[R-SIG-Finance] Portfolio Value at Risk - A conceptual problem

[Brian G. Peterson]

On Wed, 20 Oct 2010 02:41:43 -0700 (PDT), Amy Milano
<milano_amy at yahoo.com>
wrote:
> Dear all,
> 
> I am having following conceptual problem when I am trying to find out
> Value at Risk (VaR) for the portfolio. I am just giving an indicative
> portfolio.
> 
> (a) stocks (equity) of 3 different companies say e.g.
> 
> E1   500 equity shares
> E2 1000 equity shares
> E3   100 equity shares
> 
> I have closing prices for last 1 year (i.e. say 250 days) and thus I
> obtain 250 portfolio values by multiplying the respective number of
equity
> shares by respective closing prices and add them.
> 
> Thus, I have 250 portfolio values. I obtain 249 portfolio returns using
> "LN". 
>
> Problem (A) 
> 
> My problem is is my method of calculating returns correct?

No.

Don't worry about weights yet.  Get the returns for each individual series
before sorting out your portfolio weights.  You have all the information,
so you should use it.

The function 'Return.calculate' from 'PerformanceAnalytics' will do what
you want, but the calculation isn't hard.  If 'pr' is your variable of
prices,

pr/Lag(pr, k = 1) - 1

will give you simple returns (which I typically recommend using with daily
series), or 

diff(log(pr))

will give you compound returns.  I typically want a simple return series
for each asset, and will turn it into a compound series later, only if
required, to look at total portfolio return. Sticking with simple returns
avoids adding compounding estimation errors into your calculations later
on.

You want to calculate returns on each price series without worrying about
your invested amount.  It makes everything else simpler.

> In the sense, should I calculate returns for all these 3 companies
> separately (unlike calculating the portfolio value by adding the values
of
> these 3 companies together) and then carry out the further analysis like
> calculating the correlation matrix etc.


There's a function for VaR too that is likely more sophisticated than
anything you would do by hand...

Typically, if you have all the information, why wouldn't you use it?

If you have a simple or compound return series for all the instruments in
your portfolio, then you can readily calculate the portfolio return,
portfolio risk, and contributions to risk.  All you need are weights.  Take
the capital required to establish each of your positions, add it all up. 
this is 100% of your capital.  Now, the capital for opening each position
divided by the total capital is the percent weight you've invested in each
position.

The function 'Return.portfolio' will take your per-instrument returns, and
calculate your portfolio return (assuming no rebalancing, though there's a
function for that too). It can also calulate you 'contribution' to total
return from each of the assets.


> Problem (B)
> 
> If I were to consider returns separately for the above three companies,
> what will happen if there are say 5000 companies (equity only) in my
> portfolio? How do I handle these many companies?


See above.  These functions are routinely used on very large portfolios.

 
> Problem (C) 
> 
> How do I proceed if besides having equity, I also have debt and forex
> transactions also. (Please note that I am asking these questions
> (especially Problem (C) form calculating returns point of view as say
for
> Forex transactions, I consider the spot exchange rates and the LIBOR
rates
> (depending on the currency and the maturity period) as risk factors and
> calculate the Mark to Market (MTMs) values.


If you have a series of MTM 'prices' use these in step A above.


> So my problem basically is how do I arrive at returns in a portfolio.
> 
> I apologize if I have not put up the problem in correct and short words.
> Please forgive and guide me,

Hopefully this helps.

You should find most of the other functions you need for univariate and
portfolio risk (SharpeRation, VaR, ES, etc.) in PerformanceAnalytics as
well.

Regards,

   - Brian

-- 
Brian G. Peterson
http://braverock.com/brian/
Ph: 773-459-4973
IM: bgpbraverock