Find the rate of continuous compounding equivalent to daily compounding of \(90\%\), if we assume that a year has \(365\) days.
The three year bond has the face value USD 100, and pays coupons annually according to the following schedule: In the first year, the bond pays a coupon of USD \(5\), and in the second year it pays USD \(10\). At the maturity, the owner of the bond receives only the face value and no additional coupon payments are issued. Assume that the continuously compounding rate is \(9\%\). Find the price of this bond.
Compute the risk measured by the standard deviations \(\sigma_{K}\) for the risky security whose return depends on the market scenario:
\[ \begin{array}{|c|c|c|}\hline \mbox{Scenario} & \mbox{Probability}& \mbox{Return }K \newline \hline \omega_1& 0.3& 2\%\newline \hline \omega_2&0.7 & 22\%\newline \hline\end{array} \]
Three risky securities have expected returns \(\mu_1=10\%\), \(\mu_2=20\%\), \(\mu_3=9\%\), standard deviations \(\sigma_1=0.15\), \(\sigma_2=0.25\), \(\sigma_3=0.25\), and correlations \(\rho_{12}=0.4\), \(\rho_{23}=0.1\), and \(\rho_{31}=-0.3\).
Suppose that there are several risky securities and that their efficient frontier is given by \(\sigma=\sqrt{0.29-4\mu+20\mu^2}\).