If you have 9 million to invest in a bond, with the liability at the end of November 2020 to be distributed normally with a mean of $12 million and a standard deviation of $1 million what is the number of bonds you would purchase for optimal asset-liability management? The liability is to be met in 4 years.

The accrued coupon payment from the bond appreciates at the 1-year T-bill rate of 4%.

The bond has face value of $100, price of $85.00, coupon of 5.25%, matury of November 30 2021, YTM of 8.87%, it is a BB rated bond.

Use a one year debt migration matrix of bonds, and forward curves:

Rating	Year 1	Year 2	Year 3	Year 4	Year 5
AAA	0.42	0.87	1.27	1.63	1.5
AA	0.58	0.67	1.31	1.27	1.99
A	0.66	1.64	1.45	1.95	2.15
BBB	1.19	1.46	2.65	2.75	2.6
BB	1.98	3.65	4.76	4.58	4.42
B	3.62	4.63	4.12	4.48	4.36
CCC/C	4.78	8.34	11.73	15.76	19.24

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