2. Consider the following one-year transition matrix.

Initial Rating	Rating at Year-End (%)
	AAA	AA	A	BBB	BB	B	CCC	Default
AAA	90.81	8.33	0.68	0.06	0.12	0	0	0
AA	0.70	90.65	7.79	0.64	0.06	0.14	0.02	0
A	0.09	2.27	91.05	5.52	0.74	0.26	0.01	0.06
BBB	0.02	0.33	5.95	86.93	5.30	1.17	0.12	0.18

a. What is the likelihood that a bond will begin and end the year with an A rating?

b. What is the likelihood that a bond will be downgraded from AA to A?

c. What is the likelihood that a bond will be upgraded from BBB to A?