Deudas del Estado

more detail in Table F.1. We used various data sources to inform our analysis, including Trax, Thomson Reuters and UBS Delta.

𝑍 − 𝑠𝑝𝑟𝑒𝑎𝑑𝑖,𝑡= 𝛼 + 𝛽1𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑣𝑎𝑟𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦𝑖𝑡 + 𝛽2𝐴𝑚𝑖ℎ𝑢𝑑 𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑖𝑡 + 𝛽3𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑘𝑒𝑡𝑚𝑎𝑘𝑒𝑟𝑠𝑖𝑡 + 𝛽4𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑠𝑐𝑜𝑟𝑒𝑖𝑡 + 𝛽5𝐵𝑖𝑑 𝑎𝑠𝑘 𝑠𝑝𝑟𝑒𝑎𝑑𝑖𝑡 + 𝛽6𝐶𝑜𝑢𝑝𝑜𝑛 𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽7𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒𝑖𝑡 + 𝛽8𝑇𝑖𝑚𝑒 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑖𝑡 + 𝜀𝑖𝑡 Where 𝛼 is a constant, and i represents the bond issue at time t.

Table F.1: Definition and sources of variables used in the analysis

Variable Definition Source

Dependent variable Z-spread The spread between the bond yield and the specific _{country’s equivalent Libor curve.} UBS Delta

Independent variables

Liquidity drivers Liquidity variability 30-day standard deviation of bid-ask spreads. Trax

Amihud liquidity

The Amihud (2002) measure of liquidity is a price impact measure that captures the daily price response (in basis points) scaled to turnover. Specifically, the following ratio is used: Average of (absolute daily return / trading volumes).

Trax and Thomson Reuters

Number of market makers

Number of market makers quoting bid and ask

spreads for the specific bond in that month. Trax

Liquidity score

A weighted score for each bond issue that is aggregates quoted price, volumes traded, amounts issued, amounts outstanding and trade enquiries information.

UBS Delta

Bid-ask spread The spread quoted by market makers for buying _{and selling bonds, scaled to price.} Trax Control variables: time

varying bond-specific and firm specific

characteristics

Coupon rate The interest that is stated on the bond when it is _issued. Trax Hazard rate Model-based measure of a firm’s default risk. UBS Delta Time to maturity The time left, in years, before the bond matures and

is redeemed.

Thomson Reuters

Table F.2: Summary statistics for variables used in the analysis

Variable Observations

(over the 4 time periods) Mean Std. Dev. Min Max

Z-spread 2938 113.2 98.5 -286.0 857.8

Liquidity variability 2955 6.0 6.2 0.0 42.2

Amihud liquidity 2947 1.0 16.6 0.0 777.9

Number of market makers 2968 7.7 2.5 0.2 15.8

Liquidity score 2963 5.9 1.1 2.0 8.0 Trading volume 2980 28600000 166000000 10000 6990000000 Bid-ask spread 2969 55.1 40.8 0.3 439.4 Coupon rate 2980 5.1 1.3 0.5 9.8 Hazard rate 2967 256.8 144.9 -190.4 989.8 Amounts issued 2980 768766 1854495 13500 50000000 Yield 2938 2.6 1.6 -1.9 10.6 Time to maturity 2947 9.1 37.5 0.1 994.5 Source: PwC analysis

The summary statistics for the data used in our analysis are shown in Table F.2.

We used a panel data approach as it allows us to control for individual heterogeneity across our bond sample, such as time-invariant variables that cannot be observed or measured, e.g. differences in the business practices across the corporations that issues the bonds; or variables that change over time but not across bonds such as international market factors. This then allows us to isolate the impact of variables that vary over time on corporate bond spreads.288 We use a fixed effects approach with robust standard errors (so that the model is robust to

heteroscedasticity) in our panel data model, which assumes that individual-specific effects are

uncorrelated with the independent variables. Under the fixed effects approach, each unit (in this case,

288 _{“The key insight is that if the unobserved variable does not}

change over time, then any changes in the dependent variable must be due to influences other than these fixed characteristics.”, Stock and Watson, (2003).

289 _{In order to test whether a fixed effects or random effects model}

is appropriate in this context, we use the Hausman test which compares the two models with a null hypothesis that the random

each bond issue) has its own systematic baseline. We used a number of specification tests all of which found the fixed effects model to be preferred over the random effects model.289

F.4

Key findings

The results in Table F.3 show that each of the liquidity drivers have a statistically significant relationship with z-spread at the 10% level, meaning that a decline in liquidity (as measured by the number of market makers, bid-ask spread, Amihud liquidity and volatility in bid-ask spreads), increases the z-spread on corporate bonds. Furthermore, the signs of the coefficients are consistent with prior expectations, for example, a one-unit reduction in the number of market makers increases the z-spread by 1.9 basis points.

effects model is preferred. We consistently get a p-value less than 0.05, which suggests that the fixed effects model is preferred to random effects. In addition, we also used the Sargan-Hansen test, which unlike the Hausman test, is robust to the presence of heteroscedasticity. The Sargan-Hansen test also found the fixed effects model to be the preferred model.

Table F.3: Results for the impact of market makers on corporate bond spreads

Z-spread Coefficient Robust standard error

Liquidity variability 0.334* 0.196

Amihud liquidity 0.646* 0.210

Number of market makers -1.913* 0.681

Liquidity score -4.95* 1.641 Bid-ask spread 0.227* 0.055 Coupon rate 60.333* 16.707 Hazard rate 0.554* 0.017 Time to maturity -9.011* 1.152 Constant -224.393* 84.488 Number of observations 2847

Bond fixed-effects Yes

Wald chi2(27) 634.94

Probability > chi2 0.000

*** Significant at the 1% level; ** Significant at the 5% level; *Significant at the 10% level Source: PwC analysis

Using the regression results from Table F.3 we provide a simple separation of the contribution of liquidity drivers to the z-spread on average across the bond sample. This separation is shown in Figure F.1. Despite a declining average z-spread across the sample, the contribution of the liquidity drivers has remained broadly stable over the 4 year period. This suggests there has been no material changes in liquidity risk premia investors require for holding European corporate bonds (in contrast to the falling premium for credit risk) and is consistent with our analysis of CDS spreads and work by the Bank of England.

Within this analysis, the liquidity drivers are working in different directions. We find that the reduction in bid-ask spreads over the period has put downward pressure on our calculation of the liquidity risk premia. These low bid-ask spreads may have been influenced by changes in trading behaviour, as discussed in Chapter 4 and may be a poor measure of changes in market liquidity. They may have dragged down our estimate of the liquidity risk premia in Figure F.1.

Figure F.1: Composition of z-spread for European corporate bonds

Source: PwC analysis. We note that there may be interactions between the different factors that explain the liquidity risk premia. We have not explicitly accounted for these but we note that results are consistent with our CDS analysis and the Bank of England’s findings.

0 50 100 150 200 2011 2012 2013 2014 Z -s pre a d (bps)

Contacts

To discuss this report, please speak to your PwC contact or one of the following:

Miles Kennedy

Financial Services Advisory Direct: +44 207 212 4440

Email: [email protected]