I think that you need to factor in inflation to make it more meaningful – E.g. You might find that companies that survive an economic slump are more efficient and so inflation reduces. Then the real return in the following few years is greater than implied here.

]]>To answer your question in one sentence: ‘yes, and I think I did’

To answer it in detail:

I am trying to get at a number that represents the annualized return (lets call it R) between two points in time. Lets call the value of the index at the beginning of that period ‘A’ and the value after ‘n’ year ‘Z’. Then R represents a return which if we got every year, and compounded, would grow our investment at value A to be worth Z after ‘n’ years. Given that, I am not concerned with the value of the investment at any point between A and Z (for this analysis), so the definition of R cannot be affected by any interlying values.

My original definition for the calculation of R was:

R = ((Z/A)^(1/n))-1

You asked whether I was taking the geometric mean of the returnS.

There is only one return in my calculation process, as I only am concerned with two points in time, which yeilds only one return.

However, we can use the geometric mean of ‘A’ and ‘Z’ to get at ‘R’, as:

R = ( Geo(A,Z)/A )-1

(where Geo() is the geometric mean function)

i.e. R is the geometric mean of A and Z, divided by A, minus 1.

to expand:

R = (((A.Z)^(1/n))/A)-1

Since A and Z are both values of an index, they could both be divided by any factor ‘K’ and the definition of R would still hold, so:

R = ((((A/K).(Z/K))^(1/n))/(A/K))-1

Now set ‘K’ to equal ‘A’, and cancel, and we get:

R = ((((1).(Z/A))^(1/n))/(1))-1

so

R = ((Z/A)^(1/n))-1

Which get us back to the original definition of R.

So in long, and in short, ‘yes’, this could be thought of as a measure of geometric mean đź™‚

]]>what i meant to say was:

Good stuff!

Were you trying to take the Geometric Mean for the Returns? If so, wouldnâ€™t you divide (month B closing price-month A closing price) by month A closing price (B-A/A) for each month instead of just (B/A)???

I would have probably used (B-A/A) for returns each month and then taken the Mean for each year to get an average return.

Very interesting stuff though!

]]>Were you trying to take the Geometric Mean for the Returns? If so, wouldn’t you divide (month B closing price-month A closing price) by month A closing price for each month instead of just ** ???**

I would have probably used for returns each month and then taken the Mean for each year to get an average return.

Very interesting stuff though!

]]>Things I take away:

1) Raw eyeballing says you’re likely to get 6-8% return which is a lot less than the 10% that is quoted as the long term average. As other people have said dividends change this (hopefully for the better)

2) 10yr gives you the best chance to get >10% returns. Interesting.

I’d like to see dividends and cost averaging tried out.

]]>Including dividends will shift the curve to the right, but what will it do to the variance? I’m pondering that now.

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