Factores Externos al Desarrollo del Sector Exportador Peruano

The static data analysis shows that the performance of the vintages deteriorated over the reporting period, with higher and more rapid growth of defaults in the assets originated in later periods. This may be due to relaxed credit granting standards by the originator, or may reflect the impact of adverse economic conditions on borrowers. When defaults start to occur earlier in a vintage, it may indicate a relaxation in credit standards, while later defaults may represent a change in economic conditions (Dommisse et al., 2005:3). Dynamic analysis frequently masks these types of trends, which is why static data is important to the securitisation process.

4.4 Binomial Expansion Technique

A number of methods can be used to estimate the expected loss for asset-backed securities, ranging from Monte Carlo simulation techniques, which are fairly accurate but cumbersome to implement, to rather simple single-event models, which are easy to implement, but much less accurate. Cifuentes and O’Connor (1996:1 to 4) describe an alternative to simulation or single-event models, which is the binomial expansion technique (BET) that combines the best of both worlds: a high degree of accuracy coupled with computational friendliness and is well suited to the rating of collateralised debt obligations.

The binomial expansion technique is based on the diversity score concept. The idea is to use the diversity score to build a hypothetical pool of uncorrelated and homogeneous assets that will mimic the default behaviour of the original pool.

Let D be the diversity score of the collateral pool. Then the behaviour of the collateral pool can be modelled using a fictitious portfolio consisting of D bonds, each of which has the same par value (total collateral par value divided by D). It is also assumed that all these bonds have the same probability of default, determined by the weighted average probability of default of the collateral pool.

Then, as far as defaults are concerned, the behaviour of this homogeneous pool of D assets can be fully described in terms of D possible scenarios: one default, two defaults … up to D defaults. The probability Pj that scenario j (j defaults) could happen can be computed using the binomial formula:

Pj =

In the formula p presents the weighted average probability of default of the collateral pool (stressed by the appropriate factor).

Let Ej be the loss for the note to be rated under scenario j. The loss, expressed as a percentage, can be computed by taking the present value of the cash flows received by the note holder, assuming there are j defaults, and using the note coupon as the discount factor.

The total expected loss, considering all possible default scenarios, is then calculated as follows:

Expected loss =

∑

Additional modelling complexities arise in real situations, which must address issues such as amortisation and reinvestment rates. Non-homogeneous portfolios, such as those where a few bonds account for a large portion of the portfolio, may require some modification of the binomial expansion method.

4.5 Calculation of Credit Enhancement

The rating agency uses the results from the static data analysis of defaults and recoveries to formulate a base case⁶⁴ assumption for portfolio losses. The base case loss assumption is then stressed by applying a target rating multiplier to it which is appropriate for the stress experienced at a target rating. From this is deducted the base case recovery rate in order to find the credit enhancement level for each target rating.

Example: Typical rating agency⁶⁵ multipliers for each target rating level are as follows:

AAA 5x

AA 4x

A 3x

BBB 2x

BB 1.5x

B 1x

Assuming a base case loss projection of 2.5%, and a 40% recovery rate, the following credit enhancement levels would be required for each target rating:

AAA 5 x 2.5% x (1 - 0.4) = 7.5%

AA 4 x 2.5% x (1 - 0.4) = 6.0%

A 3 x 2.5% x (1 - 0.4) = 4.5%

BBB 2 x 2.5% x (1 - 0.4) = 3.0%

BB 1.5 x 2.5% x (1 - 0.4) = 2.25%

B 1 x 2.5% x (1 - 0.4) = 1.5%

One of the significant features of securitisation as a structured finance device is that the rating is a target, not a fait accompli. Every securitisation transaction has the potential to result in a given rating.

For example, if an ‘AAA’ rating is targeted in a loan pool originated by an A-rated originator, all that is required, is to work out the level of credit enhancement or subordinated interest (Kothari, 2003:259).

64 Expected performance under a non-stressed economic scenario.

65

5. COMBINING QUANTITATIVE AND QUALITATIVE MODELS

5.1 Limitations of Statistical Models

Statistical models have revolutionised risk management by providing the credit analysis process with efficiency, speed, accuracy and consistency, and by maximising the quantification of risk. However, statistical models have limitations. Some of these limitations relate to the quality and exact meaning of the data, whereas other factors simply cannot be quantified. Ernst (2001:2 - 6) describes the limitations of statistical models as expressed below.

5.1.1 Unreliable or Erroneous data

The output of statistical models can only be as good as their underlying data. All models are driven by numbers that represent a translation of certain forms of data, for example historic default rates and recovery rates. This data is generated by human and potentially unreliable sources or processes. In addition to errors occurring once the data has been originated, any later conversion or manipulation of the information can result in erroneous input. Accordingly, it is important to understand the data’s sources, how it was calculated and what it means.

5.1.2 Not Random, Limited or too Small Sample

If historic performance data, on the basis of which future performance is projected, derive from a selected sample, or from the performance of only one type of loan or loans originated in only in one region, the projected performance will only be accurate with respect to that narrow sample. Similarly, loan-by-loan models, whose projected default rate is based on an historical correlation among loan characteristics such as loan-to-value or debt-to-income ratios, will not be statistically accurate if the data sample on which the historic correlation is based was too small, or was not selected at random.

5.1.3 Historic Data not Always a Good Proxy for Future Performance

Statistical models rely on past data. However, past data is insufficient because it represents a sequence rather than a set of independent observations as demanded by the laws of probability. It is natural to expect a sequence of historic events to repeat or maintain itself in the future. However,

“wild” events are bound to happen at some point, the only question is when. An example of such an unexpected event was the New York stock market crash of 1987. On 19 October 1987, also known

as “Black Monday”, the Dow Jones industrial index collapsed by 22.6%, nearly double the percentage drop of the index on 29 October 1929. From the close of trading on 13 October 1987 to the close of trading on 19 October 1987, the Dow fell by almost a third, resulting in a loss in value of shares of approximately one trillion dollars. Some market observers calculated that the 19 October crash was a 27 standard deviation event, which should only occur with the probability of 10 to the 160^th power, a virtual impossibility.

5.1.4 The Tail Loss Probability Distribution is Crucial, but Difficult to Quantify

Arguably the most important role of models in the context of securitisation rating is an assessment of the loss probability distribution on the issued securities. Based on the input of asset pool characteristics, historic performance data and other relevant assumptions, the model suggests a certain probability for each loss scenario, with respect to each of the rated classes.

Chart 4.4 below gives a basic illustration of the loss probability distribution, with loss scenarios in the middle of the spectrum having the highest probability, with a gradual reduction in probability as the loss scenarios are approaching the extreme ends of the spectrum (very low or very high losses).

Normal Distribution of Loss Probability

P ro bability

Source: M oody's Loss