March 2010
Intermediate to advanced
238 pages
5h 59m
English
Content preview from Portfolio Optimization
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Chapter 3
The Capital Asset Pricing
Model
3.1 The Capital Market Line
This section will deal with a variation of the model of the previous
section. In addition to the n risky assets, we will now suppose there
is an additional asset with special properties. This asset will be risk
free and as such will have a zero variance and a zero covariance with
the remaining n risky assets. A good example of a risk free asset is
Treasury bills or T-bills.
Let x
n+1
denote the proportion of wealth invested in the risk free
asset and let r denote its return. The expected return of this portfolio
is
µ
p
= µ
1
x
1
+ µ
2
x
2
+ ··· + µ
n
x
n
+ rx
n+1
= (µ
′
, r)
x
x
n+1
.
Its variance is
σ
2
p
= x
′
Σx =
x
x
n+1
′
Σ 0
0
′
0
x
x
n+1
.
41
42 The Capital Asset Pricing Model Chap. 3
The covariance matrix for this ...
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