Consider portfolios with positions in the US and Indian equity markets. The $($annual$)$ expected return and standard deviation of returns for the $2$ markets are as follows:

US India E$[$r$]10\%22\%$ SD$[$r$]20\%35\%$

The correlation between the returns is $0\mathrm{.}2.$

In addition, assume that the $($annual$)$ risk$-$free $($T$-$bill$)$ rate is $5\%.$

Calculate the expected returns and standard deviations of the following portfolios:

$50\%$ in the risk$-$free asset, rest in $50\%$ US and $50\%$ India

$110\%$ in the portfolio of $50\%$ US and $50\%$ India, finance by borrowing at

risk$-$free rate

What are the weights for investing in the risk$-$free asset and the portfolio that invests $50\%$ in the US and $50\%$ in India $($the $$risky asset$)$ that produce same return as India? What is the expected standard deviation of that portfolio?