Calculation of expected return
Expected Return = w1 * r1 + w2 * r2
where w1 = Weight of T bill
r1 = Return on T bill
w2 = Weight of Index
r2 = Return on Index
w1 | r1 | w1 * r1 | w2 | r2 | w2 * r2 | (w1 * r1) + (w2 * r2) |
0 | 5% | 0.00% | 1 | 8% | 8.00% | 8.00% |
0.2 | 5% | 1.00% | 0.8 | 8% | 6.40% | 7.40% |
0.4 | 5% | 2.00% | 0.6 | 8% | 4.80% | 6.80% |
0.6 | 5% | 3.00% | 0.4 | 8% | 3.20% | 6.20% |
0.8 | 5% | 4.00% | 0.2 | 8% | 1.60% | 5.60% |
1 | 5% | 5.00% | 0 | 8% | 0.00% | 5.00% |
Calculation of variance of the portfolio
Variance = w12 * ơ12 + w22* ơ22 + 2 * ρ1,2 * w1 * w2 * ơ1 * ơ2
where, w1 = Weight of T Bill
ơ1 = Standard deviation of T Bill
w2 = Weight of Index
ơ2 = Standard deviation of Index
ρ1,2 = Correlation between asset T Bill and Index
It must be noted that ơ1 = Standard deviation of T Bill will always be zero.
Thus,
Variance = w22* ơ22
w2 | ơ2 | w22 | ơ22 | w22* ơ22 |
1 | 20% | 1 | 4.00% | 4.00% |
0.8 | 20% | 0.64 | 4.00% | 2.56% |
0.6 | 20% | 0.36 | 4.00% | 1.44% |
0.4 | 20% | 0.16 | 4.00% | 0.64% |
0.2 | 20% | 0.04 | 4.00% | 0.16% |
0 | 20% | 0 | 4.00% | 0.00% |
For Problems 10 through 12: Consider historical data showing that the average annual rate of return...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 27% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with...
1. Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 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%. Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 27% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%. calculate the utility levels of each portfolio for an investor with A = 3 Assume the utility...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 30% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%. Calculate the utility levels of each portfolio for an investor with A= 2. Assume the utility function...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 33% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels of each portfolio for an investor with A-3. Assume the utility function is...
Problem 6-11 Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 33% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels of each portfolo for an investor with A2. Assume the utility...
Consider historical data showing that the average annual rate of return on the S&P 500 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%. Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 28% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%. Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 34% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5% Calculate the utility levels of each portfolio for an investor with A-3. Assume the utility function is...
You received no credit for this question in the previous attempt. Problem 6-12 Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 35% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels...