Q4. Consider historical data showing that the average annual rate of return on the S&P portfolio over the past 90 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 20% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%.

a)Calculate the expected return of portfolios invested in T-bills and the S&P 500 index with weights shown in the table below.(10 marks)

b)Calculate the standard deviation of portfolios invested in T-bills and the S&P 500 index with weights shown in the table below.(10 marks)

Weight_Bills Weight_Index

0 1

0.2 0.8

0.6 0.4

0.8 0.2

1 0