salimah.arab
New Member
Hi,
I need a few clarifications related to the var co-var method. Would appreciate a response.
1- The variance covariance matrix essentially captures the diversification impact due to the co-movement of assets that constitute a portfolio. If, Instead of computing volatility from the matrix, it is computed from portfolio returns the result should be the same. For instance, return of a two-asset portfolio is the weighted average of individual returns. Let's say we create a history of such weighted average returns over the past using the current weights and historical prices. Now apply standard deviation formula to this series. Because the series is arrived at by aggregating individial returns, it has thus accounted for the diversification so the standard deviation of this series is actually a covariance adjusted volatility.
2- A variation of this approach could be using a series of actual mark to market values of the portfolio instead of weighted average returns. For example, in our two-asset portfolio, we can assume the holding to be constant and using the historical prices we can compute past MTM values so portfolio MTM on day-1 is price of asset 1 x holding 1 + price of asset 2 x holding 2 and so on and so forth. Using this series, we can compute log normal returns and hence compute volatility. Again, because the portfolio MTM is a sum total of individial MTM values, it is diversified. I understand this is a violation of how portfolio return is defined in portfolio theory but there is nothing intrinsically wrong with defining it this way.
My question is, is this interpretation correct, conceptually as well as mathematically. Also which of the two is a better way of implementing VaR?
Let me know if an excel example will help.
