# Portfolio Value at Risk - A conceptual problem

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## Portfolio Value at Risk - A conceptual problem

 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? 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. 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? 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. 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, With regards Amy               [[alternative HTML version deleted]] _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Portfolio Value at Risk - A conceptual problem

 You can use the valuation of the whole portfolio to calculate the returns. That is probably the easiest approach. That should reduce your Problem C -- it shouldn't matter what your assets are as long as you have valuations for them at each timepoint. I'm guessing that you might have tried approach B and got a different answer. If so, then the following should tell you what went wrong: http://www.portfolioprobe.com/2010/10/04/a-tale-of-two-returns/(You can do it that way, but it's a bit trickier.) On 20/10/2010 10:41, Amy Milano 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? > 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. > > 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? > > 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. > > 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, > > With regards > > Amy > > > > > > > > > [[alternative HTML version deleted]] > > > > > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions should go. -- Patrick Burns [hidden email] http://www.burns-stat.comhttp://www.portfolioprobe.com/blog_______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Portfolio Value at Risk - A conceptual problem

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## Re: Portfolio Value at Risk - A conceptual problem

 In reply to this post by Patrick Burns-2 Dear Amy, assuming you have sufficient amount of historical data, you should calculate return collectively, because calculating return separately will destroy the correlation pattern implicit within the historical quotes therefore you may not address properly the diversification effect in your VaR figure. Instead of directly valuing portfolio (and then portfolio return) based on historical quotes I would prefer to find out the historical realized return (may be logarithmic or percentage) and construct a hypothetical price distribution (by taking antilog or something like) for next day (assuming VaR horizon is 1 day) and then find the possible distribution of portfolio values for next day. This always makes sense as price series is never stationary/stable but returns are. Here the fact is to find answer like, previously on some date I got that return therefore what if same return gets realized from 1 day holding. This inference you can never make had you taken raw price because 1 year back price may be 50pt lower than current level, hence in a single day you can never achieve that level (ofcourse assuming tomorrow another layman brother would not fall on your head!) of price but with return you can. Thanks, Arun
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## Re: Portfolio Value at Risk - A conceptual problem

 On 10/20/2010 08:24 AM, Arun.stat wrote: > > Dear Amy, assuming you have sufficient amount of historical data, you should > calculate return collectively, because calculating return separately will > destroy the correlation pattern implicit within the historical quotes > therefore you may not address properly the diversification effect in your > VaR figure. > > Instead of directly valuing portfolio (and then portfolio return) based on > historical quotes I would prefer to find out the historical realized return > (may be logarithmic or percentage) and construct a hypothetical price > distribution (by taking antilog or something like) for next day (assuming > VaR horizon is 1 day) and then find the possible distribution of portfolio > values for next day. This always makes sense as price series is never > stationary/stable but returns are. Here the fact is to find answer like, > previously on some date I got that return therefore what if same return gets > realized from 1 day holding. This inference you can never make had you taken > raw price because 1 year back price may be 50pt lower than current level, > hence in a single day you can never achieve that level (ofcourse assuming > tomorrow another layman brother would not fall on your head!) of price but > with return you can. I prefer to have all the individual returns so that I can also do component risk contribution.  If you simply use univariate portfolio returns, you lose the interdependence between the assets, and can't find out the *contribution* to the overall portfolio risk, only the result. Component risk measures sum to the univariate portfolio risk, so you get that too. # e.g. ###### require(PerformanceAnalytics) data(edhec) VaR(edhec,portfolio_method="component") ES(edhec,portfolio_method="component") ###### Weights, of course, may also be applied. Cheers,     - Brian -- Brian G. Peterson http://braverock.com/brian/Ph: 773-459-4973 IM: bgpbraverock _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Portfolio Value at Risk - A conceptual problem

 In reply to this post by Amy Milano Dear sirs, Thanks a lot for your valuable inputs. That will certainly help me to look ahead and understand the Value at Risk in a right perspective. Regards Amy --- On Wed, 10/20/10, Brian G. Peterson <[hidden email]> wrote: From: Brian G. Peterson <[hidden email]> Subject: Re: [R-SIG-Finance] Portfolio Value at Risk - A conceptual problem To: "Arun.stat" <[hidden email]> Cc: [hidden email] Date: Wednesday, October 20, 2010, 2:28 PM On 10/20/2010 08:24 AM, Arun.stat wrote: > > Dear Amy, assuming you have sufficient amount of historical data, you should > calculate return collectively, because calculating return separately will > destroy the correlation pattern implicit within the historical quotes >  therefore you may not address properly the diversification effect in your > VaR figure. > > Instead of directly valuing portfolio (and then portfolio return) based on > historical quotes I would prefer to find out the historical realized return > (may be logarithmic or percentage) and construct a hypothetical price > distribution (by taking antilog or something like) for next day (assuming > VaR horizon is 1 day) and then find the possible distribution of portfolio > values for next day. This always makes sense as price series is never > stationary/stable but returns are. Here the fact is to find answer like, > previously on some date I got that return therefore what if same return gets > realized from 1 day holding. This inference you can never make had you taken > raw price because 1 year back price may be 50pt lower than current level, > hence in a single day you can never  achieve that level (ofcourse assuming > tomorrow another layman brother would not fall on your head!) of price but > with return you can. I prefer to have all the individual returns so that I can also do component risk contribution.  If you simply use univariate portfolio returns, you lose the interdependence between the assets, and can't find out the *contribution* to the overall portfolio risk, only the result. Component risk measures sum to the univariate portfolio risk, so you get that too. # e.g. ###### require(PerformanceAnalytics) data(edhec) VaR(edhec,portfolio_method="component") ES(edhec,portfolio_method="component") ###### Weights, of course, may also be applied. Cheers,    - Brian -- Brian G. Peterson http://braverock.com/brian/Ph: 773-459-4973 IM:  bgpbraverock _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.               [[alternative HTML version deleted]] _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.