Know Annual Return and Standard Deviation, so what is final return?

M

Matt1234au

Hi

Say an investment has an annual return of 10%, with a standard deviation of 20%

I put in $100 so at year end I have 110

At end of year 2 I have $121

At end of year 3 $133.10

However the Std is 20% so really isn't it true that my final return will lie between an upper and lower amount?

If so what would it be and how would you calculate it, just 133.10 +/- 20% or something more complicated?

Or is it 133.10 plus/minus the sum of annual variance?

Thanks in advance

Matt
 
Quote from Matt1234au:

Say an investment has an annual return of 10%, with a standard deviation of 20%

I put in $100 so at year end I have 110

At end of year 2 I have $121

At end of year 3 $133.10

However the Std is 20% so really isn't it true that my final return will lie between an upper and lower amount?

If so what would it be and how would you calculate it, just 133.10 +/- 20% or something more complicated?

Or is it 133.10 plus/minus the sum of annual variance?
More...

At the end of three years you have $ 133.10. Initial capital is $ 100.00. One way to calculate return is Cumulative Annual Growth Rate (CAGR) = profit * 100 / years of data / initial capital

so

($ 133.10 - $ 100) * 100 / 3 years / $ 100 initial capital = 11.03 % per year with occasional equity fluctuations (positive and negative) of about 20 %.
 
Quote from Matt1234au:


Or is it 133.10 plus/minus the sum of annual variance?
More...
Try alpha minus sigma squared over two. So:

.10 - ( .20^2 ) / 2 = .08

Variance adjusted probable annual growth rate would
be eight percent.

So three year would be 1.08^3 - 1 = 0.26 or twenty-six
percent.

Explained in more detail in the attached paper, among
others.
 

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Quote from Matt1234au:

Hi

Say an investment has an annual return of 10%, with a standard deviation of 20%

I put in $100 so at year end I have 110

At end of year 2 I have $121

At end of year 3 $133.10

However the Std is 20% so really isn't it true that my final return will lie between an upper and lower amount?

If so what would it be and how would you calculate it, just 133.10 +/- 20% or something more complicated?

Or is it 133.10 plus/minus the sum of annual variance?

Thanks in advance

Matt
More...

I think 20% is too high for investments. Maybe ok for trading.

If I recall correctly from statistics -- and please if wrong someone correct me -- it means that with such investment you have:

68.27% of the annual returns lie between $100 +/- $20
95.45% between $100 +/- $40
99.73% between $100 +/- $60

which means that if you invest there is a probability you will lose a significant portion of you money.

For such low return I would not accept a standard deviation more than 5%.

Alex
 
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