Assessment of the liquidity level of Russian bonds using the computer modeling is an extremely important task which involves development of appropriate measures of bond liquidity. We found that the liquidity measures (proxies) used by academic researchers and professional portfolio managers have some shortcomings: serious interpretation di culties which reduce practical applicability; absence of hierarchy of the liquidity \dimensions"; too much data necessary to properly assess the level of liquidity. We propose a system of indicators to assess the liquidity in the bond market which consider volume being the highest level of the hierarchy of the of liquidity \dimensions", time being the second highest level of the hierarchy, and price being the lowest level of the hierarchy. We suggest calculating the indicators only as averages for the period as indicators at a moment are objectively less informative due to a rather low level of liquidity of the Russian bond market.
Currently, there is a high demand for computer modelling of nancial assets management, especially bonds management. As a less risky nancial instruments than stocks, bonds are widely used by the Pension Fund of the Russian Federation (PFR) and private pension funds, which are legally responsible for reliability, pro tability and safety of accumulated pension savings. Implementation of these legal requirements is achieved through comprehensive control over the investment processes of the pension savings which involve modeling in order to determine the expected return, risk, and other important investment characteristics. Quite often bonds form a signi cant proportion of the investment portfolio of other groups of investors.
The appropriate software should be used to ensure the control and to improve the e ciency of investment decisions. Thus, in the years 2002{2003 PFR has implemented a program named \Stock Portfolio Optimization System", which helps to optimize the model stock portfolio based on historical and forecast data of the relevant stock indices [18].
For investors, one of the most important investment characteristic of a bonds issue is its liquidity. Assessment of the liquidity level of Russian bonds using the computer modeling is an extremely important and urgent task. On the one hand, investors operating on the domestic bond market recognize the growing risk of raising the average global interest rates; hence, they tighten requirements for the liquidity level of the bond issues that they include in the bond portfolios. On the other hand, given the actual \closing" of the external bond markets, the Russian bond issuers are interested in increasing the borrowing volumes at the domestic bond market and, accordingly, are willing to \adjust" to meet the investors' preferences.
However, there is no generally accepted criteria of the bond market liquidity in the existing economic and nancial literature. Even the basic term \market liquidity" is, in fact, interpreted by scientists ambiguous. As a result, there is a diversity of liquidity measures (or proxies) suggested by researchers and used by professional investors, but all of the measures have serious shortcomings.
In this article, we de ne the bond's (bond issue's) liquidity as being an ability to transact a bond issue of a certain volume, during a certain time period, and at a certain price. We develop a system of indicators that helps to solve the problem of assessing the liquidity in the bond market. 2
Systematizing the existing research, we can distinguish at least two major approaches to understanding the economic essence of the liquidity: i) one-dimensional approach, which treats asset liquidity only as the ability to \be converted in the money" (the very ability to sell the asset on the market is crucial), and ii) multidimensional approach based on the recognition of the complex nature of liquidity. Within the latter approach, the time required to sell the asset and the price at which it (potentially at least) can be sold are taken into account in addition to the actual ability \to be sold".
In this article we use the multidimensional approach that to the greatest extent takes into account the investment preferences of the bond market participants. Hence, following the general de nition of the nancial asset liquidity, proposed by V. Rodina [17], we consider the bond's (bond issue's) liquidity as an ability to transact a bond issue of \a certain amount, during a certain time period, and at a certain price."
A detailed review of liquidity (or illiquidity) measures used in the literature is presented in van Loon et al. [16]. The authors divide all measures, or proxies, of illiquidity for corporate bonds into three classes. A rst class combine measures of illiquidity related to transaction costs including the simple bid-ask spread [4, 10,11]. A second class of illiquidity measures describes market depth by assessing the price impact of trades [15], and trying to capture the daily price response associated with a one currency unit of trading volume [3, 5, 6, 9, 12]. A third class of liquidity proxies is referred to as trading intensity variables, which frequently cover both measures based on turnover and zero-trading-days [8]. In addition to using individual liquidity proxies, various aggregate proxies have been used [13].
