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.
In week seven, we'll finish our discussion

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of estimation theory with a practical
problem of estimating the value at risk in

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the constant expected return model.
One of the things that we'll concentrate

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on is computing a standard error for value
at risk to show how accurate value at risk

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is.
And we'll see that it's, it's actually

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quite difficult to get an analytic formula
for the standard error.

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This will serve as a motivation for
learning about the bootstrap which is a

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computer simulation technique that we can
use to let the computer compute standard

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errors for estimates instead of using
mathematics, you know, to derive

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analytically what these things are.
So, we'll do a review of the bootstrap and

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show how it's related to Monte Carlo's
simulation, and then we'll apply for

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bootstrap for computing standard errors
for all of our estimators of the

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parameters of the constant expected return
model.

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After estimation theory, then we'll move
into the last topic in review of

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statistics and this is hypothesis testing.
We'll see that once we have an estimated

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model we often would like to test
hypothesis about the model and these

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hypothesis could be about,
You know, values of the parameters of the

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model, for example.
You know, is the mean zero or is the

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volatility greater than ten%?
And some hypotheses are about verifying or

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refuting the assumptions of the model. For
example.

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Are the returns actually normally
distributed?

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So we'll do a review of hypothesis
testing, the various concepts of setting

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up hypothesis tests and the alternative.
and a discussion of what test statistics

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are.
And then, we'll do applications of

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hypothesis tests to the constant expected
return model.

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We'll look at hypothesis for particular
coefficient values, you know, could be

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testing whether the mean is equal to zero,
or the mean of one asset return is equal

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to another asset return.
We'll also look at test of hypothesis of

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the distribution of acid returns.
And in particular, we'll look at the

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hypothesis of whether or not returns are
normally distributed or not.

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And then, we'll also look at hypothesis
for the assumptions that the returns are

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not auto correlated over time.
So we'll have a hypothesis test for no

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auto correlation.
And then, finally, we'll end our

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hypothesis testing by looking at the
hypothesis that the parameters are

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constant over time.
And here, we'll make use of rolling

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statistics.
We'll look at, like, things like rolling

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means, and rolling variances, and rolling
correlations, and we'll use these rolling

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estimates to determine whether or not the
hypothesis that parameters are constant,

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you know, is validated by the data.