JP4384795B2 - Bond characteristic calculation system - Google Patents

Description

【００３０】
なお、数１では、償還価格が１００円の債券を対象としている。
【００３１】
平均スプレッド算出部２３は、個別スプレッド算出部２２が算出した個別スプレッドＳＰ_i、および時価ウェイト算出部２１が算出した時価ウェイトＷ_iを取得して、基準日の市場の平均スプレッドＳＰ_AVを算出する。平均スプレッド算出部２３は、ここで算出した平均スプレッドＳＰ_AVを、債券インデックスデータベース４５に登録する。ここでは、特に事業債の平均スプレッドを、以下の式で算出する。
【００３２】
【数２】

【００３３】
修正デュレーション算出部２５は、債券属性データベース４１、４２、４３を参照して、各銘柄のデュレーションＤｕｒおよび修正デュレーションＭＤｕｒを算出する。具体的には以下の式で算出する。修正デュレーション算出部２５は、ここで算出した修正デュレーションＭＤｕｒを債券インデックスデータベース４５に登録する。
【００３４】
【数３】

【００３５】
Ｃ_i：ｉ番目のキャッシュフロー（＝クーポン＋償還金）
Ｔ_i：キャッシュフロー発生までの期間
ｒ：半年複利年利回り
【００３６】
【数４】

【００３７】
なお、数３および数４では、半年ごとにクーポンの支払があるタイプの債券を対象としている。
【００３８】
ここで、デュレーションＤｕｒおよび修正デュレーションＭＤｕｒは、市場の金利水準の変化に対する各債券の価格変化の感応度（金利感応度）を示すものであることが知られている。
【００３９】
以上説明した処理により、債券インデックス算出システム２は、債券インデックスを算出し、債券インデックスデータベース４５に蓄積する。債券インデックス算出システム２は、随時処理を行い債券インデックスを算出することができる。
【００４０】
価格感応度算出システム３は、債券インデックスデータベース４５に蓄積されたデータに基づいて、以下に説明するような統計的な処理を行う。処理結果の信頼性を確保するためには、ある程度以上のポイント数のデータが必要である。そこで、本実施形態においては、月末取引日の債券インデックスが、たとえば４０ヶ月分以上蓄積されている場合に以下の処理を行うものとする。
【００４１】
実績スプレッド感応度算出部３１は、債券インデックスデータベース４５を参照し、個別スプレッドが算出されている各銘柄について実績スプレッド感応度ＳＰＳ_ACTを算出する。実績スプレッド感応度算出部３１は、算出した実績スプレッド感応度を債券特性記憶部３５に記憶する。
【００４２】
ここで、「スプレッド感応度」とは、市場の平均スプレッドの変化に対する各債券の個別スプレッドの変化率をいう。すなわち、スプレッド感応度は、平均スプレッドが１ポイント変化したときに、各債券の個別のスプレッドがどれだけ変化するかを定量的に示すものである。したがって、スプレッド感応度は、市場のスプレッド水準の変化に対する各債券の個別スプレッドへの影響度を表している。
【００４３】
また、当該銘柄の個別スプレッドから算出したスプレッド感応度を「実績スプレッド感応度」といい、後述する処理により実績スプレッド感応度から推定したスプレッド感応度を「推定スプレッド感応度」という。特に区別せず、単に「スプレッド感応度」というときは、実績スプレッド感応度および推定スプレッド感応度のいずれも含むものとする。
【００４４】
実績スプレッド感応度は、具体的には以下のように算出する。まず、債券インデックスデータベース４５から過去４０ヶ月分の平均スプレッド４５２、およびスプレッド感応度算出対象銘柄の個別スプレッド４５４を取得する。本実施形態では、個別スプレッドの数が４０ヶ月分に満たない場合でも、一定数（たとえば１２ヶ月分）以上ある銘柄は、実績スプレッド感応度の算出対象銘柄とする。個別スプレッドの数が一定数に満たない銘柄については、実績スプレッド感応度の算出対象外とする。したがって、実績スプレッド感応度の算出対象銘柄群と算出対象外銘柄群とが存在する。
【００４５】
図７に示すように、前月末の個別スプレッドＳＰとの差分（変化量）ΔＳＰ、および前月末の平均スプレッドＳＰ_AVとの差分（変化量）ΔＳＰ_AVを求める。そして、図８に示すような、平均スプレッドの変化量ΔＳＰ_AVをＸ軸、個別スプレッドの変化量ΔＳＰをＹ軸としたＸ−Ｙ平面上にデータ６０１（図中の●。図中では１ヵ所のみ符号を付す。）をプロットする。このデータに基づいて、単回帰分析、たとえば最小二乗法を用いて直線に近似する。すなわち、Ｙ＝ＡＸ＋Ｂの形に近似して、ＡとＢを求める。ここで求めたＡが、すなわち実績スプレッド感応度ＳＰＳ_ACTである。この処理を各銘柄について行い、各銘柄のごとに実績スプレッド感応度を算出する。なお、本実施形態では単回帰分析を用いているが、必ずしもこれに限定されない。たとえば、単回帰分析以外の線形近似、あるいは、任意の多項式近似を用いてもよい。
【００４６】
推定スプレッド感応度算出部３２は、債券特性記憶部３５、事業債属性データベース４２、および非国債非事業債属性データベース４３を参照して、実績スプレッド感応度および債券属性に基づいてスプレッドベータを推定し、推定スプレッド感応度ＳＰＳ_ESTを得る。推定スプレッド感応度算出部３２は、算出した推定スプレッド感応度を債券特性記憶部３５に記憶する。スプレッド感応度の推定は、業種ごと、または債券種別ごとに行う。
