Time in default

The second aspect of the “in default” period we consider is its length. That is, after a rm is declared to be in default to a bank, how long does it take until a bank declares that the rm is no longer in default? Figure 4.1 shows how the default duration evolved over time.

Figure 4.1: Number of quarters in default

6

From Figure 4.1 we see that the default duration is not extremely long.

Overall, more than 50% of rms exit default in 5 quarters or less and more than 25% of rms exit default in 2 quarters or less. Over time, the median duration does not vary signicantly, ranging between 3 and 6 quarters. The

rst quartile of the distribution of default durations remains unchanged during the full period. Regarding the rest of the distribution, the story is somewhat dierent. In particular, the 25% longest default spells are longer than 14 quarters and during the sample period this number oscillates between 11 and 15 quarters.

If severity and length of the default episodes are positively correlated, then it seems that over time the importance of the least problematic events did not change much. We reach this conclusion because we see that the rst quartile of the default duration distribution is fairly stable throughout the sample period. On the other hand, from the variability of the third quartile of the default distribution, it seems that the importance of the more severe cases oscillated signicantly during the sample period.

To complement the results in Figure 4.1, we present estimates of the sur-vival and hazard functions for the “in default” period (Figures 4.2 and 4.3).⁵⁶

From these gures, two important results emerge. First, default spells can be very long. Even though the third quartile of the distribution is less than

56The survival function is dened as the probability of remaining in default until w:

V(w) = Pr(W  w) = 1  I (w). The hazard function is dened as the probability of a rm leaving default in the time interval [w> w + gw), conditional on being in default:

k(w) = limPr(wW w+gw|W w)

gw > gw $ 0. W denotes the time a rm remains in default.

Figure 4.2: Default duration

Note: Analysis time defined as quarters since the beginning of the first default episode. The survivor estimate is defined as the probability of remaining in default until t: S(t)=Prob(T>=t)=1 - F(t).

0.000.250.500.751.00

0 20 40 60

analysis time Kaplan-Meier survival estimate

Figure 4.3: Hazard function for the time in default

Note: Analysis time defined as quarters since the beginning of the first default episode. The hazard function is defined as the probability of a firm leaving default in the time interval [t t +dt ), conditional on being in default: h(t ) = lim Prob(t <=T <t +dt | T >=t )/dt , as dt ->0. In the figure, the hazard is censored at 24 quarters, covering 95% of all observations.

14 quarters, more than 10% of episodes last more than 24 quarters (6 years).

This result is visible in the survival function (Figure 4.2). Second, the exit rate of default drops sharply in the rst 2 years, from around 20% to slightly more than 6%. This is important because it suggests that when a default episode is not resolved within the rst four to six quarters, then it takes substantially longer to be resolved.

An interesting question is how the default amounts evolve as default dura-tion increases. Tables 4.2A and 4.2B shed light on this quesdura-tion.

Ta bl e 4 . 2 A - Ev o l uti o n o f the fi rm s' si tua ti o n si nce the beg i nni ng o f the defa ul t epi so de

N umber o f o bserva ti o ns

Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Fi rm s i n de fa ul t fo r:

(in quarters)

1 165,165 31,919 2,870 37.9 13.9 375,300 30,170 2.47 2.0 1.3 1.0 68.9 66.7

2 110,208 48,675 5,000 49.9 36.9 327,402 26,302 2.37 2.0 1.4 1.0 75.2 100.0

3 86,674 63,107 7,071 58.4 67.3 315,105 24,890 2.32 2.0 1.5 1.0 79.2 100.0

4 70,016 77,239 9,510 64.4 88.4 307,386 25,115 2.31 2.0 1.6 1.0 82.0 100.0

5 60,348 87,083 11,220 69.5 98.9 296,448 24,753 2.28 2.0 1.7 1.0 84.3 100.0

6 50,377 96,381 12,450 72.8 100.0 332,136 24,773 2.29 2.0 1.8 1.0 85.9 100.0

7 42,618 106,597 14,690 75.4 100.0 291,051 26,115 2.31 2.0 1.8 1.0 87.1 100.0

Ta bl e 4 . 2 B - Fi rm a nd l o a n cha ra c teri sti cs fo r defa ul t epi so de s wi th di fferent to ta l dura ti o ns

