downside deviation for hedge funds

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theCFAway

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page 135, vol 5, question 12 on cfai text, part A
Can someone tell me how cfai got 28.78 as their numerator for the downside deviation?
since the numerator formula for downside deviation is sum of (return-threshold)^(2), did cfai take (3.5-.4167)^2+(4-.4167)^2+(-2-.4167)^2+….+(-3.2-.4167)^2 straight thru to get the numerator? It seems like an awful lot of calculation and maybe i’m making mistakes typing it in my calculator but i’m not getting the 28.78.
The same question for part B, how did the 0.6133% get derived?
thanks!
 
12(A) - since downside deviation, consider only months where return is less than 0.4167 (monthly hurdle rate). So, (-2-0.4167)^2 + (-2-.4167)^2+(-1-4167)^2+(-1-4167)^2+(-3.2-0.4167)^2 .. would give the numerator 28.78..
12(B) .. {[(1.035)(1.04)…(1-0.032)^(1/12)]-1} will give..0.6133%. Its the Geometric Mean of the monthly returns.
 
Use your calculators data/stat sheet.
Input (rate - hurdle rate) into the memory slots, then go to stat sheet function Sum(X^2) and divide by n-1.
DO NOT use the Stdev(X) function.
 
NagCFA,
  • why not use the average of monthly return in the sortino numerator? AND
  • why not directly use the componded annual return rather than first deriving implied monthly and than multiplying by 12?
 
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