【００４７】
たとえば、実績スプレッド感応度の算出対象外に分類される銘柄は、発行されてから間もない銘柄が含まれる。これは以下の理由による。つまり、これらは月末データのデータ数が少ないので、実績スプレッド感応度を算出しても、その信頼度は十分でないと考えられる。このため、そのような銘柄については、他の銘柄の実績スプレッド感応度から推定してスプレッドベータを求めることとした。また、同様に実績スプレッド感応度の算出対象外である一部の地方債等のように、時価等の市場での取引データを十分に収集できない銘柄についても、スプレッド感応度を推定する。
【００４８】
さらに、実績スプレッド感応度は、実測値に基づいて算出されたものであるため、さまざまな特殊要因による誤差を包含すると考えられる。このため、後述するスプレッドベータおよびポートフォリオ・スプレッドベータの算出に用いるために、実績スプレッド感応度の算出対象銘柄についても、推定スプレッド感応度を算出することが好ましい。
【００４９】
具体的には、同一の業種（非国債非事業債については債券種別）に属する銘柄について、推定スプレッド感応度算出部３２は、事業債属性データベース４２および非国債非事業債属性データベース４３から、格付４４５と残存期間４４６を取得する。格付けは複数存在するので、以下の処理では一定のルールに基づき、最適な格付４４５を用いる。推定スプレッド感応度算出部３２は、実績スプレッド感応度が算出されている銘柄について、さらに債券特性記憶部３５から実績スプレッド感応度を取得する。
【００５０】
そして、実績スプレッド感応度の算出対象銘柄については、図９に示すような、格付ＢＲをＸ軸、残存年数ＮをＹ軸、スプレッド感応度ＳＰＳをＺ軸にとった３次元空間にデータ７０１（図中の×。図中では１ヵ所のみ符号を付す。）をプロットする。プロットされたデータ７０１に基づいて、重回帰分析を行い、当該３次元空間内の平面７０３に近似する。すなわち、推定スプレッド感応度算出部３２は、Ｚ＝ａＸ＋ｂＹ＋ｃのａ，ｂ，ｃを決定する。したがって、少なくとも３つ以上のデータ７０１が必要である。このようにして、同一業種について、一つの平面を求める。これは、同一の業種の債券は、共通した性質を有すると考えられるからである。なお、本実施形態では、スプレッド感応度の推定に格付と残存年数を用いたが、必ずしもこれに限定されない。たとえば、格付と残存年数に加えて、他の債券属性を用いてもよい。
【００５１】
実績スプレッド感応度の算出対象外の銘柄については、上で求めた平面７０３と、債券の残存年数Ｎ_iおよび格付ＢＲ_iから推定スプレッド感応度ＳＰＳ_ESTiを算出する。実績スプレッド感応度が求められている銘柄の債券についても同様に、推定スプレッド感応度ＳＰＳ_ESTjを求める。
【００５２】
ポートフォリオ・スプレッドベータ算出部３３は、債券特性記憶部３５を参照して、各銘柄のスプレッドベータβを算出する。また、ポートフォリオ・スプレッドベータ算出部３３は、さらに、ポートフォリオ情報記憶部３６を参照し、各銘柄のスプレッドベータおよびポートフォリオ情報に基づいて、ポートフォリオ・スプレッドベータ（以下、「ＰＳＢ」と称する。）を算出する。ポートフォリオ・スプレッドベータ算出部３３は、算出したスプレッドベータ、およびＰＳＢを債券特性記憶部３５に記憶する。
【００５３】
ここで、「スプレッドベータ」とは、各銘柄のスプレッド感応度と金利感応度との積をいう。すなわち、スプレッドベータは、平均スプレッドが１ポイント変化したときに、各債券の価格がどれだけ変化するかを定量的に示すものである。したがって、スプレッドベータは、市場のスプレッド水準の変化に対する債券の価格変化の感応度（各債券の価格感応度）を表している。
【００５４】
また、「ポートフォリオ・スプレッドベータ（ＰＳＢ）」とは、ポートフォリオを構成する各銘柄のスプレッドベータと当該銘柄が当該ポートフォリオに占める割合との積の総和をいう。すなわち、ＰＳＢは、市場の平均スプレッドが１ポイント変化したときに、そのポートフォリオ価値がどの程度変化するかを定量的に示すものである。したがって、ＰＳＢは、市場のスプレッド水準の変化に対するポートフォリオ価値の変化の感応度（ポートフォリオ価値感応度）を表している。
【００５５】
具体的には、ポートフォリオ・スプレッドベータ算出部３３は、債券特性記憶部３５から推定スプレッド感応度を取得し、債券インデックスデータベース４５から修正デュレーションを取得する。そして、各銘柄について、スプレッドベータとして推定スプレッド感応度および修正デュレーションの積を求める。
【００５６】
また、ポートフォリオ・スプレッドベータ算出部３３は、ポートフォリオ情報記憶部３６、債券属性データベース４１、４２、４３および債券日次データベース４４を参照して、時価ウェイト算出部２１と同様の処理により、各銘柄のポートフォリオにおける時価ウェイトを算出する。ポートフォリオ・スプレッドベータ算出部３３は、各銘柄のスプレッドベータと時価ウェイトの積を求め、ポートフォリオを構成する全銘柄について、この積の総和を算出する。この総和がＰＳＢである。ポートフォリオ・スプレッドベータ算出部３３は、自己のポートフォリオのみならず、市場全体を一つのポートフォリオとみて、市場のＰＳＢも算出する。
【００５７】
