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P=2 
12
Q
P’ = 
12
This is the derivative and it tell us the slope of the line
P
Slope = 
12
Q
4
2
y
f’ =
1x
this is the slope of the line (it varies because slope isn’t constant)
f’ =
1x
2
this tells us what direct the function is going in
x
To Optimize a Function:
1. Take the derivative
2. Set it equal to 0 and solve for x
3. Take the second derivative
If f’’<0 – we have a maximum
If f’’ >0 – we have a minimum
If f’’ = 0 – we have an inflection
X=
1 4
Expected Return is essentially the mean of the past results, which is the most likely next occurrence
riance
tells us how far the observed values are from the mean, over all of our observations added together and then divided T. This is in squ
andard deviation
just gets rid of the squared returns to tell us how the observations varied from the mean on average.
OR
We subtract 1 to account for errors
OR
Covariance
tells how things move together
Positive: move together
Negative: don’t move together
*If you take the covariance of a security against itself, you get the variance!
OR
89.2
= 17.84*6
=
.83
3X2
3X3
2X2
2X1
1X2
1X1
F
E
D
C
B
A
Referred to as an element, categorized by row: this is element 1X2
1
1
2
2
3
3
1
1
2
1
3
1
4
2
1
1
2
3
4
a
b
a
b
a
Taking the
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 Spring '09
 HUANG,JINGZHI

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