There is a strong positive correlation between the stock A and stock B. What is the correlation coefficient between the returns of two stocks having a covariance of 0.00546? The variance of the stocks A and B are 0.0039 and 0.0082 respectively.Р”В¬orr(R A, R B) = Var(R A, R B)/ РџС“(R A)РџС“(R B)Р”В¬orr(R A, R B) = 0.00546/(0.06245)(0.09055) = 0.9655 It is not good for measuring the non-linear relationship.Р”В®xample 7: Calculating correlation coefficient between two variables It does not specify the factors that cause the linear relationship between the two variables. The magnitude matters rather than sign when looking at the strength of the relationship. Two variables with a correlation coefficient of -0.80 are more strongly related to each other than the two variables with a correlation coefficient of +0.50. A correlation coefficient of zero indicates no linear relationship between two random variables. A correlation coefficient of -1 indicates a perfect negative correlation between two random variables. A correlation coefficient of +1 indicates a perfect positive correlation between two random variables. It has no units and lies between -1 to +1. It measures the strength of the relationship between two random variables. It is calculated by dividing the covariance between two variables divided by the product of their standard deviations. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

It does not tell anything about the strength of the relationship between the two variables. The returns of two stocks are given below for three interest rate scenarios.Р”В¬alculate and interpret the covariance of return for stock A and stock B.Р”В®xpected return of stock A, E(R A) = 0.20*0.05 + 0.50*0.12 + 0.30*0.14= 0.112Р”В®xpected return of stock B, E(R B) = 0.20*0.02 + 0.50*0.09 + 0.30*0.18 = 0.103 Two variables having a covariance of 100 may not have a strong relationship than two variables having a covariance of 50.Р”В®xample 6: Calculating covariance between two variables It does not tell anything about the strength of the relationship between two variables. It is dependent on the data and scaling of data and can take extremely large values. The covariance has comparability issues across data sets having different scales.

A zero covariance means that the two variables are unrelated. A positive covariance means that the two variables move in the same direction. The covariance of a variable with itself is equal to its variance which is always positive.Р”Р„ negative covariance means that the two variables move together in the opposite direction. It can range from negative infinity to positive infinity. Variance = Var(X) = EР”В¬ovariance is symmetric i.e. It also signifies the risk.Р”В®xample 5: Calculating variance and standard deviation The unit of standard deviation is the same as that of the variance, and it is easier to interpret. The standard deviation is the positive square root of the variance. Variance measures the risk or dispersion. When all the values are equal, then the sum of squared terms equal zero, and the variance is zero. The variance of a random variable is the expected value of squared deviation from the random variable's expected value.Р”Р„ variance is a number greater than or equal to zero because it is the sum of squared terms. The expected value of a random variable is the probability-weighted average of the possible outcomes of the random variable.Р”В®(X) = Expected value of random variable X = РІв‚¬вЂP(X i)X iР”В¬alculation of portfolio expected return: The expected return of a portfolio with n securities is a weighted average of the expected returns on the component securities.Р”В®(R P) = w 1E(R 1) + w 2E(R 2) +. We have already discussed the expected value and its calculation. CFA level I / Quantitative Methods: Basic Concepts / Probability Concepts / Expected value, standard deviation, covariance, and correlation of returns on a portfolio

R weighted standard deviation