なお、本実施形態では、ポートフォリオ・スプレッドベータ算出部３３の処理で推定スプレッド感応度を用いているが、必ずしもこれに限定されない。すなわち、実績スプレッド感応度を用いてもよい。また、同様に、修正デュレーションの代りにデュレーションを用いてもよい。
【００５８】
上記実施形態で求めた自己のポートフォリオのＰＳＢと、市場全体のＰＳＢとを比較することにより、市場のスプレッドが変化したときに、ベンチマーク（市場平均）の収益変化に対して、自己のポートフォリオの収益変化の程度を定量的に把握することができる。その検証結果を、図１０および図１１に示す。
【００５９】
図１０は、ＰＳＢおよびデュレーションをベンチマークと同一にしたファンドの収益率、およびベンチマークの収益率の推移を示している。このグラフの横軸は時間（年月）、縦軸は1999年3月末を基準とした累積収益率（左軸）およびポートフォリオとベンチマークの収益率の差（右軸）である。すなわち、両者はほぼ重なっていることが分かる。
【００６０】
図１１では、ベンチマークとＰＳＢが同一（ＰＳＢ＝１．２）のファンド、ＰＳＢが１．８のファンド、ＰＳＢが０．６のファンド、および、ベンチマークのそれぞれの収益率の推移を示している。このグラフも、横軸は時間（年月）、縦軸は1999年3月末を基準とした累積収益率である。
【００６１】
これらのグラフから明らかなように、債券市場で資金を運用するファンドマネージャーは、スプレッドの変動予測結果を含むシナリオに基づいて、ポートフォリオの銘柄入れ替え等を行ってＰＳＢを調整することにより、ベンチマークを上回る収益をあげることができる。もしくは、ＰＳＢがベンチマークと同じになるように調整することにより、自己のポートフォリオの収益がベンチマークの収益に追随することを可能とする。
【００６２】
さらに、図１４に示すように、ここで説明したＰＳＢの調整と、従来の金利水準の予測結果に基づくデュレーション調整とを組み合わせて統合管理し、個別銘柄を選別してポートフォリオを構築することにより、より確実にリスクを把握することができるようになる。
【００６３】
また、債券特性記憶部３５に記憶された債券またはポートフォリオの特性を示す各種情報は、図示しない出力手段により出力することができる。たとえば、図１２および図１３に示す帳票を出力する。
【００６４】
図１２では、ベンチマークと自己のポートフォリオについて、債券種別ごとにそれぞれの特性を対比した帳票の一例を示している。図１３では、あるファンドについてのさまざまな情報と併せて、本システム１で算出した情報を表示した帳票例を示している。
【００６５】
なお，上記実施形態において、特定の機能を実現する場合、その機能実現のために必要な処理部のみを残し、その他の処理部等を省略することができる。
【００６６】
【発明の効果】
本発明によれば、市場のスプレッド水準の変化に対する個別の債券の特性を明らかにするための尺度を求めることができる。
【００６７】
さらに、本発明によれば、市場のスプレッド水準の変化に対するポートフォリオ全体の特性を明らかにするための尺度を求めることができる。
【図面の簡単な説明】
【図１】本発明の一実施形態に係る債券特性およびポートフォリオ特性算出システムの全体構成を示すブロック図である。
【図２】各処理部と、データベース群４１〜４５および各記憶部３５、３６との間のデータの流れ図である。
【図３】（ａ）は、国債属性データベース４１および非国債非事業債属性データベース４３が記憶するデータの種類を示す説明図であり、（ｂ）は、事業債属性データベース４２が記憶するデータの種類を示す説明図である。
【図４】債券日次データベース４４が記憶するデータの種類を示す説明図である。
【図５】債券インデックスデータベース４５が記憶するデータの種類を示す説明図である。
【図６】個別スプレッドの算出方法を説明するための図である。
【図７】個別スプレッドと平均スプレッドのそれぞれの差分の算出方法を説明するための図である。
【図８】実績スプレッド感応度の算出方法の一例を説明するための図である。
【図９】推定スプレッド感応度の算出方法の一例を説明するための図である。
【図１０】ＰＳＢとデュレーションをベンチマークと同一にしたファンドと、ベンチマークの収益率の変動を示すグラフである。
【図１１】ＰＳＢの異なるファンドと、ベンチマークの収益率の変動を示すグラフである。
【図１２】出力帳票の一例を示す図である。
【図１３】出力帳票の他の一例を示す図である。
【図１４】デュレーションおよびポートフォリオ・スプレッドベータを統合管理して、ポートフォリオを構築するためのイメージ図である。
【符号の説明】
１…コンピュータシステム、２…債券インデックス算出システム、３…価格感応度算出システム、２１…時価ウェイト算出部、２２…個別スプレッド算出部、２３…平均スプレッド算出部、２４…無リスクレートカーブ算出部、２５…修正デュレーション算出部、３１…実績スプレッド感応度算出部、３２…推定スプレッド感応度算出部、３３…ポートフォリオ・スプレッドベータ算出部。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a computer system for determining the characteristics of each bond or portfolio with respect to changes in average spread in the bond market.
