Pricing of Japanese Government Bonds: Influence of Futures Prices, Repo Rates, and Supply-Demand Conditions of Specific Issues
April 4, 2001
The levels of long-term interest rates are determined by the daily movements in the government securities market. In order to understand the mechanics of how government securities are priced and how such prices would fluctuate, it is important to examine, for example, the arbitrage between cash, futures and repo markets, and the supply and demand for each issue of government securities. Turning to the Japanese Government Bond (JGB) market, the market has become the largest government bond market in the world in terms of amounts outstanding. Nevertheless, there seems to be latitude for further improvements, including market liquidity. This issue of Market Review will look into one instance when problems surfaced, in the summer of 1999. At that time, the prices observed in the futures and cash markets--where any differences are expected to be quickly arbitraged away-- deviated considerably as uncertainty over Y2K mounted in Japanese markets. The differences reached unprecedented levels. The focus will be on the deterioration of arbitrage functions, distortions in the yield curve, and lower market liquidity, all of which affected the pricing of JGB's.
In August 1999, significant anomalies were observed in the JGB market. Deviations between prices in the cash and futures markets 1 reached four times the usual levels. In the repo market, bonds could not be borrowed unless one was willing to pay a fee of more than 2 percent p.a., in an environment where the interbank funding rate was practically 0 percent p.a. (Chart 1). Meanwhile, the distortions in the JGB yield curve, as measured by aggregate deviations of the prices of individual issues from theoretical levels,2 increased fourfold in just one week. Such a development could only be understood from detailed examinations into the arbitrage relations that exist between cash, futures and repo markets of JGB's, and between individual issues of JGB's.
- Generally, the "gross basis" (the difference between cash market price and futures price adjusted by conversion factor) immediately after the change in the most actively traded contract in the futures market is just under one yen (the average from the beginning of 1998 to June 1999 was 0.95 yen). This widened to 3.56 yen on August 17.
- Computed from aggregating differences between the yields of individual issues and corresponding rates derived from a theoretical yield curve (See Chart 4).
In theory, the prices of government securities, which can be considered (credit) risk-free assets, are equivalent to the sum of discounted cashflows accruing to a security when held to maturity. However, looking at the day to day prices for each issue in the markets, there are instances where prices for two issues with equivalent cashflows differ considerably, or where price movements cannot be accounted for by changes in theoretical prices. This shows that while the day to day price movements are grounded on theoretical prices, they are also influenced by arbitrage transactions and the supply and demand of individual issues.
This issue of Market Review looks at the arbitrage relations that exist between cash, futures and repo markets of JGB's, and between individual issues of JGB's, which is a key factor in understanding the mechanics of pricing in the JGB market. The main finding is that recently, deterioration in arbitrage relations tended to persist in JGB markets against the background of globally observed exit of arbitrageurs since autumn 1998, resulting in ineffective hedging and increased risks.3 The deterioration of market liquidity in the summer of 1999 seems to reflect such increased vulnerabilities of the market.
- 3For further details, see Yosuke Shigemi, Sotaro Kato, Yutaka Soejima, and Tokiko Shimizu "Market Participants' Behavior and Pricing Mechanisms in the JGB Markets -- Analysis of Market Developments from the End of 1998 to 1999--" (Financial Markets Department Working Paper Series 00-J-4, March 2000, in Japanese: English to be released soon).
Chart 1 Cash Bonds, Futures, and Repo Rates; Arbitrage Opportunities Left Unexploited
Note: Basis (gross basis) is the difference between cash and futures prices.
Arbitrage between Markets under Normal Conditions
As of January 2000, there are 92 different issues of 10-year JGB's. Of these, the most actively traded issues are the most recent issue (on-the-run issue) and the "cheapest to deliver" (CTD) issue. The latter is the cheapest issue that can be delivered to settle JGB futures contracts. This active trading in the CTD issue underscores the structure of the JGB markets, where JGB futures are relatively more liquid than the cash market. As a result, the market's view of long-term interest rates is first reflected in JGB futures, and the CTD issue that moves in line with futures is actively traded. The prices of other issues are based on the CTD issue with allowances for supply and demand of each issue.
