Introduction to Computational Finance and Financial ...
You can't see this text!
Introduction to Computational Finance and Financial Econometrics
Portfolio Theory with Matrix Algebra
Eric Zivot
Spring 2015
Eric Zivot (Copyright ? 2015)
Portfolio Theory
1 / 54
Outline
1 Portfolios with Three Risky Assets Portfolio characteristics using matrix notation Finding the global minimum variance portfolio Finding efficient portfolios Computing the efficient frontier Mutual fund separation theorem again
Eric Zivot (Copyright ? 2015)
Portfolio Theory
2 / 54
Example
Example: Three risky assets
Let Ri (i = A, B, C) denote the return on asset i and assume that Ri follows CER model:
Ri iid N (?i, i2)
cov(Ri, Rj) = ij
Portfolio "x":
xi = share of wealth in asset i xA + xB + xC = 1 Portfolio return:
Rp,x = xARA + xBRB + xC RC .
Eric Zivot (Copyright ? 2015)
Portfolio Theory
3 / 54
Example cont.
Stock i A (Microsoft) B (Nordstrom) C (Starbucks)
?i 0.0427 0.0015 0.0285
i 0.1000 0.1044 0.1411
Pair (i,j) (A,B) (A,C) (B,C)
ij 0.0018 0.0011 0.0026
Three asset example data.
In matrix algebra, we have:
?A 0.0427
?=
?B
=
0.0015
?C
0.0285
A2 AB AC (0.1000)2 0.0018 0.0011
=
AB
B2
BC
=
0.0018
(0.1044)2
0.0026
AC BC C2
0.0011 0.0026 (0.1411)2
Eric Zivot (Copyright ? 2015)
Portfolio Theory
4 / 54
Outline
1 Portfolios with Three Risky Assets Portfolio characteristics using matrix notation Finding the global minimum variance portfolio Finding efficient portfolios Computing the efficient frontier Mutual fund separation theorem again
Eric Zivot (Copyright ? 2015)
Portfolio Theory
5 / 54
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- finding the expected value and standard deviation of a
- mean variance skewness kurtosis portfolio optimization
- optimal risky portfolios efficient diversification
- mean variance portfolio analysis and the capital asset
- chapter 7 portfolio theory edu
- capital asset pricing model homework problems
- introduction to computational finance and financial
- outline new york university
- expected return methodologies in morningstar direct asset
- portfolio analysis in rportfolio analysis in r
Related searches
- introduction to business finance pdf
- introduction to finance 15th edition
- introduction to finance books
- introduction to finance online course
- introduction to finance ppt
- introduction to finance pdf book
- introduction to finance textbook
- introduction to finance pdf
- healthcare finance and financial management
- introduction to finance and accounting
- introduction to corporate finance pdf
- define finance and financial management