[0002]
[Prior art]
When funds are managed in the bond market, investment performance is often evaluated using the average (total market) rate of return in the bond market as a reference (benchmark). In other words, fund managers who manage funds in the bond market aim to make their portfolios profit above benchmarks. This type of operation is called a “benchmark beat (exceed) type”.
[0003]
When building a portfolio, fund managers forecast changes in interest rates across the market and spreads (yield gap) with Japanese government bonds. Based on the prediction result, the portfolio brands are replaced so as to exceed the market benchmark. At this time, the duration of the entire portfolio or the modified duration is adjusted based on the prediction result of the interest level, and a benchmark beat type portfolio is constructed. Here, duration or modified duration represents the sensitivity of the price or value of an individual bond or the entire portfolio to changes in interest rates.
[0004]
[Problems to be solved by the invention]
On the other hand, the adjustment based on the spread level prediction results has conventionally been an adjustment by swapping stocks based on a comparison between the composition ratio of bond types such as government bonds and business bonds and the composition ratio of benchmarks.
[0005]
However, regarding spread level changes, there was no quantitative measure equivalent to the duration of interest rate changes. For this reason, the portfolio was built based on the experience and intuition of the fund manager.
[0006]
Accordingly, an object of the present invention is to provide a system or the like for obtaining a scale for clarifying characteristics of individual bonds with respect to changes in market spread levels.
[0007]
Another object of the present invention is to provide a system or the like for obtaining a measure for clarifying characteristics of the entire portfolio with respect to changes in market spread level.
[0008]
[Means for Solving the Problems]
According to the first aspect of the present invention, the following processing is performed. That is, from the means for storing information indicating individual spreads at N points of time different from each other (N is 2 or more) and information indicating market average spreads at the same N points of time as the individual spreads, Information indicating individual individual spreads and information indicating N market average spreads are obtained. Based on the N individual spreads and the N market average spreads, the sensitivity of the change in the individual spreads with respect to the change in the market average spread is calculated for the bond of the calculation target issue.
[0009]
According to the second aspect of the present invention, the following processing is performed. That is, for a plurality of bond bonds constituting the portfolio, information relating to the bond composition ratio is acquired from means for storing information related to the bond composition ratio of each brand in the portfolio. Information on the sensitivity of the bond price change is acquired from the means for storing information on the sensitivity of the bond price change to the market interest rate change for all stocks constituting the portfolio. Information on the sensitivity of the change of the individual spread is acquired from the means for storing information on the sensitivity of the change of the individual spread of each brand with respect to the change of the spread level of the market. Based on the information on the composition ratio of the bonds, the information on the sensitivity of the bond price change, and the information on the sensitivity of the individual spread change, the change in the value of the portfolio with respect to the market spread level change Calculate the sensitivity.
[0010]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, a computer system 1 for calculating bond characteristics and portfolio characteristics according to an embodiment of the present invention will be described with reference to the drawings.
[0011]
FIG. 1 shows an overall configuration diagram of a computer system 1. The system 1 includes a bond index calculation system 2 that calculates indices and the like in the bond market, a price sensitivity calculation system 3 that calculates price sensitivity of bonds, and database groups 41 to 45. Both the bond index calculation system 2 and the price sensitivity calculation system 3 are configured by a computer system. Each processing unit or each function described below is realized, for example, when a computer executes an application program for performing each process. In addition, the system 1 can be realized by using a single computer, or can be realized by distributing processing using a plurality of computers.
[0012]
The bond index calculation system 2 includes, as internal functions, processing units such as a market price weight calculation unit 21, an individual spread calculation unit 22, an average spread calculation unit 23, a risk-free rate curve calculation unit 24, and a modified duration calculation unit 25. ing.
[0013]
The price sensitivity calculation system 3 includes an actual spread sensitivity calculation unit 31, an estimated spread sensitivity calculation unit 32, and a processing unit of a portfolio spread beta (PSB) calculation unit 33, a bond characteristic storage unit 35, and portfolio information. A storage unit 36 is provided.
[0014]
The bond characteristic storage unit 35 stores information related to characteristics of individual bonds or the entire portfolio. For example, the individual spread sensitivity, the estimated spread sensitivity, the spread beta, the portfolio spread beta of one's own portfolio, and the portfolio spread of the entire market calculated by each of the processing units 31, 32, and 33 Beta (each term will be described later) is stored.
[0015]
The portfolio information storage unit 36 stores information regarding its own portfolio. For example, with respect to bonds of a plurality of brands constituting a portfolio, information on the composition ratio of bonds of each brand in the portfolio is stored. For example, the number of units of brands constituting the portfolio and the number of units of the brands in the entire market are stored.
[0016]
The database group included in the system 1 includes a government bond attribute database 41, a business bond attribute database 42, a non-government bond non-business bond attribute database 43, a bond daily database 44, and a bond index database 45.
[0017]
The government bond attribute database 41, the business bond attribute database 42, and the non-government bond non-business bond attribute database 43 (hereinafter collectively referred to as “bond bond attribute database”), as will be described in detail later, bond attributes of each bond type. I remember information. In other words, the government bond attribute database 41 manages information related to attributes for each issue of Japanese government bonds (hereinafter simply referred to as “government bonds”). The business bond attribute database 42 manages information related to attributes for each brand of the business bond. The non-government bond non-business bond attribute database 43 manages attribute information for each brand for government bonds such as local bonds, government-guaranteed bonds, and bonds other than business bonds. Such information can be registered by an operator from a registration screen (not shown).
