Valuing a Government of Canada bond is like valuing a house
After months of searching, you find the perfect house. But is the seller’s price reasonable? One way to find out is to compare it with the prices of similar houses for sale in the neighbourhood. But unlike the other houses, this house comes with a basement suite. Even if you don’t plan to rent out the suite, another interested buyer might. The potential income from renting the suite could make this house more expensive to purchase than other similar houses.
In a sense, bond markets are like housing markets. Just like renting out a suite in your house, bond owners can earn income by renting out their bonds in the repurchase agreement (repo) market. In this note, we measure how important different factors such as rental income are for explaining why similar Government of Canada (GoC) bonds can have different values.
We find that expensive bonds tend to earn higher rental income and tend to be traded frequently. We also find that large positive changes in rental income and trading volume can make these bonds more expensive than similar bonds, by up to 2.5 basis points (bps) and 5 bps, respectively. Cheap bonds tend to have longer tenors and times to maturity. These bonds are typically harder and costlier to trade. Market participants may therefore value them less.
Buying a house is a big decision. You want to consider all the relevant factors such as the amenities of the house, the neighbourhood and potential rental income before making an offer. Our results are important for bond market participants because we show that rental income, trading activity, tenor and time to maturity influence how buyers and sellers value GoC bonds.
The importance of rental income for GoC bonds also suggests that the functioning of the repo market can influence the bonds’ value. Berger-Soucy, Fontaine and Walton (2019) find that there is a cap on rental income in this market. This cap could impair the repo market’s functioning. This is because the link that we find between rental income and the value of bonds could break down as rental income approaches the cap. This cap on rental income for GoC bonds can be thought of as rent regulation for houses or apartments. When rents are capped, bonds could be rented out below their market value. This could prevent the efficient allocation of bonds among buyers and sellers who value them most.
Similar Government of Canada bonds can have different values
A challenge that arises when comparing houses is that every house is different. The common approach is to gauge the price of a house given its characteristics in relation to comparable houses in the same neighborhood. Likewise, for bonds, we compute relative value by looking at a handful of bonds with similar maturities. We closely follow the approach introduced by Fontaine and Nolin (forthcoming). Specifically, for each bond, we use the values of three other bonds with very similar maturities to interpolate the value of this bond given its duration and convexity. The measure of relative value is simply the difference between the value of the bond and the value of this portfolio of similar bonds. In all cases, we use only nominal GoC bonds issued with tenors of 30 years or less.
If investors valued bonds based only on their payoffs, the relative value measure would be zero for all bonds. In practice, relative value can be important because investors care about other factors beyond payoffs. To get a sense of the magnitudes of relative value for GoC bonds, we study their levels at different percentile ranks in our sample. Chart 1 shows these levels in our sample from 2013 to 2018. Expensive bonds have positive relative values, whereas cheap bonds have negative ones. The chart shows that bonds stay within a small range of relative value, from as much as 8 bps for expensive bonds to around -5 bps for cheap bonds. This is a narrow range compared with the longer historical series reported by Fontaine and Nolin (forthcoming).
Chart 1: Distribution of relative value
Sources: FTSE TMX and Bank of Canada calculations
Expensive bonds are more liquid and can earn greater rental income than cheap bonds
We consider a short list of factors often thought of to explain relative values of bonds. These factors range from conditions in the bond market, such as market liquidity and rental income, to bond-specific characteristics, such as time to maturity and tenor (see the Appendix for a full list). We check whether each factor is related to relative value. To do so, we simply calculate the difference in the average value of each factor for expensive and cheap bonds.
Chart 2 shows that expensive bonds offer higher rental income than cheap bonds. It also shows that expensive bonds are more liquid, which is captured in trading volume, benchmark status and price impact (Gungor and Yang 2017). Investors value liquid bonds because they can be sold easily and quickly with little transaction costs. Chart 2 also shows that expensive bonds have shorter tenors and times to maturity than cheap bonds. These bonds also tend to be more liquid (see Bulusu and Gungor 2018).
Chart 2: Factors related to relative value
Sources: Canadian Depository for Securities, Thomson Reuters and Bank of Canada calculations
Trading volumes and rental incomes are important for valuing expensive bonds
In this section we re-examine the factors related to relative value. We ask which are most useful for explaining the relative value of expensive bonds. To do this, we use a regression framework (see the Appendix for details). In this regression framework, we group certain highly correlated factors such as tenor and time to maturity together. For completeness, we also include indicators of conditions in financial markets, such as volatility and interest rates.
Chart 3 illustrates how useful each factor is for explaining the relative value of expensive bonds. Specifically, the size of each box in the chart represents how much of the variation of relative value is explained by each factor. It shows that tenor and time to maturity, trading volume and benchmark status, general financial market indicators, and rental income are all important.
Tenor and time to maturity are constant or change slowly over time. These factors can help us understand persistent differences in relative value between bonds. Rental income and trading volume, however, can change quickly and help us understand differences due to market conditions. Trading volume, rental income and financial market indicators are more important than tenor and time to maturity for bond market participants because their values can change quickly.
Chart 3: Usefulness for relative value of expensive bonds
Sources: FTSE TMX, Canadian Depository for Securities, Thomson Reuters, Bloomberg and Bank of Canada calculations
Next, we look at how large changes in these factors can affect the relative value of expensive bonds. Chart 4 shows the relative value of expensive bonds that corresponds to different levels of rental income and trading volume in our sample. There is an increase of almost 2.5 bps in relative value when a bond’s rental income changes from the 1st to 99th percentile in our sample. The same change in trading volume corresponds to an increase of almost 5 bps. These changes in relative value are important because they correspond to the observed range reported in Chart 1.
