Opinions wanted on math related questions e.g. Annualised volatility

Posted on 2011-09-09
Last Modified: 2012-06-21

I'm currently creating some policy frameworks and models relating to risk in the hedge fund landscape and have a few questions which I would like input from people in the mathematical background.

1. When talking about ANNUALISED VOLATILITY, what do people consider this to mean?  Is this annualised VOL since inception of a fund, annual vol of the last x number of monthly returns, annualised vol of the last full year or annualised vol of current year to date?  In nearly all situations I have seen, there have been no clarifications on the investment manager's data sheets, so it can be interpreted differently unless the definition is considered standardised.

2. What do people define as "draw-down"?  I consider it to mean, if a fund has 12-months of returns and three of those (non consecutive months) were losing months, then I would say that the fund had 3 monthly drawdowns.

But then when I google search it, I see the some definitions are peak to trough which could mean 3 positive months to form a peak, two consecutive up month and then 4 down months.  The highest to the lowest would then be the drawdown as a percentage.  This seems odd to me.

I have even seen some people define drawdown as "only consecutive down months".

View appreciated.
Question by:abdb469
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Accepted Solution

TommySzalapski earned 300 total points
ID: 36510322
You have discovered a common problem in this area. A lot of terms are either poorly defined or misunderstood. It is important that you clarify what you mean by those terms when you use them to avoid confusion.

If the word volatility was used by itself, it should be taken to mean volatility since the beginning.
Annual volatility should refer to the volatility over a year.

A drawdown is technically the difference between a peak and a trough and is usually expressed as a percentage. investopedia defines it well.
LVL 37

Assisted Solution

TommySzalapski earned 300 total points
ID: 36510339
Your idea of a "drawdown month" as a month that is in the "drawdown period" is not a standardized term but it should be readily apparent what you mean to anyone knowledgeable in the field.

Author Comment

ID: 36510639

yes I saw the investopedia definition some time ago, but I didnt necessarily agree with it.  Because I have seen different people use it differently, I found it quite frustrating not knowing exactly what they were referring to incase it meant something else.

Thanks.  Let's see if anymore people comment.
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LVL 37

Assisted Solution

TommySzalapski earned 300 total points
ID: 36511580
Just for reference

Collins English Dictionary: drawdown [1]
2. a continuous decline in an investment or fund, usually expressed as a percentage between its highest and lowest levels

So it's really just a decrease from the peak but usually refers to a trough (low point). It can refer to the drop from the peak to the current value if it is in a declining state. I missed that earlier, sorry.

Now, from a mathematical standpoint, a 'peak' is defined according to your frame of reference. If a fund has been in steady decline all month, then the peak for that month would be day one. So a monthly drawdown could be defined as a month that ends lower than it started. But, if you used the life of the fund prior to that month as the frame of reference, then the peak could be in a different month. The definition isn't rigorous enough to force everyone to use it the same way.

The important thing is to just be consistent and explicit in your own usage of any ambiguous term.

[1] "drawdown." Collins English Dictionary - Complete & Unabridged 10th Edition. HarperCollins Publishers. 09 Sep. 2011.
LVL 27

Assisted Solution

aburr earned 100 total points
ID: 36512066
"yes I saw the investopedia definition some time ago, but I didnt necessarily agree with it.  Because I have seen different people use it differently, I found it quite frustrating not knowing exactly what they were referring to incase it meant something else."
You have hit upon the basic difficulty. There is no definition with which somebody does not disagree.
Sometimes this is because people waqnt to use a definition that shows whatever they are doing in the best possible light.
This is a common difficulty. Consider efforts to standardize computer useage. Creating html definitions is like pulling teeth. Even industry organizations have trouble. The hedge fund industry has no industry wide organization to enforce standard definitions. You are stuck with ambiguity.

Author Comment

ID: 36512254
I agree with your comments, and the definition i.e. from peak to its lowest level.  I guess, like you pointed out, people dont always name their time horizon, which I suppose by default is the whole period available.

However, as you also pointed out the defintion, the word "continuous" has significance, because I equate "continuous" with "consecutive" so that if the fund declines every month by 1% (from say 20%) in a 12-month period, except for the 12th month in which it increases by 5%, the drawdown could be argued that it is the difference between 20% (starting) and 14% (end period), therefore drawdown is 6%.  That is one way of looking it I think?

The other, using the same example except this time the positive month is month 6 where again it increases by 5% that month, then I would say the drawdown is capped at the point of the break in the overall trend, so that by the end of month six, the fund has increased by 5% back to 20% again.
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Assisted Solution

Callandor earned 100 total points
ID: 36512389
Annualized volatility is volatility that has been calculated over a small period of time and is now extrapolated to what it would be over a year.  This would be similar to the percentage gain number that is frequently used.

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