[0018]
Specifically, as shown in FIGS. 3A and 3B, the government bond attribute database 41 and the non-government bond non-business bond attribute database 43 have an issuer code 411 (representing a bond issuer as a data item). 431), a bond type 412 (432) such as a government bond, a local bond, and a business bond, a bond code 413 (433) for uniquely identifying the bond of the brand, a bond brand name 414 (434), It has a residual amount 415 (435) of the bond of the brand, a maturity date 416 (436) of the bond of the brand, and a coupon rate 417 (437) of the bond of the brand. The business bond attribute database 42 similarly has, as data items, an issuer code 421, a bond type 422, a bond code 423, a bond brand name 424, a remaining amount 425, a maturity date 426, and a coupon rate 426. It has an industry 428 to which it belongs.
[0019]
The bond daily database 44 stores various information (for example, transaction data, ratings, etc.) in the market for each bond for each bond. For example, as shown in FIG. 4, the bond daily database 44 has, as data items, transaction date 441, bond code 442, yield 443, market price 444, rating 445, remaining period 446, and government bond yield 447 for the corresponding period. . The rating 445 can be rated by a plurality of rating agencies (in this case, four ratings 1 to 4).
[0020]
The bond index database 45 stores information used in a price sensitivity calculation system such as a bond market index. For example, as shown in FIG. 5, the bond index database 45 includes, as data items, a transaction date 451, an average spread 452 of the transaction date, a bond code 453 of an individual bond, an individual spread 454 of the bond, and a modified duration of the bond. 455. The bond index database 45 accumulates past data. The bond code 453, the individual spread 454, and the modified duration 455 have only the stocks for which the individual spread and the modified duration are calculated, respectively.
[0021]
FIG. 2 is a data flow chart showing what information the processing units of the bond index calculation system 2 and the price sensitivity calculation system 3 exchange with the database groups 41 to 45 and the storage units 35 and 36. is there.
[0022]
The risk-free rate curve calculation unit 24 refers to the government bond attribute database 41 and the bond daily database 44 to calculate a risk-free rate curve 500 on a certain transaction date (hereinafter referred to as “reference date”). Here, the risk-free rate curve is a yield curve of government bonds.
[0023]
Specifically, the following processing is performed. There are several issues of government bonds with different remaining periods. Therefore, the risk-free rate curve calculation unit 24 obtains the maturity date 416 from the government bond attribute database 41 for each brand and obtains the remaining years. The risk-free rate curve calculation unit 24 further obtains the yield 443 of the reference date for each issue from the bond daily database 44. Then, for example, yield data 501 of each brand (X in the figure. In the figure, only one symbol is shown on the XY plane in which the remaining years and yields are taken on the X axis and the Y axis, respectively, as shown in FIG. Plot.). Based on the plotted data 501, a risk-free rate curve 500 is calculated by performing, for example, cubic spline interpolation.
[0024]
The individual spread calculation unit 22 refers to the bond daily database 44, and uses the risk-free rate curve 500 calculated by the risk-free rate curve calculation unit 24, and uses the individual spread SP for each issue. _i Is calculated. The individual spread calculation unit 22 registers the individual spread calculated here in the bond index database 45. The calculation of the individual spread is performed on a group of issues composed of issues whose transaction data such as yield is stored in the bond daily database 44.
[0025]
Specifically, the individual spread calculation unit 22 acquires the maturity dates 426 and 436 of the target issue from the business bond attribute database 42 and the non-government bond non-business bond attribute database 43 and obtains the remaining years. The individual spread calculation unit 22 acquires the yield 443 for the reference date of each bond from the bond daily database 44. According to the remaining years and yields of each brand, the individual spread is obtained by plotting the yield data 502 (● in the figure. Only one symbol is attached in the figure) on the XY plane shown in FIG. In other words, for each bond, the yield difference with the government bond with the same remaining age is obtained, and this is calculated as the individual spread SP. _i And
[0026]
In this embodiment, the yield difference with the government bond is used as the spread of each bond, but the present invention is not necessarily limited to this. For example, the spread may be a difference with a yield of a bond other than a government bond or a yield with a reference such as a swap rate.
[0027]
The market price weight calculation unit 21 refers to the bond attribute databases 41, 42, 43 and the bond daily database 44, and for the index target brand, the ratio of the market capitalization of each brand to the total market capitalization of the whole target brand (market price weight) : W _i ) Is calculated.
[0028]
Specifically, the market value weight calculation unit 21 acquires the residual amounts 415, 425, and 435 of the bonds from the bond attribute databases 41, 42, and 43. From the bond daily database 44, the market price 444 of each bond on the reference date is acquired. Market weight W of each bond _i Is obtained by the following equation.
[0029]
[Expression 1]

[0030]
In Equation 1, bonds with a redemption price of 100 yen are targeted.
[0031]
The average spread calculator 23 is an individual spread SP calculated by the individual spread calculator 22. _i , And the market price weight W calculated by the market price weight calculation unit 21 _i To get the average spread SP of the market on the base date _AV Is calculated. The average spread calculation unit 23 calculates the average spread SP calculated here. _AV Is registered in the bond index database 45. Here, the average spread of business bonds is calculated using the following formula.
