![]() You may understand this better when we deal with its implementation. Here is a quick explanation of what is going on in that formula. X = this is the n x k excess return matrix. The formula to create a variance covariance matrix is as follows – ![]() In general, if there are ‘k’ stocks in the portfolio, then the size of the variance covariance matrix will be k x k (read this as k by k). The size of the variance covariance matrix for a 5 stock portfolio will be 5 x 5. The following 5 stocks constitutes my portfolio – I’d have loved to take up a portfolio of this size to demonstrate the calculation of the variance covariance matrix, but then, it would be a very cumbersome affair on excel and there is a good a newbie could get intimidated with the sheer size of the matrix, hence for this reason, I just decided to have a 5 stock portfolio. A well diversified (high conviction) portfolio typically consists of about 10-15 stocks. If not, here is a great video from Khan Academy which introduces matrix multiplication –Īnyway, continuing from the previous chapter, let us now try and calculate the Variance Covariance matrix followed by the correlation matrix for a portfolio with multiple stocks. Please do note – it is advisable for you to know some basis on matrix operations. Soon we will take up an example and I guess you will have a lot more clarity on this. Think about it, if there are 5 stocks, then this matrix should convey information on the variance of a stock and it should also convey the covariance of between stock 1 and the other 4 stock. Well, is it just one matrix i.e the ‘Variance Covariance matrix’. Just to clear up any confusion – is it ‘variance covariance matrix’ or is it a variance matrix and a covariance matrix? Or is it just one matrix i.e the ‘Variance Covariance matrix’. How one can identify trading risk and ways to mitigate the same.īefore we proceed any further, I’ve been talking about ‘Variance Covariance matrix’. Of course, we will also take a detailed look at risk from a trader’s perspective. This will also include a quick take on the concept of ‘value at risk’. While we are at it we will also discuss ‘asset allocation’ and how it impacts portfolio returns and risk. Portfolio variance tells us the amount of risk one is exposed to when he or she holds a set of stocks in the portfolio.Īt this stage you should realize that we are focusing on risk from the entire portfolio perspective. Remember, our end goal is to estimate the portfolio variance. Once we are through with this part, we use the results of the correlation matrix to calculate the portfolio variance. To make sense of this, we need to develop the correlation matrix. However, the ‘variance covariance’ matrix alone does not convey much information. In this chapter we will extent this discussion to estimate the ‘variance co variance’ of multiple stocks this will introduce us to matrix multiplication and other concepts. ![]() In order to estimate the variance co variance and the correlation of a multi stock portfolio, we need the help of matrix algebra. The discussion on variance and co variance was mainly with respect to a two stock portfolio however we concluded that a typical equity portfolio contains multiple stocks. Co variance on the other hand is the variance of a stock’s return with respect to another stocks’ return. ![]() Variance is the deviation of a stock’s return with its own average returns. In our discussion leading to portfolio risk or portfolio variance, we discussed two crucial concepts – variance and co variance. Having understood the basic difference between these two types of risk, we proceeded towards understanding risk from a portfolio perspective. We started this module with a discussion on the two kinds of risk a market participant is exposed to, when he or she purchases a stock – namely the systematic risk and the unsystematic risk. Let us begin this chapter with a quick recap of our discussion so far. ![]()
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