Max holds a portfolio of $$8$ million that consists of AA$-$rated bonds and BBB$-$rated bonds.

The amount invested in the AA$-$rated bonds is $$6\mathrm{.}5$ million. The two classes of bonds are

independent and the one$-$year probabilities of default for the AA$-$rated and the BBB$-$rated

bonds are $3\%$ and $5\%$ respectively. The recovery rate for AA$-$rated bonds is $50\%$ and the

recovery rate for BBB$-$rated bonds is $35\%.$ Given that the AA$-$rated bonds have defaulted,

Max disposes the bonds in a distress exchange for $30\%$ of their expected recovery value

and invests this amount in the same BBB$-$rated bonds. Calculate the value of the new

portfolio. Then, find the one$-$year expected credit loss of the new portfolio