In the Russian research literature, studies of the bond market liquidity measurement are rather new (started from late 1990s) and in fact represented by very few specialized research and also by developments of the professional securities market participants. It is noteworthy that many of those Russian researchers who recognize the multiplicity of liquidity measurement use sets of only few of all possible bond market liquidity measurements and ignore the other. The most systematic studies in this area are the works of A. N. Chaykun [7] and P. F. Kolesov [14], which will be later discussed in details. 3
A.N. Chaykun examines the bond market liquidity in the context of its \projections" (in fact, the term \projection" is synonymous with the term \dimension"), each of which has its own set of indicators: 1. the \time" projection: { \number of transactions" during a certain time period M ; { \trading frequency" TF , which is determined by the following formula: where NT D { number of trading1 days with the bond issue since it was issued; NSD { total number of days since the bond issue was issued; 2. the \price" projection: { \Illiquidity ratio"2 (Amihud's ratio) KA de ned by the formula: TF =
NT D
N SD KA = j P j
V = p
D
R
(
{ \turnover" (or trading volume) V ; { \size of transaction" V M , de ned as: { \turnover ratio" KT , which is calculated by the formula:
V M = KT =
V M
V
CBI
(
CBI { the nominal volume of the bond issue; 4. the \transaction cost" projection: { bid-ask spread S, which is calculated as:
S = PS min
PD max; where PS min { the best price asked for the bond issue; PD max { the best price bid for the bond issue.
The majority of other researchers, recognizing \multidimensionality" of the bond market liquidity in general, try to measure it using a \narrow" set of indicators. In particular, P.F. Kolesov [15] considers it possible to measure the bond market liquidity in a somewhat di erent way, proposing to use the "two basic indicators of securities liquidity: 1. time during which the security can potentially be sold; 2. potential nancial losses when it is sold.
Without o ering a clear algorithm for calculating the rst indicator (time of the bond sale { ES ), he considers it possible to calculate the potential nancial losses through the relative spread SR (or the relative bid-ask spread) by using the following formula:
SR =
PS min
PD max PS min
100%: S =
Pn i=1 (PS min n
PD max) ; In addition, the researcher suggests to use such an indicator as the average spread S for the period: where n { the number of observations.
Some of the securities market professional participants followed a di erent way. Accepting the presence of several liquidity \dimensions", they prefer to develop their own 'universal' liquidity indicators, trying to \unite" several existing measurements. Thus, the experts of the nancial group \DOHOD" o er to use so called \bond liquidity index" (LI), which is an \index for assessing the liquidity of a particular bond in relation to the liquidity of the market (quotation list) on which it is traded on the basis of estimates of the average trading volume and the number of transactions", de ned by the formula [2]:
LI =
Vi V a
M Ti b M T ; where Vi { \i-th bond average daily trading volume during the previous ve trading days"; V { \average daily trading volume for all bonds of the same quotation list to which i-th bond belongs during the previous ve trading days"; M Ti { \average number of i-th bond transactions during the previous ve trading days"; M T { \average daily number of trades with all bonds of the same quotation list to which i-th bond belongs during the previous ve trading days"; a { special factor equal to 0.3; b { special factor equal to 0.7.
JSC \Gazprombank" uses its own indicator for assessing the national bond
market liquidity [1]. The specialists of the bank point out: \In general, liquidity
is assessed only on a qualitative level based on expert estimates of the market
participants. Subjectivity of the assessments, increase in the number of traded
assets, the high volatility of nancial markets { all this leads to poor quality
of liquidity risk assessment, which is not conducive to e ective investment
decisions". They o er to use the indicator of nancial instrument's market liquidity:
L = pL1 L2;
(
In our view, all of the above elaborations in assessing the liquidity of the bond market have some shortcomings: { they all have serious interpretation di culties and, accordingly, are di cult to be applied in practice. In other words, using the above indicators, the investor can identify the bond issue which has the highest liquidity among those for which the calculations are made, but the investor doesn't actually get an answer for a very important question: is the particular bond issue's liquidity level satisfactory for the investor? { they are characterized by the absence of hierarchy of the liquidity \dimensions": in fact, explicitly or implicitly their equivalence is assumed, which is highly debatable statement due to the possibility of di erences among investors' preferences; { all of the proposed indicators imply that investors have a large enough amount of information (primarily the absolute spread value for bond issues over an extended time period) necessary to properly assess the level of liquidity, which is not always the case, as the vast majority of private investors do not create nor systematically update specialized information databases on the bond market liquidity level.
