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Cont'd on statistics, can we use projected data (25 years) to get standard deviation, correlation, covariance on expected return?
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But dont it compounded the forecasting errors that you already have
If the data just provides a linear price path with no variance, then computing standard deviation and covariances using the projected data will be meaningless. If, however, the projected returns are projected for different scenarios, then you can compute a forward looking standard deviation and covariance. You will have to supply probability estimates for each node, however. In fact, computing standard deviation and covariance in this form, is really no different than valuing a stock option using a binomial option pricing model.
No it will not compound the forecasting error. For example, suppose we are computing the standard deviation, covariance, and average return of the market and section A over the next year. The return distribution is defined as follows:
Good Scenario: 25% return
Bad Scenario: -30% return
Normal Scenario 10% Return
Good Scenario: 15%
Bad Scenario: -20%
Normal Scenario: 8%
Good Scenario: 10%
Bad Scenario: 10%
Normal Scenario: 80%
The expected return of Security A is:
.10*.25+.10*-.30 + .8*.10 = 7.5%
The variance of Security A's returns is
.1*(.25-.075)^2+ .1*(-.3-.075)^2 + .8*(.1-.075)^2 = 0.0176
The standard deviation is
sqrt(.1719) = 13.28%
Using the same process, the sample mean and standard deviation of the market are:
5.9% (average) and 8.88%
The covariance is
.1*(.25-.075)*(.15-.059) + .1*(-.3-.075)*(-.20-.059)+.8*(.10-.075)*(.08-.059)
Correlation is 0.9943 (i.e. 1.17%/(8.88%*13.28%) = 0.9943)
Beta is 1.49 (i.e. (13.28%/8.88%)*.9943 = 1.49
Thanks, i've tried to figure out for past few weeks, whats variable to correlate with, u've cleared my doubt. Thanks again valuator.
But may i know how do you calculate the market good and bad scenario? Usually, we based on market data and company situation to do scenario for firm/projects return.
The scenarios and probabilities are subjective. Unfortunately, market participant's do not have crystal balls. We have to estimate the scenarios and assign subjective probabilities to their outcomes. Most likely, everyone's scenarios and probabilities will be different. You have to form well reasoned scenarios and probabilities based upon your expectations for return and risk in light of the current economic environment.