In the JGB repo market, where JGB's are borrowed/lent against funds, the repo rate is based on another arbitrage relationship--between repo transactions and positions involving simultaneous transactions in cash and futures markets. As the delivery of bonds and cashflows generated by repo transactions can be replicated by combining transactions in cash and futures markets, 4 prices determined in one market should determine the prices in the other. Having said this, it must be noted that the repo rate and the "implied repo rate," which is calculated from prevailing prices in cash and futures markets, can deviate from time to time reflecting supply and demand in each market. Nevertheless, any deviations are usually arbitraged away, resulting in consistent pricing in the three markets.
- 4The flows of funds and securities resulting from a "reverse repo" transactions (initially lending securities for funds and returning funds for securities at a future point in time) is replicated by combining short cash positions and long futures positions.
Arbitrage between Issues under Normal Conditions
The prices of 10-year JGB's are determined by adjusting theoretical prices, which are calculated from remaining maturities and coupon rates, for supply/demand premia for each issue. The expectation is that if the characteristics of two issues are alike, prices will be determined by cashflow characteristics. An issue of higher coupon might be preferred over another with a lower coupon. Otherwise, one should find similar prices for issues with similar coupons and maturities, but investors may actually prefer one issue to another. For example, they may prefer issues that trade around par to avoid recognizing amortization losses. As a result, there exist differences between prices of issues in the cash market that cannot be explained by differences in cashflows.
Developments during 1999 -- the Deterioration of Arbitrage Relations between Cash and Futures Markets, and Less Effective Hedging through Futures
Dealers would fill orders from customers and thus provide liquidity in the secondary market for government securities. In the process, dealers need to hedge against price fluctuations of the inventories that they carry. The preferred instruments for such operations are futures, which has a relatively deep and liquid market. This however, hinges on the fact that cash and futures markets move in line most of, if not all, the time. One factor behind such a strong arbitrage relations between cash and futures markets is the use of the price of CTD issue as a benchmark for pricing other issues of JGB's.
According to the responses to a questionnaire sent to major market participants by the Bank of Japan Financial Markets Department, 5 market participants saw that it had become more difficult to hedge cash positions with futures contracts from the middle of 1999, when the market became unstable. This view can be confirmed by comparing the performance of typical pricing engines with actual prices observed in the market between December 1998 and January 2000 (Chart 2). Pricing engines (1) based on the prices of other issues, (2) based on the prices of CTD issue, (3) based on swap market activities, and (4) the combination of (2) and (3) were compared. From this, it is apparent that the performance of pricing engine based on CTD issue prices deteriorated markedly from mid-1999 to autumn 1999, corresponding to the period when respondents to the above questionnaire noted the weakening of arbitrage relations.
Looking back on events then, on June 8, 1999, there was a change in CTD issue just before the most actively traded contract switched from June 1999 contract to September 1999 contract. This was the result of a rapid relative decline in the prices of next-to-CTD issue (2nd issue of 20-year JGB's), 6 and the relative appreciation in the prices of the CTD 187th issue of 10-year JGB's for June 1999 contract.
Behind such a development was the high level of open positions in June 1999 futures contract, which hovered around 15 trillion yen up until just a few days before trading for the contract would be closed, an extremely high level compared to the amount outstanding of the original CTD issue (187th) at about 8 trillion yen. The risk for not being able to settle the contracts by delivery was, therefore, high for those firms that shorted futures without holding cash securities. As fails were not sanctioned in Japan, 7 the firms that shorted attempted to get hold of cash securities no matter the price, and the price of 187th appreciated rapidly.
The sudden change in the CTD issue disrupted arbitrage transactions between cash and futures markets. Many dealers had created "short-basis" arbitrage positions, shorting 187th in the cash market and purchasing June 1999 futures contract, taking advantage of highly liquid market in 187th. The sudden change in the CTD for June 1999 contract undermined these positions because 187th would not be delivered when the futures contracts were settled. At the same time, the rising prices of 187th widened the "basis" (the differences in cash and futures prices), which worked against firms shorting the basis by selling cash and buying futures. Attempts to limit losses and unwind these positions by selling back futures further depressed futures prices, and aggravated the widening of the basis.
