# Risk models in loan portfolios

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Posted by Amit on January 03, 19101 at 02:45:04:

can u help me with the following problem......

The spread equation for return on assets generated on a portfolio of loans is in essence:

APR (Annual percentage rate charged)
+ Fees (Membership fee, late fee etc.)
- NIE (Non Interest Expenses, for example, salary, rent etc.)
- COF (Cost of Funds)
- Credit Losses
= ROA (Return on Assets)

Generally, return generated is intended to be commensurate with risk taken. Frequently, risk is simplistically and erroneously thought to be the Credit Loss line of the spread equation. However, if one thinks of risk as the uncertainty of estimates in all elements of the spread equation, risk can be more accurately (if less precisely) estimated. If a bank estimates the spread equation for a portfolio as above, then the true equation is:

APR + e1 + Fees + e2 - NIE + e3 - COF + e4 - Credit Losses + e5
= ROA + e6

where ei is the error in estimation for each term. Specifically, e6 is the risk to the portfolio.

Given a portfolio, such as a credit card loan portfolio, where the numbers of accounts is relatively high (greater than 500,000 accounts) and loan sizes are relatively low (\$1,000 to \$10,000) what is the correlation between the error terms of the components of total return? What is the correct way to think of the risk-return relationship so that we have a very high probability (>95%) to make a profit?

If we assume that e4 << e3 < e1 < e2 << e5 and further, that since management can have a strong effect on APR, Fees, and NIE, the distribution of e1, e2 and e3 are discrete distributions and e4 and e5 are normally distributed, what is the relevance of the distribution of e6 on the risk-return relationship?

In a practical application, the distributions of ei will not be well known, and the distribution of e6 in particular will be difficult to assess. What then is an appropriate management tool for controlling the risk in a given portfolio such that ROA is commensurate with total risk?

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Thanx....

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