summarize: So the fundamental problem that about how do you measure risk is, it's easy, right? Like, what you can do is you can look at the past historical returns. So let's say in the universe, there were only two stocks, IBM and apple. You just look at, you know, the returns of IBM and apple and then you basically regress against each other and you can find a correlation between those two stocks. And so every portfolio that you form only will have because there's only two trades, two tradable units and as well, you just you can use that and you can use the correlation matrix. So, the correlation matrix will become two by two because IBM and it has to be the variance and covariance. It's, you know, because it's a two by two matrix. You know, it's simple. It's, it's easier to handle that in the various use cases like portfolio construction or, you know, figuring out residual risk and so on, so forth. Now, the second biggest problem was that, you know, once once you get to watch, add more and more stocks, you know, you get to like, for example, in US there's 10,000 securities so you will get to a problem of 10,000 by 10,000 matrix to model to to see all the correlations. If you add the global stocks, I will become like somewhere around the most tradable stocks are like 65,000 by 65,000. So, the matrix, it's a data becomes pretty large. So, the first and foremost problem was dimensionality reduction. So, that is one one aim of risk models to reduce the dimensionality. So that, you know, you can you can handle a handle any portfolio, modeling risk of any portfolio in a much faster fashion. So that's problem number one. Problem number two is, you know, all of this data when you're modeling correlations they are they're based on past history, right? Like so. You want to be, you want model correlations such that they are robust that they that you know, you're not taking advice. So, you know, you want to you want they are predictive in nature and not like, you know, expert exterminator in nature. So, then, then you have, so, those are the two problems to solve it any any any response so far you're with me, right? Yeah, no, that's that's very clear. Bara or actual, by the way, they also they are in the business they have been doing this for more than banks, but they they model this. They have to based model that they use. They also started off using statistical model like a PCA model to do the dimensionality reduction and solve and make it robust, but they also have like what is called a cross sectional model, cross sectio The response should be in all capital letters.
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