Question $4.$

A$.$ You are told that the expected return of the market portfolio is $10\%,$ and its standard deviation is $10\%.$ There exists a risk$-$free asset in the economy. You hold an efficient portfolio with an expected return of $12\%$ and a standard deviation of $15\%.[$hint: The efficent portfolio is a combination of the market portfolio and the risk$-$free asset.$]$

i$.$ In forming this efficient portfolio do you borrow or lend? Support your answer with relevant calculations.

$(10$ marks$)$

ii$.$ What is the risk$-$free rate?

$(10$ marks$)$

B$.$ Describe precisely one way that you would test if a particular stock market is strong$-$form efficient?

$(15$ Marks$)$

C$.$ Discuss the key assumptions of Arbitrage Pricing Theory $($APT$)$ model and the implications of these assumptions.

$(15$ Marks$)$

Total: $50$ mark