Finance bonds

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  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? (9 marks)

  1. A portfolio has beta (𝛽) of 1, expected return 9%, Jensen’s alpha

equal to 𝛼, idiosyncratic variance 𝑉ar(πœ–), and total variance equal to 0.11.

The risk-free rate (π‘ŸπΉ) is 3%, the average return on the market index (𝐸(π‘Ÿπ‘€))

is 7%, and the variance of the market index (𝑉ar(π‘Ÿπ‘€)) 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?

Sample Solution

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