Given the shortcomings of the listed above indicators, to solve the problem of assessing the liquidity in the bond market, we propose to construct a system of indicators based on the following hierarchy of the of liquidity \dimensions": volume (the highest level of the hierarchy) { time { price (the lowest level of the hierarchy). And we consider reasonable to calculate these indicators only as averages for the period (indicators at a moment are objectively less informative due to a su ciently low level of liquidity of the national bond market).
Thus, we propose to use the following indicators to assess the potential scope of a transaction with the bond issue:
T V PS =
Pn PSi i=1 100
FSi COB ; where PSi { ith o er price, expressed as a percentage; FSi { number of bonds in ith o er; COB { nominal value of one bond; n { number of observations (trading days). 2. average total value of bonds bided:
T V PD =
Pn PDi i=1 100
FDi COB
; n n (11) (12) (13) (14) (15) where PDi { price of ith bid, expressed as a percentage; FDi { number of bonds in the ith bid; 3. average total value of bonds available for a transaction:
T V = T V PS + T V PD : 2
In this case, a key indicator for the assessment of the amount of bond liquidity is the average market value of bonds available simultaneously to transact, while other indicators are considered as auxiliary, allowing to analyze the liquidity of the bond issue in more detail.
To evaluate the potential time to transact bonds, we propose to use the percentage of trading days characterized by a satisfactory level of liquidity: WSL = nSL n 100%; where nSL { number of trading days characterized by a satisfactory level of liquidity.3
To assess such a measurement of bond liquidity as a price, we suggest to calculate the average spread corresponding to the required volume of the transaction:
SRV =
Pn i=1 (PSRV n
PDRV ) ; 3 The level of liquidity is satisfactory when actual average total value of bonds available for a transaction exceeds the required by the investor. (16) (17) where PSRV { average ask price of bonds corresponding to the required transaction volume, which is determined by the formula: PDRV { average bid price of bonds corresponding to the required transaction volume, which is determined by the formula:
PSRV =
PiR=V1 PSi FSi COB
PiR=V1 FSi COB
; PDRV =
PiR=V1 PDi FDi COB
PiR=V1 FDi COB :
If the value of bonds o ered for purchase or sale does not reach the required volume, the indicator's value can not be identi ed correctly, and the bonds issue is not considered as the one that meets the investor's liquidity requirements (for the price \dimension").
The speci cs of this indicator is a greater representativeness that allows more than just a comparison of the bonds' best bids and asks (such a comparison does not take into account the actual ask and bid volumes) through comparing the average prices that would realize if the required bond volume were transacted. 4
We have applied the suggested set of indicators to the bond market by using a hypothetical example. Suppose that a private investor operating on the Russian bond market needs to purchase short-term bonds (with maturity date is up to August 31, 2016, inclusively). His required liquidity volume (T V ) is not less than 1,000,000 rubles; the percentage of trading days characterized by a satisfactory liquidity level (WSL) is not less than 40%, with a maximum term of a position opening equals to ve trading days; average spread for the required transaction volume (SRV ) is no more than 0.50%, and the required transaction volume is equal to 200,000 rubles.
At the calculation time (July 25, 2016) the investor's maturity requirements were met by 8 bond issues, but for the two of them { AbsolyutB-5 with the maturity date of July 27, 2016, and GPB BO-05 with the maturity date of August 1, 2016 { the trading was stopped (\frozen") because the maturity date was close. Calculations of the proposed indicators for the remaining 6 bond issues are given in Table 1.
Results of the bonds' liquidity evaluation clearly show that all investor's
requirements are satis ed by only one bond issue (Alpha BO-9) within the analyzed
bond issues totality formed by the term to maturity.
4 Source: The Moscow Exchange, http://moex.com/ru/marketdata/bulletins/
The system of indicators and bond liquidity analysis algorithm proposed in the
paper can be embedded in a computer decision support system designed for
selection and ranking bonds by the liquidity criteria. The computer support will
signi cantly increase the e ciency of decision-making when investing in bonds,
making it easier for investors to assess a large number of simultaneously traded
securities. In the proposed algorithm, using system of liquidity indicators instead
of one criteria will boost the e ciency of investment decisions and, on the other
hand, requires computer support for technical simpli cation and improvement
of assessment reliability.
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deterioration: A study of liquidity in the US corporate bond market during nancial
crises. Journal of Financial Economics 105(
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