[0032]
[Expression 2]

[0033]
The modified duration calculation unit 25 refers to the bond attribute databases 41, 42, and 43 to calculate the duration Dur and the modified duration MDur of each brand. Specifically, it is calculated by the following formula. The modified duration calculation unit 25 registers the modified duration MDur calculated here in the bond index database 45.
[0034]
[Equation 3]

[0035]
C _i : I-th cash flow (= coupon + redemption)
T _i : Period until cash flow occurs
r: Half year compound interest rate
[0036]
[Expression 4]

[0037]
In Equations 3 and 4, bonds of the type with coupon payments every six months are targeted.
[0038]
Here, it is known that the duration Dur and the modified duration MDur indicate the sensitivity (rate sensitivity) of the price change of each bond with respect to the change in the market interest rate level.
[0039]
By the processing described above, the bond index calculation system 2 calculates a bond index and stores it in the bond index database 45. The bond index calculation system 2 can calculate a bond index by performing processing at any time.
[0040]
The price sensitivity calculation system 3 performs statistical processing as described below based on data accumulated in the bond index database 45. In order to ensure the reliability of the processing result, data having a certain number of points or more is required. Therefore, in the present embodiment, the following processing is performed when the bond index of the month end trading date is accumulated for, for example, 40 months or more.
[0041]
The actual spread sensitivity calculation unit 31 refers to the bond index database 45, and the actual spread sensitivity SPS for each issue for which an individual spread is calculated. _ACT Is calculated. The actual spread sensitivity calculation unit 31 stores the calculated actual spread sensitivity in the bond characteristic storage unit 35.
[0042]
Here, “spread sensitivity” refers to the rate of change of the individual spread of each bond relative to the change of the average spread in the market. In other words, the spread sensitivity quantitatively indicates how much the individual spread of each bond changes when the average spread changes by one point. Thus, spread sensitivity represents the impact of each bond on individual spreads to changes in market spread levels.
[0043]
Moreover, the spread sensitivity calculated from the individual spread of the brand is referred to as “actual spread sensitivity”, and the spread sensitivity estimated from the actual spread sensitivity by the process described later is referred to as “estimated spread sensitivity”. No particular distinction, and simply “spread sensitivity” includes both actual spread sensitivity and estimated spread sensitivity.
[0044]
Specifically, the actual spread sensitivity is calculated as follows. First, the average spread 452 for the past 40 months and the individual spread 454 of the spread sensitivity calculation target issue are acquired from the bond index database 45. In the present embodiment, even when the number of individual spreads is less than 40 months, brands having a certain number (for example, 12 months) or more are assumed to be performance price sensitivity calculation brands. For stocks for which the number of individual spreads is less than a certain number, the actual spread sensitivity will not be calculated. Accordingly, there are a calculation target stock group and a non-calculation stock group for the actual spread sensitivity.
[0045]
As shown in FIG. 7, the difference (change) ΔSP from the individual spread SP at the end of the previous month, and the average spread SP at the end of the previous month _AV Difference (change amount) ΔSP _AV Ask for. Then, the change amount ΔSP of the average spread as shown in FIG. _AV Is plotted on the XY plane with the X axis as the X-axis and the individual spread change ΔSP as the Y axis (● in the figure. Only one symbol is attached in the figure). Based on this data, a simple regression analysis, for example, a least square method is used to approximate a straight line. That is, A and B are obtained by approximating the form of Y = AX + B. The A obtained here is the actual spread sensitivity SPS. _ACT It is. This process is performed for each brand, and the actual spread sensitivity is calculated for each brand. In addition, although this embodiment uses single regression analysis, it is not necessarily limited to this. For example, linear approximation other than simple regression analysis or arbitrary polynomial approximation may be used.
[0046]
The estimated spread sensitivity calculation unit 32 refers to the bond characteristic storage unit 35, the business bond attribute database 42, and the non-government bond non-business bond attribute database 43, and estimates the spread beta based on the actual spread sensitivity and the bond attributes. Estimated spread sensitivity SPS _EST Get. The estimated spread sensitivity calculation unit 32 stores the calculated estimated spread sensitivity in the bond characteristic storage unit 35. Spread sensitivity is estimated for each industry or bond type.
[0047]
For example, brands classified as not subject to calculation of actual spread sensitivity include brands that have just been issued. This is due to the following reason. In other words, since the number of end-of-month data is small, it is considered that the reliability is not sufficient even if the actual spread sensitivity is calculated. For this reason, for such issues, the spread beta was estimated by estimating from the actual spread sensitivity of other issues. Similarly, spread sensitivities are also estimated for stocks that cannot sufficiently collect transaction data in the market such as market prices, such as some local bonds that are not subject to calculation of actual spread sensitivities.
[0048]
Furthermore, since the actual spread sensitivity is calculated based on actual measurement values, it is considered that errors due to various special factors are included. For this reason, in order to use for calculation of spread beta and portfolio spread beta, which will be described later, it is preferable to calculate the estimated spread sensitivity for the stocks for which the actual spread sensitivity is calculated.
