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Thread Subject:
Interpretation of emaxdrawdown results

Subject: Interpretation of emaxdrawdown results

From: Andreas Steiner

Date: 16 Jul, 2011 18:56:09

Message: 1 of 5

With the function emaxdrawdown, it is very easy to generate results larger than one. For example emaxdrawdown(0.05,0.25,30)=1.2206
I interpret this that from peak to bottom, one has lost 122.06%. Losses larger than 100% are only possible if the peak is positive and the bottom negative. Financial assets are typically assumed to have a lower price limit of zero (a stock price can't drop below zero, for example).

Either my interpretation of the result is wrong or then an operation is missing to convert the results of emaxdrawdown into an interpretable figure.

Rgrds,
Andi

Subject: Interpretation of emaxdrawdown results

From: Roger Stafford

Date: 16 Jul, 2011 20:32:09

Message: 2 of 5

"Andreas Steiner" wrote in message <ivsms9$5ef$1@newscl01ah.mathworks.com>...
> With the function emaxdrawdown, it is very easy to generate results larger than one. For example emaxdrawdown(0.05,0.25,30)=1.2206
> I interpret this that from peak to bottom, one has lost 122.06%. Losses larger than 100% are only possible if the peak is positive and the bottom negative. Financial assets are typically assumed to have a lower price limit of zero (a stock price can't drop below zero, for example).
>
> Either my interpretation of the result is wrong or then an operation is missing to convert the results of emaxdrawdown into an interpretable figure.
>
> Rgrds,
> Andi
- - - - - - - - - - -
  You have assumed that the format of 'emaxdrawdown' is what is called 'return' (percentage.) However according to the documentation of 'emaxdrawdown', it can only have either 'arithmetic' or 'geometric' formats. Read the documentation at:

 http://www.mathworks.com/help/toolbox/finance/emaxdrawdown.html

and at:

 http://www.mathworks.com/help/toolbox/finance/maxdrawdown.html

In the first of these it states: "Note: To compare the actual results from maxdrawdown with the expected results of emaxdrawdown, set the Format input argument of maxdrawdown to either of the nondefault values ('arithmetic' or 'geometric'). These are the only two formats emaxdrawdown supports."

That would indicate that 'emaxdrawdown' never uses percentage for its output format.

Roger Stafford

Subject: Interpretation of emaxdrawdown results

From: Andreas Steiner

Date: 16 Jul, 2011 21:11:08

Message: 3 of 5

> However according to the documentation of 'emaxdrawdown', it can only
> have either 'arithmetic' or 'geometric' formats.
This does not make a difference...
emaxdrawdown(0.05,0.25,30) = 1.2206
emaxdrawdown(0.05-0.5*0.25^2,0.25,30) = 1.5051
...in both cases, I cannot interpret the results.

> Read the documentation
I have done that.

> "Note: To compare the actual results from maxdrawdown with the expected results
> of emaxdrawdown, ...
This is not my question, my question is: "what is the interpretation of emaxdrawdown results > 1?".

> That would indicate that 'emaxdrawdown' never uses percentage for its output
> format.
If the result is not a percentage figure - what is the unit of the output and what is it supposed to represent?

With regards,
Andi

Subject: Interpretation of emaxdrawdown results

From: Roger Stafford

Date: 16 Jul, 2011 23:05:13

Message: 4 of 5

"Andreas Steiner" wrote in message <ivsupc$o2h$1@newscl01ah.mathworks.com>...
> If the result is not a percentage figure - what is the unit of the output and what is it supposed to represent?
- - - - - - - - - -
  It is some expected value derived from the theory of Brownian motion. My guess is that its units are derived from the mu and sigma values, along with the time period unit. It is something you will have to find out for yourself. I cannot help you any further with it.

Roger Stafford

Subject: Interpretation of emaxdrawdown results

From: Roger Stafford

Date: 17 Jul, 2011 23:41:08

Message: 5 of 5

"Andreas Steiner" wrote in message <ivsupc$o2h$1@newscl01ah.mathworks.com>...
> ........
> emaxdrawdown(0.05,0.25,30) = 1.2206
> ........
> If the result is not a percentage figure - what is the unit of the output and what is it supposed to represent?
- - - - - - - - - - -
  I couldn't resist coming back to your problem, Andreas, so I did Monte Carlo simulations of a Brownian motion with drift and diffusion using your parameters (mu = .05, sigma = .25, T = 30) to see if my understanding of 'emaxdrawdown' agrees with your results. (I don't have the Financial Toolbox.) My results after four series of 5000 runs each were: 1.2111, 1.2135, 1.2279, and 1.2111 for an overall average of 1.2159, which agrees pretty well with your result of 1.2206 .

  From the success of these runs I conclude that the parameter 'mu' has units of a certain 'value' per unit time and sigma^2 has units of value^2 per unit time. The output will then be in units of this same 'value'. This means that if you multiply mu and sigma by a factor of, say, four, the output should also be multiplied by four. On the other hand if you multiply the parameter T by four, divide mu by four and divide sigma by two, (the square root of four,) the result should remain the unchanged. You can test this directly to see if my surmise is correct.

  If all this is correct, this should clear up the matter of receiving an output value of more than one. This presumably has nothing to do with percentages or proportional parts but relates to the 'value' possessed by a one-dimensional Brownian motion with your assigned parameters.

Roger Stafford

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