Corporate bonds are rated based on their likelihood of default. Instead of investing in just

one low grade, you want to examine the effect on the expected return and variance of forming

a portfolio of investment grade $($e$.$g$.,$ AAA$)$ and non$-$investment grade bonds. The probability

of default in a year for the investment grade is $0\mathrm{.}01(1\%)$ while the probability for the lower

grade bonds is $0\mathrm{.}22($or $22\%).$ The correlation between the default rates is $0\mathrm{.}1.$ Calculate the

expected return and the standard deviation of investing $50\%$ of your portfolio in investment

grade bonds and the other $50\%$ in non$-$investment grade bonds and also the variance.