[0049]
Specifically, the estimated spread sensitivity calculation unit 32 uses the business bond attribute database 42 and the non-government bond non-business bond attribute database 43 for ratings belonging to the same industry (bond type for non-government non-business bonds). 445 and remaining period 446 are acquired. Since there are a plurality of ratings, in the following processing, an optimal rating 445 is used based on a certain rule. The estimated spread sensitivity calculation unit 32 further acquires the actual spread sensitivity from the bond characteristic storage unit 35 for the brand for which the actual spread sensitivity is calculated.
[0050]
As shown in FIG. 9, data 701 (in a three-dimensional space with the rating BR as the X axis, the remaining years N as the Y axis, and the spread sensitivity SPS as the Z axis as shown in FIG. X in the figure. Only one place is attached in the figure.) Is plotted. Based on the plotted data 701, multiple regression analysis is performed to approximate the plane 703 in the three-dimensional space. That is, the estimated spread sensitivity calculation unit 32 determines a, b, and c of Z = aX + bY + c. Therefore, at least three or more pieces of data 701 are necessary. In this way, one plane is obtained for the same industry. This is because bonds in the same industry are considered to have a common property. In the present embodiment, the rating and the remaining years are used for estimating the spread sensitivity, but the present invention is not necessarily limited to this. For example, other bond attributes may be used in addition to the rating and remaining years.
[0051]
For stocks that are not subject to the calculation of actual spread sensitivity, the plane 703 obtained above and the remaining number of years N _i And rating BR _i Estimated spread sensitivity SPS _ESTi Is calculated. Similarly, bonds with stocks for which actual spread sensitivity is required are similarly estimated spread sensitivity SPS. _ESTj Ask for.
[0052]
The portfolio spread beta calculation unit 33 refers to the bond characteristic storage unit 35 and calculates the spread beta β of each issue. Further, the portfolio spread beta calculation unit 33 refers to the portfolio information storage unit 36 and calculates a portfolio spread beta (hereinafter referred to as “PSB”) based on the spread beta and portfolio information of each brand. To do. The portfolio spread beta calculation unit 33 stores the calculated spread beta and PSB in the bond characteristic storage unit 35.
[0053]
Here, “spread beta” means the product of spread sensitivity and interest rate sensitivity of each stock. In other words, the spread beta quantitatively indicates how much the price of each bond changes when the average spread changes by 1 point. Thus, spread beta represents the sensitivity of bond price changes to changes in market spread levels (the price sensitivity of each bond).
[0054]
“Portfolio spread beta (PSB)” refers to the sum of the products of the spread beta of each issue that makes up the portfolio and the proportion of that issue in the portfolio. In other words, the PSB quantitatively indicates how much the portfolio value changes when the average spread of the market changes by 1 point. Therefore, PSB represents the sensitivity of portfolio value changes (portfolio value sensitivity) to changes in market spread levels.
[0055]
Specifically, the portfolio spread beta calculation unit 33 acquires the estimated spread sensitivity from the bond characteristic storage unit 35 and acquires the modified duration from the bond index database 45. Then, for each brand, the product of the estimated spread sensitivity and the modified duration is obtained as a spread beta.
[0056]
Further, the portfolio spread beta calculation unit 33 refers to the portfolio information storage unit 36, the bond attribute databases 41, 42, 43, and the bond daily database 44, and performs the same process as the market value weight calculation unit 21 to perform the process of each issue. Calculate the market weight in the portfolio. The portfolio spread beta calculator 33 obtains the product of the spread beta and the market value weight of each issue, and calculates the sum of the products for all issues constituting the portfolio. This sum is PSB. The portfolio spread beta calculator 33 calculates not only its own portfolio but also the entire market as one portfolio, and calculates the PSB of the market.
[0057]
In this embodiment, the estimated spread sensitivity is used in the processing of the portfolio spread beta calculation unit 33, but the present invention is not necessarily limited to this. That is, the actual spread sensitivity may be used. Similarly, a duration may be used instead of the modified duration.
[0058]
By comparing the PSB of the own portfolio obtained in the above embodiment and the PSB of the entire market, when the market spread changes, the profit of the own portfolio against the change in the benchmark (market average) profit The degree of change can be grasped quantitatively. The verification results are shown in FIGS.
[0059]
FIG. 10 shows the rate of return of a fund whose PSB and duration are the same as the benchmark, and the trend of the rate of return of the benchmark. The horizontal axis of this graph is time (year and month), and the vertical axis is the cumulative rate of return (left axis) based on the end of March 1999 and the difference between the portfolio and benchmark rate of return (right axis). That is, it can be seen that the two are almost overlapped.
[0060]
FIG. 11 shows changes in the return rates of a fund with the same benchmark and PSB (PSB = 1.2), a fund with a PSB of 1.8, a fund with a PSB of 0.6, and a benchmark. In this graph, the horizontal axis is time (year and month), and the vertical axis is the cumulative rate of return based on the end of March 1999.
[0061]
As is clear from these graphs, fund managers managing funds in the bond market outperform the benchmark by adjusting the PSB by swapping portfolios, etc., based on scenarios that include spread fluctuation forecast results. You can make a profit. Alternatively, by adjusting the PSB to be the same as the benchmark, it is possible for the earnings of its portfolio to follow the benchmark earnings.
[0062]
Furthermore, as shown in FIG. 14, by integrating and managing the PSB adjustment described here and the duration adjustment based on the prediction result of the conventional interest rate level, by selecting individual stocks and building a portfolio, The risk can be grasped more reliably.
