# How to calculate standard deviation cone around expected returns?

I would like to evaluate the returns of an investment manager who has given me their return and volatility expectations for their fund. I would like to calculate both 1 and 2 standard deviations from what is expected. The chart below by Bridgewater Associates is what I am trying to replicate.

• @noob2 Would you convert the comments to an answer so that I can properly upvote =P – Helin Sep 6 '19 at 1:22

The green line is a straight line with slope 18% (the expected annual alpha). The thin purple curve is $$\sigma \sqrt{t}$$ above and below the green line, where t is the time in years since inception. The thick purple curve is twice as far from the green line, i.e. $$\pm 2 \sigma \sqrt{t}$$ from the line. And $$\sigma$$, the annual standard deviation, is also 18%.