Description
4 questions
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Explanation & Answer
Kindly see attached files with the answer to the different questionsI've included both a pdf and a doc version so that you can use any of them if you can't read the equations used in the calculation of the different variables
Problem 1.
Average rates of return for each year taking into account the stock price from the previous year:
𝐴𝑅𝑅(𝑠𝑒𝑐𝑜𝑛𝑑 𝑦𝑒𝑎𝑟) = 9 − 12 = −$3
𝐴𝑅𝑅(𝑡ℎ𝑖𝑟𝑑 𝑦𝑒𝑎𝑟) = 7 − 9 = −$2
𝐴𝑅𝑅(𝑓𝑜𝑢𝑟𝑡ℎ 𝑦𝑒𝑎𝑟) = 6 − 7 = −$1
𝐴𝑅𝑅(𝑓𝑖𝑓𝑡ℎ 𝑦𝑒𝑎𝑟) = 8 − 6 = $2
Annual rates of return:
𝐴𝑅𝑅(𝑠𝑒𝑐𝑜𝑛𝑑 𝑦𝑒𝑎𝑟) =
𝐴𝑅𝑅(𝑡ℎ𝑖𝑟𝑑 𝑦𝑒𝑎𝑟) =
7−9
= −0.22
9
𝐴𝑅𝑅(𝑓𝑜𝑢𝑟𝑡ℎ 𝑦𝑒𝑎𝑟) =
𝐴𝑅𝑅(𝑓𝑖𝑓𝑡ℎ 𝑦𝑒𝑎𝑟) =
9 − 12
= −0.25
12
6−7
= −0.14
7
8−6
= 0.33
6
Arithmetic average rate of return over the 5-year period:
𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝐴𝑅𝑅 =
(−0.25) + (−0.22) + (−0.14) + 0.33
= −0.0704 = −7.04%
4
Geometric average rate of return over the 5-year period:
4
𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝐴𝑅𝑅 = (√(1 − 0.25) ∗ (1 − 0.22) ∗ (1 − 0.14) ∗ (1 + 0.33) − 1) = −0.0964 = −9.64%
Analysis:
The geometric average rate of return provides a better approximation to the annual rate of return over the
considered period as it takes into account the compounding effect of interest rates.
Annual rate of return for the third year:
𝐴𝑅𝑅(𝑡ℎ𝑖𝑟𝑑 𝑦𝑒𝑎𝑟) =
7−9
= −0.22 = −22%
9
Problem 2.
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎...
