# Downside deviation calculation

Reading 25 practice problem 12 gives hedge fund returns (%) for each of 12 months as: Jan 3.5 Feb 4.0 Mar -2.0 Apr -2.0 May -1.0 Jun 0.9 Jul -1.0 Aug 1.7 Sep 2.7 Oct 3.7 Nov 0.4 Dec -3.2 Hurdle rate is 5% per year which is monthly hurdle of 5%/12=0.4167%. What is the calculation to get downside deviation for hedge fund? = (28.78)^1/2 / (12-1)^1/2 x (12)^1/2

To compute downside deviation you can specify yourself which threshold return you want to use. So i guess it is common to use the hurdle rate when it comes to hedge funds. Not sure about common practice. Anyone here using this tool in real life? Anyways, here in the practice problem they don’t specify which one you should use. Since it is up to the user to decide, i believe at the exam they would tell you what is the threshold rate or give you a tip at least

So you take all the monthly returns that are lower than 0.4167, you compute the difference between them and 0.4167, then ^2, sum all these figures up, and you get 28.78 (basically the downside deviation formula using 0.4167 as threshold return). Does it answer your question?

Yes, I would have done it slightly differently = [(28.78) / (12 - 1)] ^1/2 x (12)^1/2 but result is mathematically same.

How is it different? I think the three of us have the same formula (i did not copy it but i basically agree with the one given by John)

(28.78)^1/2 / (12-1)^1/2 x (12)^1/2 vs. [(28.78) / (12 - 1)] ^1/2 x (12)^1/2

^1/2 (in the first part of equation) comes after division rather then before - like 28.78 / 11 and then ^1/2.

But essentially the same.

1. Why do we multiply by 12^(1/2) to annualise the downside deviation? 2. Part B of question 12 gives annualised return of the hedge fund as: 0.6133% x 12 = 7.360% Where do they get 0.6133% from?
1. yes to annualize because it is computed based on monthly returns. Same computation as for standard deviation: you go from monthly st dev to annual st dev by multiplying by 12^(1/2)

If your question is “why 12^(1/2)” I can’t tell. I learnt this one by heart to be honest. I am not sure I will manage to learn everything I need to know before the exam, so there are things I just stupidely learn by heart. I’ll try to understand in another life…

But I am sure you can figure that out by writing down a few formulas.

1. I just figured out that if you consider you have a 20% performance fee (only counts when you are above hurdle) you get to 0.6133%.

This is twisted really. It is neither given in the question nor in the answer. Not all funds have a 20% carry! Grey area again here…

Is it fine? Let me know if you need the computation

Now, this should be an easy one but I don’t understand. Since you are at question 12 you probably have done this one already.

Question 3.B. of the same reading. Answer says:

“The unhedged return of REITs is almost 2 percentage points greater than the return of the S&P 500, whereas the hedged return is about 2 percentage points less than the S&P. Therefore, taking into account the equity return component of the NAREIT Index, this reallocation [of 10% of the portfolio from S&P 500 to REITs] could represent a slight sacrifice in return”.

Is the equity component of the NAREIT Index represented by the “NAREIT Index unhedge”? And if so, why is it a sacrifice and not an additional return?

This is the way I think about this issue:

Unhedged NAREIT index is a combination of equity like featues (liquidity / tradeability) and pure real estate exposure.

If you hedge the equity like features through S&P Index, you are left with just the pure real estate exposure.

So in this question - using NAREIT Index hedged would reduce your return by about 2%.

Hope it helps

Myriam, thanks. 1. Regarding the performance fee, this is not mentioned, so seems odd to include it. 2. How do they calculate the annualised return for the index?

1. For your question, i am also unsure of why it is a sacrifice, given that the Nareit index return is > S&P return. Can anyone shed light on this?

Yes ok but they did not mention the hurdle either and they used it in the solution.

My apologies though, I wrongly used a hurdle of 6% to make my computation. If you apply a carry of 20% and a hurdle of 6% you get right to 0.6133%. But I have no clue what they actually did. Maybe they used 6% by mistake because it is quite common to see 6% on the market.

Just for your info, here’s what I did:

Sum up all returns: 7.7%

Hurdle of 6%

You share the remaining 1.7% at 80%/20% between you and the fund manager.

So your net return is 6% + 1.7% * 0.8 = 7.36%

Divide by 12: it gives you 0.6133%

I don’t know what they finally ended up doing but if hurdle was 6% and carry was 20%, I think the above method would be correct.