• C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering.
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job.
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models.

Can someone help me understand why individual VaR is modelled seperately then combined together using correlations?

myndelsg

New Member
Couldn't we combine the portfolio first to get the distribution of portfolio log returns and then calculate the portfolio VaR from there? This way we won't have to deal with the correlation matrix?
 
Last edited:

IntoDarkness

Well-Known Member
Suppose you have 2 assets which are perfectly correlated with coefficient of -1. What do you think your combined distribution is?
 

Ken Abbott

Managing Director
And one more thing: correlations are not explicitly used by most banks. Correlation is used in the variance/covariance and Monte Carlo VaR. About 86% of a survey of 70 large banks use hist sim, which only captures correlation implicitly. This is from a survey that one of my students performed for his masters degree.
1599215278284.png
 

Chethan Pai

Active Member
C++
Couldn't we combine the portfolio first to get the distribution of portfolio log returns and then calculate the portfolio VaR from there? This way we won't have to deal with the correlation matrix?

Regards,
Joel
For ease, consider the case of a bond portfolio (relates to point 3 from Ken), apart from the rebalancing & maturity of individual bonds, we may have bonds getting called (30 day notification period) or convertibles converted (a different risk profile). Hence bottom up aggregation is a viable measure in such portfolios.

Your concern about correlation matrix is legit and this is one of the reasons why people choose factor models and estimate systematic risk using factor covariance matrix (reduced dimensions as usually K factors < N instruments). Of course there is a full security correlation matrix required for estimating idiosyncratic risk for the complete risk profile, but then it is mostly a diagonal matrix (if there are no bonds from the same issuer).
 

myndelsg

New Member
I am confused about two points about VaR still which I hope anyone can shed some light - I think it was mentioned for Monte Carlo and parametric var the correlation matrices are used - I get the point for Monte Carlo; but for parametric VaR, is there any real difference between computing the portfolio variance off the portfolio value changes (where we define value as the summation of number of stocks * price) vs handling it through w’Cw where we use the covariance matrix?
 
Top