2: Lecture Quantitative Review - Addendum
Quantitative Review: Returns on securities and portfolios Stats: means, variances, covariances, correlations, regressions BKM chapter 5
Readings:
Part A - Outline:
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How to measure returns?
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for securities & portfolios random variables, means, variances covariances and correlations
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How do returns behave?
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How do returns move together?
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Part B - Outline:
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How do returns move together?
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regressions
Correlation measures the association between two random variables. Both variables are treated equally. -> Association
Regression is another measurement. It asks what we expect a variable Y to be given another variable X. -> Prediction -> Regression can also be used when there are (Xs) that seem to impact a particular Y variable. many factors
Regression
Univariate Regression:
Yt = + X t + t Yt is the endogenous or left-hand-side variable e is intercept, is the regression slope Xt is the explanatory or right-hand-side variable t e is the regression error, shock, or residual
We do not know the true values of or . We may estimate them by running a regression (e.g. in Excel) or the formulas below:
= Y X XY
= Y X
Multivariate Regression than one explanatory Multivariate Regression: There can be more
variables, rt = or Yt+1 = + b tX+ Z t + t + 1 1,t + 2 F2,t + 3 F3,t + F t
Now there are multiple slope coefficients. There is no obvious graphical representation. Regression estimates must be calculated using a statistical software package or in Excel using the Analysis Toolbox.
Regression
Example: You are an analyst for a company called World. The chief strategist is predicting rSP500=10% for next year. What would you predict World to do the coming year?
S&P500
Regression
-> what is
and
?
Regression
Excel regression output: rWORLD_STOCKS,t = + rUS_LCAP_STOCKS,t + t
Regression
Predicted Y: rWORLD_STOCKS,t = 0.0172+ 0.771rUS_LCAP_STOCKS,t
So if rSP500=10%, then prediction rWORLD=