Question

1.Calculate the arithmetic average of the following time series of HPRs: 1%, 2%, -3%, 2%, 1%. Enter your answer as a percent expression rounded to 2 decimal places. For example, enter 0.00123 as 0.12% and 0.00456 as 0.46%.

2. A stock has a 0.9% average quarterly HPR. Calculate the annualized average HPR. Enter your answer as a percent expression rounded to 2 decimal places. For example, enter 0.00123 as 0.12% and 0.00456 as 0.46%.

3.Calculate the geometric average of the following time series of HPRs: 1%, 2%, -3%, 2%, 1%. Enter your answer as a percent expression rounded to 2 decimal places. For example, enter 0.00123 as 0.12% and 0.00456 as 0.46%.

Answer 1

Answer 1:-

The Airthematic average of the 5 year time series of HPR (  1%, 2%, -3%, 2%, 1% ) is :-

= ( 1 + 2 - 3 + 2 + 1 ) / 5 = 0.60% = 0.006

Answer 2 :-

The Anuualised Average HPR is

( 1 + r )ⁿ - 1 =  

where r is the percentage of return and n is the times

= ( 1 + .009 )⁴ - 1 = 1.036489 - 1 = 0.036489 = 3.648%

Answer 3 :- The Geometric average of the time series of HPR ( 1%, 2%, -3%, 2%, 1% )

{(1 + 0.01)*(1+0.02)*(1-0.03)*(1+0.02)*(1+0.01)}^1/5 - 1

= (1.029473)^1/5 - 1 = 1.005826 - 1 = 0.005826 = 0.5826%