- 5The survey was conducted in October 1999, against eligible counterparties for Bank of Japan (government bond related) market operations. Institutions were asked to respond to questions concerning conditions in the Japanese government securities market during 1999, including market liquidity, distortions in price formation, and the ease of hedging transactions.
- 6Contributing factors included the decision to remove 20-year issues from the list of issues eligible for delivery into futures listed on the TSE (decision on March 16, 1999, to be effective from March 2000 contract), and the decision not to take the 2nd issue of 20-year JGB at Bank of Japan's market operations (effective from June 4, 1999).
- 7In regard to fails, the Japan Securities Dealers Association published "The Guideline for Real Time Gross Settlement of Government Securities Transactions" ("The Guideline") in December 2000, in preparation for the Bank of Japan's introduction of real time gross settlement (RTGS) at the beginning of 2001. In "The Guideline", guidelines concerning fails consist of (1) definition of a fail, (2) good-faith effort to resolve a fail, (3) conditions to guidelines concerning a fail, (4) policy regarding costs incurred under a fail, (5) application of a fail based on establishment of a cut-off time, and (6) policy regarding payments and receipts in the case of internet payment and redemption prior to the resolution of a fail. At the time of the paper in 1999, however, no rules existed for failes.
Chart 2 Performance Comparison of Various Pricing Methods
Note: Shares for the pricing methods with the best fit with the actual prices for each issue were plotted.
Increase in Repo Rate Volatility -- More Risk for the Same Return
Turning to the JGB repo market, there is a theoretical arbitrage relationship between the repo rate and prices in cash and futures markets. Reviewing the conditions that existed for September 1999 and March 2000 futures contracts, which were regarded as less than liquid, one can observe high risks (high volatility of returns) relative to average returns, for an arbitrage position involving repo and a combination of cash and futures (Chart 3). In such a case, according to a response in the questionnaire above, arbitrage opportunities with potentially high returns were not exploited because the volatility of returns were deemed too high (in some cases three times more risk than average returns, Chart 3. right) from prudent risk management perspectives.
Various factors influenced this instability in the arbitrage relationship between cash and futures markets. In the futures market, the trading volume of September 1999 contract fell off and March 2000 contract became the most actively traded contract on August 9, 1999. Such a "skipping" of the next nearest maturity (the December 1999 contract) at such an early timing was unprecedented. One reason for this was that the CTD issues for September 1999 and December 1999 were 20-year issues, which were relatively illiquid. Accordingly, these contracts were not attractive to market participants, eroding their liquidity and effectiveness as hedging instruments. Meanwhile, as 20-year issues became ineligible for delivery from March 2000 futures contract onwards, the view that March 2000 contract should become the most actively traded contract at the earliest possible timing was widely shared by market participants.
Notwithstanding its status as the most actively traded contract, price of March 2000 contract moved erratically, and the basis moved sharply. This was influenced by the relative scarcity of longer-term repo transactions and the Y2K problem. In view of the arbitrage relationship that exists between the repo rate and cash and futures market prices, the repo rate is an important factor in determining the prices in the cash and futures markets. In the case of March 2000 contract, however, the reference repo rate for the seven months, from August 1999 to March 2000 was not readily available, as transactions in the Japanese repo market are concentrated on the short end, and longer-dated transactions are few. Furthermore, transactions maturing in March 2000 had to cross the end of 1999, when unforeseen problems might have surfaced due to Y2K, heightening the concerns of market participants.
Meanwhile, in the repo market, rumors surfaced around August 12, 1999 that some public sector investors would not be executing repo transactions (lending bonds) over the millennium changeover. The repo rate (which is equivalent to the difference between the rate for borrowing funds and the fee for lending securities) for CTD and other issues suddenly declined (an increase in the lending fee). At one time, the repo rate plunged to minus 2 percent and beyond. Behind such market turbulence was the fact that many market participants had shorted cash bonds assuming repo transactions would be available as usual over the end-of-1999 to cover short positions (by borrowing bonds). The initial rumor raised the specter of all public sector investment funds not lending bonds over the year-end. This added to the concerns in the market over the market liquidity of the newly most active March 2000 contract, and fueled market participants' nervousness over the liquidity of the cash and repo markets more generally.
