liquidity risk is an important liquidity dimen- sion as it is an expression of the risk that trading at some future point will involve more costs than initially assumed. The variation in the current liquidity measures of price tightness and depth can be used to approximate liquidity risk.15 the reason is that high uncertainty about the current level of liquidity can be expected to have a close correlation with high uncertainty about the future level of liquidity.
Chart 8.2 shows that liquidity in Danish gov- ernment bonds has fluctuated most in times of strong market turmoil. This can be interpreted to mean that the liquidity risk has been high- est when uncertainty in the markets has been greatest. in these periods, liquidity is also low, cf. above. so high liquidity risk typically goes hand in hand with low liquidity, as also con- cluded in many other empirical studies.
15 variation in liquidity measures is used as an expression of liquidity risk in several academic studies, see e.g. Dick-Nielsen, Feldhütter and lando (2012).
Common Components of LiqUiDity
the graphical illustrations of the various liquid- ity measures in the preceding section indicate a certain degree of correlation between these measures. For example, tight prices are typical- ly linked to large depth and low liquidity risk. however, the correlation is not perfect, and the liquidity measures seem to contribute individ- ually to explaining the overall liquidity of the asset.
This is confirmed by the principal component analysis in box 8.6, which shows that the first principal component explains most of the varia- tion in the liquidity measures of price tightness, depth and liquidity risk. The second principal component can primarily be attributed to the measure of price resiliency, explaining more than 90 per cent of the variation in this liquidity measure. This result emphasises that price resil- iency is an important dimension of liquidity that differs materially from the two better known liquidity dimensions, tightness and depth.
liquidity dimension 4: estimation of liquidity risk Chart 8.2 0 5 10 15 20 25 30
nov 07 nov 08 nov 09 nov 10 nov 11 nov 12 tightness measure volatility
2-year 5-year 10-year
std. dev. 1 2 3 4 0 5 10 15 20 25 30
nov 07 nov 08 nov 09 nov 10 nov 11 nov 12 Depth measure volatility
2-year 5-year 10-year
std. dev.
1 2 3 4
note: the vertical columns indicate periods of strong market uncertainty due to the following events: (1) lehman brothers collapses, (2) greece applies for rescue package, (3) write-down of greece’s debt is announced, and (4) spain applies for assistance for banks. liquidity risk has been approximated using the standard deviations for the tightness and depth measures (roll’s effective bid-ask spread in basis points and the price impact of transactions in basis points, respectively). For each bond, the monthly standard deviations have been calculated for the tightness and depth measures. The average of the monthly standard deviations expresses the average variation across all bonds for a given maturity segment.
pUttinG the LiqUiDity LeveL into perspeCtive
the average cost of trading danish government bonds has been 3-6 basis points of the trans- action’s market price, cf. Table 8.3.16 this level seems low, considering that a 5-year danish government bond has yielded an average ef- fective return of 2.2 per cent (220 basis points) p.a. during the same period.
to put liquidity in the market for danish government bonds into perspective, it might be interesting to compare the results with similar analyses in other government bond markets. however, this is not easy as the number of surveys is limited. Furthermore, the results may not be directly comparable as they are sensitive to the choice of estimation period, data clean- ing method, etc. with these caveats in mind, Table 8.3 indicates that the market for Danish government bonds is less liquid than the us and German markets but at the same level as the market for italian government securities.
16 the effective bid-ask spread shows the cost of an immediate pur- chase and sale of an asset. so the cost of one transaction (e.g. a purchase) is given by half of the effective bid-ask spread, in the case of Danish government bonds averaging 6.9/2 = 3.35 basis points of the transaction value.
POssiblE ExPlaNaTiONs FOr THE
lEvEl OF liquiDiTy
in the following, it is examined whether there are systematic differences in liquidity across bonds based on three characteristics: (i) out- standing volume, (ii) remaining maturity and (iii) benchmark status. in summary, the results show that bonds are more liquid if the out- standing volume is large, the remaining maturi- ty is short and the bonds have benchmark sta- tus, cf. Table 8.4. The background to the results can be explained by the following:
• a large outstanding volume increases the liquidity supply: a large outstanding volume means that more investors can potentially act as liquidity providers in the market. This sharpens competition to supply liquidity, which should result in a larger supply and better prices for investors. in the analysis this is reflected in a narrower bid-ask spread and more robust prices for bonds with a large outstanding volume. in this context it is worth noting that the liquidity risk is greater for bonds with a large outstanding volume. a possible explanation is that bonds with a large outstanding volume are traded
Principal component analysis of liquidity measures box 8.6
the degree to which the individual liquidity measure contains information not captured by the other measures can be analysed e.g. via a principal component analysis. in such an analysis, the observed variation in the liquidity measures can be related to developments in a number of non-observable underlying factors (principal components), which are mutually uncorrelated. The principal components are constructed in such a way that the first principal component explains as much as possible of the variation in the liquidity measures. The second principal component explains as much as possible of the
remaining variation in the liquidity measures not explained by the first principal component and so on and so forth.1
explanation of aggregate variation in liquidity measures
0 10 20 30 40 50 60 70 80 90 100
tightness depth resiliency liquidity risk
PC1 PC2 PC3 PC4
Per cent
measures for current liquidity
note: the chart shows the part of the aggregate variation in the individual liquidity measures explained by the individual principal compo- nents. Tightness is defined using roll’s effective bid-ask spread. Depth is defined as the price impact of a transaction. resiliency is defined on the basis of an aggregate variable reflecting the number of transactions per bond and the daily trading volume per bond. liquidity risk is defined on the basis of an aggregate variable reflecting the variation in the tightness and depth measures. all variables are standardised with a mean value of zero and a standard deviation of 1.
