlights | ||
| Issue | Index | Quote Data and Yield Notes |
| NA.PR.W | FixedReset | Quote: 22.86 – 23.50 Spot Rate : 0.6400 Average : 0.3904 YTW SCENARIO |
| HSE.PR.G | FixedReset | Quote: 24.32 – 24.80 Spot Rate : 0.4800 Average : 0.2958 YTW SCENARIO |
| IFC.PR.A | FixedReset | Quote: 20.20 – 20.50 Spot Rate : 0.3000 Average : 0.1906 YTW SCENARIO |
| BAM.PF.J | FixedReset | Quote: 25.20 – 25.56 Spot Rate : 0.3600 Average : 0.2524 YTW SCENARIO |
| BNS.PR.D | FloatingReset | Quote: 22.93 – 23.19 Spot Rate : 0.2600 Average : 0.1748 YTW SCENARIO |
| GWO.PR.Q | Deemed-Retractible | Quote: 24.41 – 24.65 Spot Rate : 0.2400 Average : 0.1578 YTW SCENARIO |