As the futures and repo markets became unstable, dealers, who manage risks on a daily basis, were forced to wind down their positions to limit mark-to-market losses arising from volatile price movements. This contributed to the decline in the liquidity of the cash market. Forces at work included the closing out of short basis arbitrage positions (i.e., short cash and long futures) by dealers to limit losses (resulting in cash buying and futures selling), similar to what happened in June 1999. As a result, there was a chain of developments: the basis widened; the implied repo rate calculated from cash bond and futures prices dipped further into negative territory (i.e., a spike in the bond lending fee); and prices in the cash market increased steeply. At the same time, dealers who had lent bonds for a longer term in the repo market were faced with widening losses, as repo rates suddenly declined, and were compelled to close out such repo positions to contain losses, resulting in a further decline in the repo rate.
Chart 3 Mean and Variance in Rate of Return on Short Basis Positions
Amplification of Issue-Specific Price Movements in the Cash Market
The extent of issue-specific price movements can be represented by the differences between the actual yield of each issue and the corresponding point on a reference yield curve (plotting theoretical yields determined by remaining maturity). Chart 4 summarizes such differences from the end of 1998 to the beginning of 2000, using yield curves plotted from information on all issues and plotted from information on liquid issues in each remaining maturity zone ("zone benchmarks"). The Chart shows seven periods (I to VII) when issue-specific price movements or the deviations from the yield curve were prominent. It can be seen that there were significant issue-specific price movements with deviations three to four times as large as usual in Periods IV, V, and VI, which corresponded to the periods of instability explained earlier--in mid-1999 when the arbitrage relations between the cash and futures markets were unstable, and between summer and fall 1999 when the liquidity in the repo market were lower.
It was pointed out in the survey (see Endnote 5) that dealers incurring losses in the volatile markets since June 1999 became reluctant to conduct arbitrage transactions taking advantage of distortions in the yield curve, resulting in a more direct reflection in the interdealer market of preferences for individual issues by investors. Chart 4 shows that the distortions in the yield curve became even larger towards the end of September, the end of the first half of the accounting year. This implies that while the arbitrage relations between markets gradually returned to normal after the turbulence in the markets in August, strains remained in the arbitrage relations between individual issues in the cash market.
In order to understand the movements of long-term interest rates, it is necessary to comprehensively monitor developments in the cash, futures, and repo markets, and also any issue-specific price fluctuations reflecting supply/demand conditions. The key rates for this purpose and determining the shape of the yield curve--prices of futures, the on-the-run issue and the CTD issue, and the repo rate--are all inter-related, but at the same time fluctuate dynamically reflecting the supply/demand conditions in each market. Behind this process is the arbitrage relationship between these markets and between individual issues. Prices in each market may move reflecting the arbitrage relationships, or they may move independently reflecting market-or issue-specific characteristics. At times, arbitrage opportunities may be left unexploited for long periods when market functioning is compromised. Market developments in 1999 offer a rich source of materials for studying the pricing mechanisms in the government securities market.
Chart 4 Developments in Spline SSR (Sum of Squared Residuals)
This is the first Market Review in English (Market Review E-series) edited by the Bank of Japan Financial Markets Department. Market Review presents topical issues in plain terms, including the essence of staff studies on market functioning and practices as well as analysis of financial statistics, in order to stimulate comments and discussions from a wide audience. The Japanese version (J-series) has been released since October 2000 on a monthly basis, from which appropriate titles will be selected for the E-series. The views expressed in the Review are those of the authors and do not necessarily represent the views of the Bank of Japan. Comments and questions as well as requests for hard copies should be addressed to Tokiko Shimizu, Manager, Financial Markets Department (email@example.com).Market Review E-series and Financial Markets Department Working Papers E-series can be obtained through the Bank of Japan's Web site.