The historical average annual rate of return on the SP/TSX Composite Index has averaged approximately 6.3% more than the Treasury bill return, and...

The historical average annual rate of return on the S&P/TSX Composite Index has averaged approximately 6.3% more than the Treasury bill return, and its standard deviation was 16.42% per year. Assume that these values are representative of investor's expectations for future performance and that the current T-bill rate is 4%.

a)     Calculate the expected return and standard deviation of portfolios invested in T-bills and the S&P/TSX Composite Index with weights as follows: (6 marks)

Portfolio A          100% T-bills; 0% Index

Portfolio B          80% T-bills; 20% Index

Portfolio C          60% T-bills; 40% Index

Portfolio D          40% T-bills; 60% Index

Portfolio E          20% T-bills; 80% Index

Portfolio F          0% T-bills; 100% Index

b)     Calculate the utility levels for each portfolio calculated above, for an investor with a degree of risk aversion of A=3.  (6 marks)

c)       Repeat the calculation in part (b) for an investor with A=5. (6 marks)

d)     What are your conclusions? (2 marks)