Portfolio Maths Question

[bernd]

Hi all,

If I run a systematic strategy that targets a 1% probability of a -20% return or worse in any rolling one-month period. This equates to approximately a 36% annualized standard deviation.

Can someone please explain the math behind this statement and derivation of the 36% annualized standard deviation?

Thanks
Bernd

 

[Jonathan Ling]

The first part of the statement basically says that the 99% monthly Value-at-Risk is 20%.

 

[ExSan]

I have coded Markowitz Portfolio in C++, Output is shown and is verified solution of the Sys Eq.
Is this a valid solution? since each W_i >1, How to interpret the results?

 

[IntoDarkness]

Well it can be interpreted as you leverage up ~64:1 for this to work

 

[ExSan]

I have this case

I have run hundreds of times this simmulation of Markowitz portfolio and this eventuatllity is frequent! What is going on, any idea?
I am trying to verify the solution; I traverse the first row from left to right and the solution col from top to bottom, and do the corresponding multiplication to verify the solution, the expected value is zero but it does happen only once in a while. My math precision is double for all operations, all my platform is C/C++ , Object Oriented
I guess a negative val of w_i corresponds to a short position