Statistics 701: Berndt chapter 2
Statistics 701: Berndt chapter 2
variance background
variance / sd
variance vs covariance
Pictures
variance formula for sums
covariance of x with x is variance of x
CAPM without risk free
eq (2.5) r
p
= sum w
j
r
j
eq (2.6) variance formula
suppose w
j
is small. In other words, consider adding a small amount to an existing portfolio
how does r change
how does variance change
if variances of two investments agree then r's must agree
Better: if variance of a &le variance of b, then return of a @le return b
But what if variances aren't equal?
CAPM with risk free (scaling variances)
need to scale investments
need to sell (borrow) something to finance new investment
actual return is: r
k
-r
f
Now we can scale to get marginal variances to match
bingo: we have an equation describing returns vs marginal variance
(r
k
-r
f
)/s
kp
is constant for all possible investments
a bounce per buck argument
Using the market to set the constant
equation holds if market
generates CAPM equation (2.16)
Doing statistics
regression view of equation
Last modified: Thu Sep 20 13:20:08 2001