1. Christensen and ejsing (2013) provide a more detailed description of principal component analyses in connection with common components
of the government yield spread to germany.
more intensively, so that changes in market sentiment are reflected more rapidly in the prices of these bonds.
• Short-term bonds fluctuate less in value: in general, it is more risky to supply liquidity in assets that fluctuate strongly in value. one of the reasons is that high volatility increases the risk of trading with investors who possess more information about the fundamental value of the asset. it is to be ex- pected that liquidity providers operate with a wider bid-ask spread and lower trading depths to compensate for the increased risk linked to supplying liquidity in risky assets. in the analysis this is reflected in wider bid-
ask spreads and lower depths for bonds with long remaining maturities (i.e. long duration).17 at the same time, the liquidi- ty risk is greater, presumably because the liquidity level is more sensitive to changes in the level of uncertainty among investors. all the same, it should be noted that trading ac- tivity is higher for bonds with long remain- ing maturities, which may indicate greater resiliency.
17 Copeland and Galai (1983) model liquidity as a (very short) option offered by liquidity providers to investors wishing to trade on the spot. since the value of the option increases with the volatility of the asset, liquidity providers will operate with a wider bid-ask spread for assets with a long duration, as the trading option for these assets has a greater risk of going in-the-money.
Comparison of liquidity across countries Table 8.3
Government bond market Period
effective bid-ask spread, basis points
Price impact of transactions, basis points
Denmark 2007 (nov.) – 2013 (Jul.) 6.9 (2.9) 5.8 (2.2)
usa 1997 (Jan.) – 2000 (Mar.) 2.4 (0.6) 0.5 (0.1)
Germany 2006 (Jan.) – 2008 (sep.) 2.9 (1.0)1 - 2
italy 2011 (Jun.) – 2012 (Nov.) 8.0 (14.0) 5.8 (4.0)
selected Eu countries 2008 (Jan.) – 2012 (Jun.) 39.63 8.93
Note: Figures in brackets denote the estimated standard deviation. results for the usa, germany and italy are based on Fleming (2003), Pelizzon et al. (2013) and Ejsing and sihvonen (2009), respectively. results for selected Eu member states are based on Eba (2013). “selected Eu member states” are those with a credit rating of at least aa3 (Moody’s) or aa- (s&P and Fitch).
source: Fleming (2003), Pelizzon et al. (2013), Ejsing and sihvonen (2009), Eba (2013) and own calculations.
1. Only quoted bid-ask spreads are available. Typically transactions take place between the best bid and ask prices, so the value stated may
overestimate the effective bid-ask spread.
2. No data is available for price impact.
3. The values have been calculated by adjusting for the effect of including countries classified as “ECai 1”, which are those with credit ratings of
aa3/aa- or higher. The high level of the effective bid-ask spread can to some extent be explained by the fact that the measure is calculated across trading days, which increases the risk that new information may affect the measure. The standard deviation for the results is not stated as it is not reported for the subgroup of ECa1 countries.
• benchmark status contributes to higher liquidity: For the key maturity segments, the central government defines a benchmark bond. liquidity in benchmark bonds can be expected to be higher than in equivalent bonds without benchmark status. One of the reasons is that benchmark bonds tend to be on-the-run issues, which results in more trading in the secondary market.18 at the same time, market making obligations are stricter for benchmark series than for other bonds. in the analysis, these two factors are reflected in a narrower bid-ask spread and more robust prices for bonds with bench- mark status. in addition, the liquidity risk is also lower for benchmark bonds.
Finally, it should be noted that the relatively low explanatory power indicates that liquidity is affected by a great many exogenous factors not included in the regression analysis.
18 several articles in the literature analyse price differences between on- the-run issues and comparable off-the-run issues. On-the-run issues are typically traded at a higher price, which can be attributed to their higher liquidity. see e.g. Krishnamurthy (2002).