Chart 4: Relative value of expensive bonds at different levels of rental income and trading volume
Sources: FTSE TMX, Canadian Depository for Securities and Bank of Canada calculations
Tenor and time to maturity are important for valuing cheap bonds
Chart 5 illustrates the usefulness of each of the factors for explaining the relative value of cheap bonds. It shows that tenor and time to maturity are by far the most useful. What this means is that, unlike for expensive bonds, the more volatile factors are much less important for cheap bonds. One common intuition is that the age of a bond represents its low liquidity and can be an important indicator of cheapness. This is true in our data. Within a narrow maturity range on the yield curve, it is true that older bonds are cheaper. But this intuition alone is also incomplete. The combination of tenor and time to maturity captures the fact that bonds with different tenors will be the cheapest when they reach different maturities. For instance, 30-year bonds are typically cheapest when they travel a range of time to maturity between 10 and 20 years. Bulusu and Gungor 2018 also show that these bonds become less liquid.
Chart 5: Usefulness for relative value of cheap bonds
Sources: FTSE TMX, Canadian Depository for Securities, Thomson Reuters, Bloomberg and Bank of Canada calculations
We identify factors that are important for explaining why similar Government of Canada (GoC) bonds can have different values. For bonds that are expensive, we find they have higher trading volume and higher rental income. These factors can make these bonds more expensive than similar bonds, by up to 5 bps. For the cheap bonds, we find that they tend to have longer tenors and times to maturity. These bonds are typically harder and costlier to trade. Market participants may therefore value them less. The importance of rental income for GoC bond values suggests that a cap on rental income could hinder the ability of these bonds to reach their market value. This could lead to misallocation of these bonds among the buyers and sellers who value them most.
To determine how much of the variation in relative value we can explain, we first regress all the factors listed in Table A-1 on the relative value of expensive and cheap bonds, respectively. We then evaluate how much of the variation explained by these original regressions is associated with each of the individual factors. We calculate this incremental variation for each factor as the difference between the variation explained by the original regression and that of a new regression that excludes the specific factor. For this step, we group together certain highly correlated factors such as tenor and time to maturity. We report this incremental variation as a share of the variation explained by the original regression for expensive and cheap bonds. This share represents each factor’s relative importance for relative value.
Table A-1: Factors that could explain relative value
|Bond characteristics||Benchmark status||The period when the bond is used as a reference to price other securities (Bulusu and Gungor 2018)||Bank of Canada|
|Bond characteristics||Outstanding amount||The total par value of a bond outstanding||Thomson Reuters|
|Bond characteristics||Tenor||The length of time until the bond’s maturity, at issuance||Bank of Canada|
|Bond characteristics||Time to maturity||The length of time between the transaction date and the bond’s maturity||Canadian Depository for Securities|
|Conditions in the bond market||Price impact||The Amihud proxy for price impact, calculated as the ratio of the absolute value of the asset return to the dollar value of trading volume (Gungor and Yang 2017)||Canadian Depository for Securities|
|Conditions in the bond market||Rental income||The difference between the Canadian Overnight Repo Rate Average and a bond’s volume-weighted average repo rate||Canadian Depository for Securities|
|Conditions in the bond market||Trading volume||The total trading volume for a bond in the cash market||Canadian Depository for Securities|
|Indicators of financial conditions||CDOR-OIS spread||The difference between the 3-month Canadian Dollar Offered Rate and overnight index swap rate||Bloomberg|
|Indicators of financial conditions||CORRA||The Canadian Overnight Repo Rate Average||Bloomberg|
|Indicators of financial conditions||Term spread||The difference between the 10-year and 1-year yields on Government of Canada bonds||Bloomberg|
|Indicators of financial conditions||VIXC||The S&P/TSX 60 VIX Index, the 30-day volatility of the stock market implied by the near-term and next-term options on the S&P/TSX 60 index||Bloomberg|
- Berger-Soucy, L., J.-S. Fontaine and A. Walton. 2019. “Price Caps in Canadian Bond Borrowing Markets.” Bank of Canada Staff Analytical Note No. 2019-2.
- Bulusu, N. and S. Gungor. 2018. “Government of Canada Securities in the Cash, Repo and Securities Lending Markets” Bank of Canada Staff Discussion Paper No. 2018-4.
- Fontaine, J.-S. and G. Nolin. Forthcoming. “Measuring Limits of Arbitrage in Fixed-Income Markets.” The Journal of Financial Research.
- Gungor, S. and J. Yang. 2017. “Has Liquidity in Fixed-Income Canadian Government Bond Markets Deteriorated?” Bank of Canada Staff Analytical Note No. 2017-10.
We thank Jean-Philippe Dion, Toni Gravelle, Michael Mueller and Guillaume Nolin for helpful comments and suggestions. We are also grateful to Alison Arnot and Nicole van de Wolfshaar for excellent editorial assistance.
Avis d’exonération de responsabilité
Les notes analytiques du personnel de la Banque du Canada sont de brefs articles qui portent sur des sujets liés à la situation économique et financière du moment. Rédigées en toute indépendance du Conseil de direction, elles peuvent étayer ou remettre en question les orientations et idées établies. Les opinions exprimées dans le présent document sont celles des auteurs uniquement. Par conséquent, elles ne traduisent pas forcément le point de vue officiel de la Banque du Canada et n’engagent aucunement cette dernière.