The covariance of the market returns with the stock’s returns is 0.005 and the standard deviation of the market’s returns is 0.05. What is the stock’s beta? A) 2.0. B) 1.0. C) 0.1. Your answer: C was incorrect. The correct answer was A) 2.0. Betastock = Cov(stock,market) ÷ ( STD MKT)2 = 0.005 ÷ (0.05)2 = 2.0 in this example, in the denominator we use .05^2QUESTION: WHY DO WE USE .20 IN THE DENOMINATOR AND NOT .2^2 ?
**** In this example, we use the standard deviation in the denominator, and NOT the variance **** Glimmer Glass has a correlation of 0.67 with the market portfolio, a variance of 23%, and an expected return of 14%. The market portfolio has an expected return of 11% and a variance of 13%. Glimmer stock is approximately: A) 4% more volatile than the average stock. B) 19% more volatile than the average stock. C) 11% less volatile than the average stock. Your answer: A was incorrect. The correct answer was C) 11% less volatile than the average stock. Beta is equal to the covariance divided by the market portfolio variance, or the product of the correlation and the ratio of the stock standard deviation to the market standard deviation. To derive the standard deviation, we take the square root of the variance. So beta = 0.67 × 0.479583 / 0.360555 = 0.891183. Glimmer shares are about 11% less volatile than the average stock. ******** Question: When computing beta, when do we use the variance in the denominator and when do we use the standard deviation?
boss 2 formulae at work:(essentially same formula, but different variants) 1. Cov/sigma market^2 2. Cov = Correlation * sigma stock * sigma market put the two together -> beta = Correlation * sigma stock * sigma market / sigma market^2 = correlation * sigma stock / sigma market.
All three of these questions ask us to compute beta ----->> Schweser question #88908: we are given “Standard deviation on the stock market index: 20%” and we use .20 in the denominator ----->> Schweser question #88907 we are given “standard deviation of the market returns is 32%” and we use .32^2 in the denominator ----->> Schweser question #86987 we are given “The variance of the market is 0.04632” and we use the variance of the market to compute beta *** I would be VERY grateful if somebody could explain when to use std and when to use variance in the denominator when computing the beta Thanks
CPK I’m sorry I just don’t get it. Can you explain the two formulas again, in simpler terms.
Cov / sigmaM^2 = Beta Cov = corr*sigmastock*sigmaM beta = cov/sigmaM^2 = corr*sigmastock*sigmaM/sigmaM^2=corr*sigmastock/sigmaM [it is simple algebraic manipulation, and just that) problems 1 and 2 were variants of this. problem 3 threw in a wrinkle - giving you the variance instead of the std deviation of the stocks… just to see if you were paying heed…
somehow I got it grazie
you always use variance in the denominator. beta = covi,m / variance market
CPAbeatsCFA if you have the qbank, please take a look at question #88908 in this example the denominator is: “standard deviation of the stock market index” somehow I’ve put together a basic understanding when to use variance in the denominator and when to use the standard deviation in the denominator. Please take a look at this question
I got it wrong by using variance in the denomimator…??? .20^2
Yes, for this example we do not use variance in the denominator. My understanding of when to use variance and when to use standard deviation in the denominator is VERY BASIC, but it seems to be working. The basic formula for beta is: cov of the stock, market / variance of market However, sometimes we have to actually compute the covariance. Covariance is: correlation x standard deviation of stock x standard deviation of the market *** However, when we compute beta (if we have to actually compute the covariance) we use: correlation x standard deviation of the stock / standard deviation of the market *** But if covariance is simply given, we just use that covariance / variance It seems to be working so far when i have to compute beta. As CPK said it is simple algebraic manipulation, but i couldn’t really put together what he was talking about, but what he said did put me in the direction of figuring out when to use variance or standard deviation
look at my posts above. both formulae are the same… Formula 1: Cov / sigmaM^2 = Beta Also-> Cov = corr*sigmastock*sigmaM So substituting in Formula 1: beta = cov/sigmaM^2 = corr*sigmastock*sigmaM/sigmaM^2=corr*sigmastock/sigmaM --> Formula 2. [it is simple algebraic manipulation, and just that) problems 1 and 2 were variants of this.
cpk is correct. It is the same formula but different variants. Q1. the formula used was: cov(market,stock)/var(stock) - 1 if standard deviation = s then var(stock) = [s(stock)]^2 Q2. we all know cov(market,stock) = corr(market,stock) x s(stock) x s(market) - 2 if we substitute 1 into 2 we get: [corr(market,stock) x s(stock) x s(market)]/var(stock) - 3 but var(stock) = s(stock) x s(stock) so 3 will be: [corr(market,stock) x s(stock) x s(market)]/[s(stock) x s(stock)] which will be equal to (you cancel s(stock)) [corr(market,stock) x s(market)]/[s(stock)] and that is what is applied in both Q2 and Q3.
idreesz the formula used was: cov(market,stock)/var(stock) - 1 should be cov(market,stock)/var(market) - 1 Var(market) is the denominator… same change to formula in -3 as well. and you would cancel s(market) not s(stock).