Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with

Question:

Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows:

W bills W index

0 ........1.0

0.2 ........0.8

0.4 ........0.6

0.6 ........0.4

0.8 ........0.2

1.0 ....... 0

Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 80 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%.

Expected Return
The expected return is the profit or loss an investor anticipates on an investment that has known or anticipated rates of return (RoR). It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these... Portfolio
A portfolio is a grouping of financial assets such as stocks, bonds, commodities, currencies and cash equivalents, as well as their fund counterparts, including mutual, exchange-traded and closed funds. A portfolio can also consist of non-publicly...