correlation

Learning objectives: Define covariance and explain what it measures. Explain the relationship between the covariance and correlation of two random variables and how these are related to the independence of the two variables. Explain the effects of applying linear transformations on the...

Session 2, Reading 9 (Part 2): This video reviews portfolio variance and covariance, where covariance is the expected cross-product. We look at correlation, which is given by the covariance divided by the product of standard deviations, and therefore standardizes the covariance into a unitless...

Learning objectives: Explain how payment frequencies and exercise dates affect the exposure profile of various securities. Explain the impact of netting on exposure, the benefit of correlation, and calculate the netting factor. Questions: 911.1. Consider the following exposure profile for a...

hi, please explain related to Paying fixed in a variance swap on an index and receiving fixed on individual what does the following statement mean: If correlation increases, so will the variance. As a consequence, the present value for the variance swap buyer, the fixed variance swap payer...

Covariance is a measure of linear co-movement between variables. Independence implies zero covariance, but the converse is not necessarily true (because variables can be dependent in a non-linear way). Here is David's XLS: http://trtl.bz/2B9nqdO

Variables are independent if and only if (iff) their JOINT probability is equal to the product of their unconditional (aka, marginal) probabilities; i.e., if and only if Prob(X,Y) = Prob(X)*Prob(Y). Further, if variables are independent then their covariance (and correlation) is equal to zero...

Can someone explain how mean & variance have been calculated in this example?

Hi @David Harper CFA FRM, I had to think about it myself for some minutes: just wanted to share this with the community here. Let's say we have 18 assets. How many correlation pairs would we have? We could go the long road writing: Asset (A,B) Asset (A,C) Asset (A,D) ... ... Asset (B,C) etc...

Learning objectives: Calculate and interpret the covariance and correlation between two random variables. Calculate the mean and variance of sums of variables. Questions: 711.1. The following probability matrix displays joint probabilities for an inflation outcome, I = {2, 3, or 4}, and an...

Hi David, In our notes (Correlation Risk Modeling and Management), we are told that another way of buying correlation is to buy call options on an index and sell call options on individual stocks of the index. I haven't quite understood this concept - i.e why it should result in a positive...

We are big fans here at BT of Gunter Meissner who is a perennial FRM author. Before his latest book was added to the syllabus (Correlation Risk Modeling and Management), his previous book Credit Derivatives: Application, Pricing, and Risk Management was assigned for several years and it's a...

Learning objective: Define correlation and covariance and differentiate between correlation and dependence. Questions: 705.1. In order to evaluate the the potential of a linear relationship between portfolio returns and a benchmark index, your colleague Richard conducted a univariate...

Hello. I wonder if my understanding is correct with regards to the impact of intra-tranche default correlation on value of different CDO tranches. 1. Equity tranche: when correlation increases, the value of the tranche increases because now there is higher chance of the underlying assets...

Hi, I have a doubt about the meaning of the hedge ratio. Hedge ratio = ρ * σ_spot / σ_fut Number of contracts = HedgeRatio * PortfolioValue / ValueFuturesContract Therefore, the lower the correlation, the lower the number of contracts. So, let's say that I have a portfolio of $ 1.000.000 of...

Dear David I have attached a spreadsheet in which I have calculated copula correlations for a Bi Variate Normal distribution and have inserted a chart on the same. I would be extremely happy if you could have a look at the same and tell me if my understanding is correct. I have used the same...

Learning outcomes: Describe how equity correlations and correlation volatilities behave throughout various economic states. Calculate a mean reversion rate using standard regression and calculate the corresponding autocorrelation. Identify the best-fit distribution for equity, bond, and default...

Learning Outcomes: Explain how correlation contributed to the global financial crisis of 2007 to 2009.Explain the role of correlation risk in market, credit, systemic, and concentration risk. Questions: 502.1. Your colleague Mary conveys to you that she has computed a Pearson correlation...

Learning outcome: Describe financial correlation risk and the areas in which it appears in finance. Questions: 501.1. Below are displayed seven pairs of (A,B) variables; e.g., (3,5), (4,4)...(7,1). The third row shows pairwise products; e.g., 3*5 = 15, 4*4 = 16. Finally, the mean, E(.), and...