N umber o f o bserva ti o ns

Mean Median Mean Median Mean Median Mean Median Mean Median Mean Median

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

To ta l dura ti o n o f

defa ul t (in quarters)

1 54,957 20,958 1,730 26.8 6.6 472,415 34,890 2.6 2.0 1.1 1.0 62.3 50.0

2 23,534 24,666 2,290 33.9 10.8 316,803 28,031 2.4 2.0 1.2 1.0 68.1 60.0

3 16,658 27,249 2,340 43.7 20.0 297,521 19,105 2.2 2.0 1.2 1.0 73.3 100.0

4 9,668 32,193 2,860 40.8 17.5 288,447 24,530 2.2 2.0 1.2 1.0 72.9 100.0

5 9,971 39,706 4,228 53.5 49.0 231,072 21,803 2.1 2.0 1.4 1.0 78.8 100.0

6 7,759 23,755 2,610 54.9 56.1 623,269 14,020 2.0 2.0 1.3 1.0 79.4 100.0

7 5,591 36,689 4,190 50.2 34.9 249,616 21,760 2.2 2.0 1.4 1.0 76.9 100.0

8 4,112 43,909 4,110 46.3 27.2 239,700 26,640 2.2 2.0 1.4 1.0 74.7 100.0

Am o unt o f c redi t

Notes: In this table are depicted firm and loan characteristics for firms with different total durations of default (between 1 and 8 quarters). In each line, the variables refer to the situation at the beginning of the default episode, for firms which default episodes lasted for x quarters. The number of bank relationships is computed as the number of loans obtained from different financial institutions (including non-monetary financial institutions).

Am o unt o f c redi t o v erdue a t sta rt o f defa ul t (euros)

Notes: In this table are depicted firm and loan characteristics for firms that have been in default for 1 quarter (line 1), 2 quarters (line 2), etc., up to 7 quarters. In each line, the variables refer to the situation in the x quarter after the default episode began. The number of bank relationships is computed as the number of loans obtained from different financial institutions (including non-monetary financial institutions).

Cre di t o verdue

In these two tables we examine two dierent perspectives on default dura-tion. First, in Table 4.2A we show what happens to the amounts in default, the credit overdue ratio and the number of bank relationships as the length of the default period increases. Second, in Table 4.2B we present the same statistics but in this case at the start of the default event, for rms with dif-ferent default durations. More specically, in Table 4.2A each row refers to the current default duration of each rm (rms that have been in default for 1 quarter, 2 quarters, etc., up to 7 quarters), whereas in Table 4.2B each line refers to rms with dierent total default durations (i.e., rms that recorded a default episode that lasted for 1 quarter, 2 quarters, etc., up to 8 quarters).

The joint analysis of these two tables indicates two important results: 1) as the default duration increases the situation worsens; and 2) the rms that stay longer in default are those with worse initial conditions, compared to

rms that exit faster. Regarding the worsening of the situation (Table 4.2A), there is a component that is somewhat mechanic, that is, the amounts overdue automatically accumulate every period. Besides this accumulation eect, there is also a true worsening of the situation. The amounts overdue and the credit overdue ratio increase signicantly with each quarter in default. Moreover, the percentage of bank relationships on which the rm defaults also increases

with default duration (rms in default borrow, on average, from more than 2 dierent banks).

Regarding the conditions rms enter default with (Table 4.2B), we see that the credit overdue ratios at the start of the event are larger for rms that ended up staying longer in default — this is visible in columns (4) and (5). Also, the total amount outstanding at the start of the default episode is, on average, larger for rms with shorter default episodes, thus suggesting that larger rms are able to leave default earlier (columns 6 and 7).

From the analysis of the default period, we conclude that the longer a

rm stays in default the more complicated its situation becomes. Another important nding is that rms that stay longer in default are also rms whose conditions at the start of the default are worse.