You wish to construct an investment portfolio with a $5\%$ standard deviation. You are considering the following two investments:

$$ A Government of Canada of Canada zero$-$coupon bond $($does not pay interest$)$ which yields $3\%?$

$$ A S&P TSE index ETF with an expected return of $10\%$ and a standard deviation of $15\%.$

$$ Assume there is no correlation between treasury bills and the stock market.

QUESTIONS:

D$)$ What are the portfolio weights? Show all calculations.

E$)$ What is the expected return on your portfolio? Show all calculations.

F$)$ Do you feel there is zero correlation between Government of Canada bonds i$.$e$.$ bonds and the S&P TSE index i$.$e$.$ the stock market? Elaborate