Ra Rb
Year 03 40% -30%
Year 04 -24% 22
Year 05 30 42
year 06 26 46
Corrleation coefficinet= -.2374
Construct a portfolio P that contains A and B in proportions of 40% in A and 60% in B and calculate the returns on the portfolio for each of the years 03 through 06.
I have no clue how to start this.... Please help.
Question: does the portfolio manager re-adjust the portfolio every year to maintain a 40/60 split.
For now, I will assume no, and assume that gains and losses are compounded.
An Excel spreadsheet is very useful for these types of operation. Assume that the initial P=100 and that in year 02 $40 is invested in A and $60 in B. In 03 A grows to 1.40*(40)=56 and B declines to .70*(60)=42.
In 04, A declines to .76*56=42.56 and B grows to 1.22*42=51.24.
Take it from here.
To calculate the returns on the portfolio for each of the years 03 through 06, you will need to follow these steps:
1. Determine the proportions of A and B in the portfolio: A is 40% and B is 60%.
2. Calculate the returns on A and B for each year using the given percentages:
- For Year 03:
- Return on A: 40% growth gives (1 + 0.40) * 40 = 56.
- Return on B: -30% decline gives (1 - 0.30) * 60 = 42.
- For Year 04:
- Return on A: -24% decline gives (1 - 0.24) * 56 = 42.56.
- Return on B: 22% growth gives (1 + 0.22) * 42 = 51.24.
- For Year 05:
- Return on A: 30% growth gives (1 + 0.30) * 42.56 = 55.328.
- Return on B: 42% growth gives (1 + 0.42) * 51.24 = 72.8928.
- For year 06:
- Return on A: 26% growth gives (1 + 0.26) * 55.328 = 69.72688.
- Return on B: 46% growth gives (1 + 0.46) * 72.8928 = 106.180288.
3. To calculate the portfolio returns, multiply the proportions of A and B by their respective returns for each year:
- For Year 03:
- Portfolio return: (0.4 * 56) + (0.6 * 42) = 22.4 + 25.2 = 47.6.
- For Year 04:
- Portfolio return: (0.4 * 42.56) + (0.6 * 51.24) = 17.024 + 30.744 = 47.768.
- For Year 05:
- Portfolio return: (0.4 * 55.328) + (0.6 * 72.8928) = 22.1312 + 43.73568 = 65.86688.
- For Year 06:
- Portfolio return: (0.4 * 69.72688) + (0.6 * 106.180288) = 27.890752 + 63.7081728 = 91.5989248.
Regarding whether the portfolio manager re-adjusts the portfolio every year to maintain a 40/60 split, the given information does not state anything about it. Therefore, for now, assume that the portfolio proportions remain constant throughout the years.
Please note that these calculations are based on the given information and assumptions provided.