Hi,
I have the following question:
Annualized Return: 6.5%
Annualized Standard Deviation: 10%
Then, what will be the +/- 2 standard deviation range of performance?
What will be the range of the holding period is 5 years?
Any tips will be greatly appreciated. Thanks.
Shams.
For a one-year holding period, the range will be 6.5% ± (2 × 10%) = (-13.5%, 26.5%).
For a T-year holding period, you need to compute the T-year µ and T-year σ:
1 + µ = (1 + 6.5%)^T, µ = [(1.065)^T] - 1
σ = 10% × √T
So the 5-year µ = [(1.065)^5] - 1 = 37.01%, the 5-year σ = 10% × √5 = 22.36%, and the ±2σ range is:
37.01% ± (2 × 22.36%) = (-7.71%, 81.73%).
(Note that this, in fact, is not accurate. The calculation of the T-year σ assumes that the annual returns are added, not compounded; trying to compute the actual T-year σ is well beyond the scope of the CFA curriculum. If they ask you this question, this is the only way they can expect you to calculate it.)
Thank you very much for your help. This makes sense but just could not conceptualize it - much appreciated.
My pleasure.
I could be completely wrong here but I remember seeing this calculated differently. Ie if return is 6.5% and standard deviation is 10%, the range for one standard deviation from the mean is 5.85% to 7.15%.
ie, 6.5, plus or minus (6.5 x .1)
Am I confused here? If so, what am I thinking of, I’m sure I’ve seen this in the textbook somewhere.
Thank you!
You might be thinking of the volatility of interest rates in a binomial interest rate tree, where they frequently quote the volatility as a percentage of the previous node’s rate.
In this example, because we’re talking about returns, it’s customary for the standard deviation to be given as an absolute percentage, not a percentage of the mean. But there’s no doubt that it can be confusing.
My pleasure.