Question

Rockville Bank is reviewing its loan portfolios to estimate how diversified their portfolios are. For internal purposes, the Bank assesses credit risk into four categories – High Quality, Average Quality, Poor Quality, and Default. Over the years, the following transition matrix has evolved:

From/to	High	Average	Poor	Default
High	80%	15%	4%	1%
Average	10%	65%	20%	5%
Poor	5%	15%	55%	25%

For example, a loan rated High Quality this year has a 80% probability of remaining High Quality next year, a 15% probability of falling to Average Quality, and so on.

Based on this data, if

This year the portfolio contains $1,050M of High Quality, $325M of Average Quality, and $85M of Poor Quality loans, giving a total loan portfolio of $1,460M.

a. Estimate the loan portfolio mix in one year.

b. Suppose the bank wishes to maintain the current relative mix of credit type, High, $1,050M/$1,460M = 72%, Average, $325M/$1,460M = 22%, and Poor, $1,050M/$1,460M = 6%. How many new loans and of what type must the bank sell during the year to maintain this relative mix?

Answer 1

All financials below are in $ mn

a. Estimate the loan portfolio mix in one year.

Please see the working below.

The nomenclature in the tables below will help you understand the mathematics.

This year's portfolio	$ mn	Nomenclature
High	1,050	A
Average	325	B
Low	85	C
Total	1,460
From/to	High	Average	Poor	Default	Nomenclature
High	80%	15%	4%	1%	D
Average	10%	65%	20%	5%	E
Poor	5%	15%	55%	25%	F
Next years' portfolio	High	Average	Poor	Default
A x D =	840	158	42	11
B x E =	33	211	65	16
C x F =	4	13	47	21
Total	877	382	154	48

Loan portfolio mix:

Total Loan (excluding default) = 877 + 382 + 154 = 1,412

High quality loan = 877 / 1,412 = 62.09%  

Average quality loan = 382 / 1,412 = 27.02%

Poor quality loan = 154 / 1,412 = 10.89%

Part (b)

Let's assume the bank sell average quality loan of A and Poor quality loan of P to bring the portfolio mix to old levels.

Hence, total loan portfolio = 1,412 - A - P

High quality loan mix = 877 / (1,412 - A - P) = 72%; hence, 1,412 - (A + P) = 877 / 72% = 1,219.10

Hence, A + P = 192.90

Total loan book now = 1,412 - (A + P) = 1,219.10

Average quality loan = (382 - A) / 1,219.10 = 22%; hence, A = 110.13

P = 192.90 - 110.13 = 82.78

The bank should sell A = $ 110.13 mn of average quality loan and P = $ 82.78 mn of poor quality loan during the year to maintain the relative mix.