# Dorfleitner's Standard Deviation

Can someone please advise how to compute the following (as my results go into thousands):

E.g. I have used

and the result (for T=12) = 580103.7261

Thanks

• Could you please describe the reference in more detail? Is it a book, paper, etc.? – skoestlmeier Jul 9 at 6:56
• It's a book Stetige versus diskrete Renditen : finanzmathematische Überlegungen zur richtigen Verwendung beider Begriffe in Theorie und Praxis. However, that's not the point because the quote above is from an academic paper, which does not mention anything other than what I have already shown in my question. – West Ray Jul 9 at 7:00
• Thanks for the reference. Be aware, that an answer may be unlikely if no one knows the concept of "Dorfleitner's Standard Deviation", so the reference is needed for a good question. Additionally, what is $r_i^d$, can you clarify the notation please (raw return, excess-return, log-return, etc.)? – skoestlmeier Jul 9 at 7:34
• Thanks. I called it "Dorfleitner's Standard Deviation" cos that's what has been used in his academic publication. rd (raw r) = arithmetic monthly return (r1+r2+r3...)/t – West Ray Jul 9 at 8:28

The formula looks like the square-root-of-$$t$$ rule for scaling return-variance, but for simple multi-period returns, not log-returns. That is, the formula shows you how to compute
$$\mbox{var}\bigg(1+R^{(\tau)}\bigg) = \mbox{var}\bigg(\prod_{t=1}^{\tau} 1+R_t\bigg)$$ starting from the expectation and variance of $$R_t$$.
In which case $$r^d$$ would be a single-period return. (The notation is unfortunate: writing $$\sigma^{\tau}_{i}$$ when $$\tau$$ is an integer.) What exactly do the values of $$\mu$$ and $$\sigma$$ show? If I take them to mean 0.9% and 2.35%, i.e. 0.009 and 0.0235, then I get an annualised vol of about 9%, which seems reasonable.