PART II: Uncertainty, Bias & Risk

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March 6 , 2018 | Posted by Charles Cowan |

PART II: Uncertainty, Bias & Risk

Analytic Focus, Blog series, part ii, 2018.03.pngGuidelines are the means of determining whether or not to make a loan. Guidelines avoid risk which is important to multiple parties. In Part I of his series, “When The Lender Deviates From The Guidelines,” Charles Cowan, Ph.D. introduced what could go wrong when guidelines are not followed. Part II dives into three key considerations, uncertainty, bias and risk.

PART II: 

The Basic Problem. . . Uncertainty vs. Bias
We don’t know who is going to repay the loan and we only have educated guesses regarding how likely a person is to repay the
loan. The guidelines are the source of that “educatedness.” If the guidelines are correct, we have a basis for making an estimate of the proportion of times loans will repay or even prepay.

In addition, we can estimate the reliability of all of our estimates. There is a range around the estimate of the likelihood that someone will repay their loan. This variability tells us how uncertain we are about this outcome. If you know the mechanism, you can estimate how many times you might roll a two with a range of outcomes.

An investor or insurer who relies on only the midpoint for this range of outcomes is betting that half the time he’ll make money and the other half of the time, he’ll lose money. Investors and insurers typically want to make money, so they’re much more interested in the tail outcomes at which point there is only a one percent chance that they will lose money.

To know this, the investor or insurer has to rely on the guidelines being followed so that the outcomes follow a fixed set of rules.

Failing to follow the rules means at the very least there will be more variability in the outcome than would be expected if the
guidelines were strictly followed. Dice – you want to substitute your dice for mine?

You want an “exception” even though I’ve rolled my dice thousands of times and know they are fair?

You know, your dice look . . . funny. Uncertainty is a fact of life. You roll, you take your chances.

When one knows the rules, risk is knowable to everyone. Now you slip in a new process, which leads to new outcomes. Our model, the one we all agreed to, has changed. If we don’t know how the model changes (like you with your funny dice), we may underestimate the chances that we will observe a default. This Is A Bias.

Return vs. Risk
Typically, interest rates are higher when the likelihood of defaults are higher. As the loan-to-value increases, so does the interest rate. These relationships are premised on realizing the average return when making a loan, assuming you know (or are very good at guessing) the likelihood of repayment and the actual loan-to-value ratio. This works great over a large number of loans but only if you’re right about the likelihoods of repayment and the loan-to-values.

If you are an investor who is buying a pool of loans, or an insurer who is offering credit enhancements on a pool of loans, or even an originator keeping the loans you originate, your expectations (or hopes) might be a bit different. Hypothetically, for a pool of loans with a 5% weighted average interest rate, one would expect an approximate 10% default rate for loans where the average loan-to-value ratio was 80%. You only realize the full 5% occurs if there are no defaults! If there are defaulted loans, the loss from the default is offset by foreclosures and sales of the underlying collateral. But if the default rate is 10% for all borrowers in the
pool, the investor only realizes 2% return instead of 5%. As noted above, this is what one expects on average.

If the default rate is better than the average, the investor makes more. If the default rate is worse than average, the investor makes less. If the default rate is substantially worse than average, the investor loses money. There is always a chance of loss. The
question is, how does one quantify the chance of loss. In turn, what is the value of this investment (the portfolio) relative to other multiple investment scenarios?

The answer comes from examining the likelihood for the full range of possible outcomes, as opposed to just the average outcome.

Uncertainty Revisited
When tracking the performance of a loan portfolio, the range of possible outcomes is WIDE.

We don’t know which or how many loans will default. The key to understanding risk and uncertainty is knowing how many loans might default and the likelihood for these estimates. The uncertainty is compounded by variation in the probabilities between borrowers. An average might be 10% as in the example above, but every borrower has his own probability of default. Some at 2%, some at 15% and so on. Similarly, there is also variation in the loan-to-value ratios between loans. Not every loan has an LTV of 80%. Some LTV’s are higher, some lower.

With all of this variation, the investor-insurer-originator has to consider the distribution of possible outcomes, not just the mean
reported in a prospectus. The distribution of possible outcomes is conditioned on the quality of loan underwriting, as deviations from established guidelines negate quantifiable rules.

The average is only the middle of the full range. It tells you very little about the risk. The truth is that the odds are greater for
fewer defaults than the average.

BUT, the width of the range of possible outcomes is the real measure of risk. How likely is a loss? How susceptible is the curve to change when the rules change? With a lot of heterogeneity, it is hard to determine where outcomes might fall. With a skew distribution of outcomes, there can be a large probability for a large number of defaults. In turn, the return from the pool would be less than 100%. In other words, a good chance there will be a loss.

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