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

Discussion in 'Risk Management' started by Matt1234au, Feb 1, 2008.

1. ### 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?

Matt

2. ### Hook N. Sinker

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 %.

3. ### Kevin Schmit

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.

• ###### maslov_optimal_strategy_risky_assets.pdf
File size:
156.4 KB
Views:
303

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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