[0063]
Various information indicating the characteristics of bonds or portfolios stored in the bond characteristic storage unit 35 can be output by an output unit (not shown). For example, the forms shown in FIGS. 12 and 13 are output.
[0064]
FIG. 12 shows an example of a form in which the characteristics of the benchmark and the own portfolio are compared for each bond type. FIG. 13 shows an example of a form displaying information calculated by the system 1 together with various information about a certain fund.
[0065]
In the above embodiment, when a specific function is realized, only a processing unit necessary for realizing the function is left, and other processing units and the like can be omitted.
[0066]
【The invention's effect】
In accordance with the present invention, a measure can be determined to characterize individual bonds relative to changes in market spread levels.
[0067]
Furthermore, according to the present invention, it is possible to obtain a measure for clarifying characteristics of the entire portfolio with respect to changes in market spread level.
[Brief description of the drawings]
FIG. 1 is a block diagram showing an overall configuration of a bond characteristic and portfolio characteristic calculation system according to an embodiment of the present invention.
FIG. 2 is a data flow diagram between each processing unit, database groups 41 to 45, and storage units 35 and 36;
3A is an explanatory diagram showing types of data stored in the government bond attribute database 41 and the non-government bond non-business bond attribute database 43, and FIG. 3B is a diagram showing data stored in the business bond attribute database 42; It is explanatory drawing which shows a kind.
FIG. 4 is an explanatory diagram showing types of data stored in a bond daily database 44;
FIG. 5 is an explanatory diagram showing types of data stored in the bond index database 45;
FIG. 6 is a diagram for explaining a method of calculating an individual spread.
FIG. 7 is a diagram for explaining a method of calculating a difference between an individual spread and an average spread.
FIG. 8 is a diagram for explaining an example of a method of calculating a result spread sensitivity.
FIG. 9 is a diagram for explaining an example of a method for calculating an estimated spread sensitivity.
FIG. 10 is a graph showing a fund whose PSB and duration are the same as those of the benchmark, and fluctuations in the return rate of the benchmark.
FIG. 11 is a graph showing fluctuations in the rate of return of funds and funds with different PSBs.
FIG. 12 is a diagram illustrating an example of an output form.
FIG. 13 is a diagram showing another example of an output form.
FIG. 14 is an image diagram for constructing a portfolio by integrating and managing duration and portfolio spread beta.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Computer system, 2 ... Bond index calculation system, 3 ... Price sensitivity calculation system, 21 ... Current value weight calculation part, 22 ... Individual spread calculation part, 23 ... Average spread calculation part, 24 ... Risk free rate curve calculation part, 25 ... modified duration calculation unit, 31 ... actual spread sensitivity calculation unit, 32 ... estimated spread sensitivity calculation unit, 33 ... portfolio spread beta calculation unit.

Claims (2)

A bond characteristic calculation system configured by a computer system to calculate bond characteristics,
A bond index database storing, for each bond, information indicating an individual spread of the bond at different points in time, and information indicating an average spread representing a spread level of the bond market at the same time as the individual spread;
A price sensitivity calculation system for calculating the price sensitivity of bonds,
The price sensitivity calculation system is:
Based on information indicating the individual spread stored in the bond index database and information indicating an average spread at the same time as the individual spread, each bond with respect to a change in the average spread of the market for the bond of the stock Actual spread sensitivity calculation means for calculating actual spread sensitivity indicating the rate of change of individual spreads,
A bond characteristic storage unit for storing information on the characteristics of the bond;
Output means for outputting information on the characteristics of the bonds stored in the bond characteristic storage unit,
The actual spread sensitivity calculation means uses a stock having a specific number of individual spreads or more as a separate spread calculation target stock group, a difference (change) ΔSP from the individual spread SP at the end of the previous month, and an average spread SP _AV at the end of the previous month. The difference (change amount) ΔSP _AV is obtained, and the average spread change amount ΔSP _AV is taken as the X axis, and the individual spread change amount ΔSP _AV is taken as the Y axis, based on the single regression analysis based on the data Is used to approximate the form Y = AX + B, and the actual spread sensitivity SPS _ACT is obtained as A. This process is performed for each issue, and the actual spread sensitivity is calculated for each issue and stored in the bond characteristic storage unit. Let
The bond property calculation system, wherein the bond property storage unit stores the calculated actual spread sensitivity as information on the property of the bond. The bond characteristic calculation system according to claim 1,
A bond attribute database storing attribute information of bonds of each bond type,
An estimated spread sensitivity calculating means for estimating the spread sensitivity,
The bond attribute database stores, as bond attribute information, information indicating the remaining period of each bond and the rating of each bond for each bond issue,
The estimated spread sensitivity calculation means includes:
The actual spread sensitivity of bonds of three or more issues belonging to the issue group stored in the bond property storage unit, the remaining period and rating stored in the bond attribute database, and the bond attribute database Based on the memorized term and rating of the bonds that do not belong to the above-mentioned stock group, it was plotted in a three-dimensional space with the rating on the X axis, the remaining years on the Y axis, and the spread sensitivity on the Z axis. Based on the data, a multiple regression analysis is performed, a, b, and c of Z = aX + bY + c are determined, and a spread sensitivity of a bond that does not belong to the stock group is estimated, and the estimated spread sensitivity is calculated. , Memorize | store in the said bond characteristic memory | storage part,
The bond property calculating system further stores the estimated spread sensitivity as information on the property of the bond.

Images