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# Difference Between Average Return and Realized Return

1. The questions for this assignment is to explain the difference between the average return calculated in Problem 10-6 (a) and the realized return calculated in
10-5. Are both numbers useful? If so, explain why.

To do this assignment the two problems had to be answered. Although you will see problem 10-5 and10-6 in this document, the answers are already indicated on this sheet. Use the date from below to answer to question which is above in red. Nothing needs to be downloaded from 10-5 because it is listed below.

Problem 10-5

Download the spreadsheet from www.aw-bc.com/berk_demarzo that contains historical monthly prices and dividends (paid at the end of the month) for Ford Motor Company stock (Ticker: F) from August 1994 to August 1998. Calculate the realized return over this period, expressing your answer in percent per month.

Problem 10-6

Using the same data as in Problem 5, compute the
a. Average monthly return over this period.

b. Monthly volatility (or standard deviation) over this period.

Total Realized Return = (1+R1)x(1+R2)...x(1+R36) = a. Arithmetic Average Monthly Standard Error
1.6789 Return: 1.595% 0.910%
(This is the amount \$1 invested in Aug-94 would have grown to by Aug-97.) b. Standard Deviation of
Monthly Return: 5.458% 3.414%
Equivalent monthly return (% per month) =
1.450% -0.224%

Date End of Month Price Dividend (end of month) Monthly Return (1+Rt) Monthly Return % (Rt)
Aug-97 43.000 1.052 5.20%
Jul-97 40.875 0.420 1.087 8.67%
Jun-97 38.000 1.013 1.33%
May-97 37.500 1.079 7.91%
Apr-97 34.750 0.420 1.121 12.10%
Mar-97 31.375 0.954 -4.56%
Feb-97 32.875 1.023 2.33%
Jan-97 32.125 0.385 1.008 0.81%
Dec-96 32.250 0.985 -1.53%
Nov-96 32.750 1.048 4.80%
Oct-96 31.250 0.385 1.012 1.23%
Sep-96 31.250 0.933 -6.72%
Aug-96 33.500 1.035 3.47%
Jul-96 32.375 0.385 1.012 1.19%
Jun-96 32.375 0.887 -11.30%
May-96 36.500 1.017 1.74%
Apr-96 35.875 0.350 1.054 5.38%
Mar-96 34.375 1.100 10.00%
Feb-96 31.250 1.059 5.93%
Jan-96 29.500 0.350 1.034 3.38%
Dec-95 28.875 1.022 2.21%
Nov-95 28.250 0.983 -1.74%
Oct-95 28.750 0.350 0.935 -6.51%
Sep-95 31.125 1.012 1.22%
Aug-95 30.750 1.060 6.03%
Jul-95 29.000 0.310 0.985 -1.48%
Jun-95 29.750 1.017 1.71%
May-95 29.250 1.078 7.83%
Apr-95 27.125 0.310 1.021 2.08%
Mar-95 26.875 1.029 2.87%
Feb-95 26.125 1.035 3.47%
Jan-95 25.250 0.260 0.915 -8.48%
Dec-94 27.875 1.028 2.76%
Nov-94 27.125 0.919 -8.05%
Oct-94 29.500 0.260 1.072 7.24%
Sep-94 27.750 0.949 -0.051
Aug-94 29.250

The questions for this assignment is explain the difference between the average return calculated in Problem 10-6 (a) and the realized return calculated in 10-5. Are both numbers useful? If so, explain why.

#### Solution Preview

Realized return per month = 1.450%
Arithmetic average return per month = 1.595%

The realized return per month as computed in Problem 10-5 is the compounded monthly growth rate of a one dollar investment for the stock from August 1994 to August 1997 for a total of 36 months while the one computed in Problem 10-6 is the sum of all the monthly returns divided by the number of months. This means that Problem 10-6 computed for the arithmetic or simple rate of return while Problem 5 computed for the compounded rate of return.

Yes, both numbers are useful. The realized rate of return computed in Problem 10-5 is useful for an investor who invested in the stock for the whole period and the number computed in Problem 10-6 would be useful for an investor who didn't adopt a buy and hold strategy for the stock.

PROBLEM

1. The questions for this assignment is to explain the difference between the average return calculated in Problem 10-6 (a) and the realized return calculated in
10-5. Are ...

#### Solution Summary

The difference between average return and realized returns are examined.

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