Financial contract 2 - Average annual return computed in two ways.

[JohanL]

First i calculate the the average annual return for the Dow jones industrial average
over the last 22 years by using the first and last value.

To continue writing my code i also need to calculate
the average return between two days separated by one year
for every day over the last 22 years.

Shouldnt these two numbers be the same?
clear

fid = fopen( 'DJ30Daily.csv', 'r' );
str = fread( fid, '*char' );
sts = fclose( fid );
str( str == '"' ) = [];
str( str == ',' ) = '.';
cac = textscan( str, '%f' );

DJ30Daily = cell2mat(cac);

DJ30Daily = DJ30Daily(121:5668);

n=length(DJ30Daily);

K=DJ30Daily(n)-DJ30Daily(1);

P=(K/DJ30Daily(1));

AverageAnnualReturnPercentLast22y = nthroot(P, 22)m=252-1;

d=n-m;

Ptot=0;for i=1:d

K2=DJ30Daily(i+m)-DJ30Daily(i);
P2=K2/DJ30Daily(i);

P2=P2+1;

Ptot=Ptot+P2;

endAverageReturnBetweenDaysSepartedBy1yearOverTheLast22years=Ptot/d
******************************

AverageAnnualReturnPercentLast22y =

1.0575AverageReturnBetweenDaysSepartedBy1yearOverTheLast22years =

1.0863

 

[mmwave]

Hello,

Thank you for sharing your code and calculations. it is important to always double check your calculations and make sure they are accurate. In this case, the two numbers should not necessarily be the same.

The first calculation, the average annual return for the Dow Jones Industrial Average over the last 22 years, is a measure of the overall performance of the stock market over a long period of time. It takes into account the first and last value of the Dow Jones Industrial Average, and calculates the average return over 22 years. This number tells us how much the market has grown on average each year over the last 22 years.

The second calculation, the average return between two days separated by one year, is a measure of the short-term fluctuations in the stock market. It takes into account the daily changes in the Dow Jones Industrial Average over the last 22 years, and calculates the average return between two days that are one year apart. This number tells us how much the market has fluctuated on average over the last 22 years.

So while both numbers are important in understanding the performance of the stock market, they are measuring different things and therefore it is not expected for them to be the same. It is important to carefully consider the context and purpose of each calculation in order to accurately interpret and compare the results.

I hope this helps clarify any confusion and encourages you to continue double checking your calculations as a scientist. Keep up the good work!