Annualized return to be used in Sortino

Reading 25, practice problem 12B asks for the Sortino ratio for the hedge fund: Sortino = (Annualized return - minimum acceptable) / downside deviation Sortino = (7.36 - 5) / 5.6 I understand how to find the other figures, but how do they get Annualized return for the hedge fund using: Month hedge fund returns % jan 3.5 feb 4 mar -2 apr -2 may -1 jun 0.9 Jul -1 aug 1.7 sep 2.7 oct 3.7 nov 0.4 dec -3.2

(1.035 * 1.04 * …)-1

-2% =0.98

How do we get hedge fund annualized return of 7.3%? (1.035x1.04x.98x.98x.99x1.009x.99x1.017x1.027x1.037x1.004x.968)-1 = 7.6%

They’re going the gemetric mean of the average return:

(1.076^(1/12)-1) *12 = 7.3%

Check out exhibit 30 on page 84. They go from an average return of 7.77% to 7.50% using the geometric mean return.

I see, they are using geometric return. But why do they *12? The geometric mean i am familiar with is: [[(1+R1)x(1+R2)x(1+Rn)]^(1/n)] - 1.

^ (1/12) that would give you a monthly return. you need to multiply that by 12 to get the annual return.

Great, thanks for the help.

I’d like to reopen this issue…

I understand how to calculate monthly to annual returns via geometric average returns

What I don’t get is, in Exhibit 30, and later Question 12, for calculating the Sortino ratio, why do they use the Geometric Mean average turned annual return instead of the total period return, which is also an annual return?

  1. For example, given monthly returns of m1 to m12… Geometrically linked total returns = (1+m1)*…*(1+m12) −1

This is the holding period return for 12 months, Exhibit 30 = 7.77%; Question 12 = 7.61%

  1. If you do the annualized returns through the geometric mean average method described in above comments, Exhibit 30 = 7.5%, Question 12 = 7.36%

I don’t know why they are different and why you should use #2 for Sortino ratio. I know that #2 is correct but there must be some mathematical justification that I am missing…

Can someone please clarify?

geometric chain linked return X is being converted to a geometric average return by (X^(1/12) - 1) * 12.

Sachin Patel and I have been having this same conversation on another thread …

Found it, thanks. However it still doesn’t explain why the geometric average annual return is used rather than chain-linked annual return, or why it’s a lower number. Oh well, I guess.

Good question!

After doing a few past exams I don’t think it’s gonna be an issue anymore… In the guideline answer they even allow for arithmetic return :slight_smile:

What is annoying is the curriculum gets into so much detail, and some of it you remember, but it’s completely ignored on the actual exam.

For example (unrelated to this post): I remember from the reading that for Yardeni model, even though they use a LT 5 year average earnings growth, the book said it might not be sustainable in the TRUE long term (b/c it’s only 5 years). And then in a past exam they said, Yardeni model accounts for earnings growth accurately… p_q

I mean… are we reading the same books here?


The Yardeni mode in comparision to the Fed Model accounts for earnings growth accurately.

However, a drawback of this assumption is that may not be reflective of actual future growth - because it’s not predictable to 100% degree.

yes Good point… In comparison to Fed model agreed…

Does that question mention a hurdle rate anywhere? Is that an assumed rate for HFs we should use if there isn’t one stated?

I think so… the hurdle rate was in the footnote.

Yes, footnote.

Footnote. That’s horrable! I would missed it in the exam. crying