1. A bond with face value $1,000 and annual coupon rate 5% has dirty price
$1,050. There are 5 more coupon payments yet to be paid, the first one
arriving in 150 days’ time. What is the clean price for the bond?
2. A portfolio has beta ( ) of 1, expected return 9%, Jensen’s alpha
equal to , idiosyncratic variance ar( ), and total variance equal to 0.11.
The risk-free rate ( ) is 3%, the average return on the market index ( ( ))
is 7%, and the variance of the market index ( ar( )) is 0.09.
Use the Treynor-Black model/formula that gives the optimal mix of the portfolio
with the market index. According to this model, how much of your wealth
should be invested in the portfolio described above, and how much should
be invested in the market portfolio?
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