       vectors with mma

• To: mathgroup at yoda.physics.unc.edu
• Subject: vectors with mma
• From: BENNINGA at wilma.wharton.upenn.edu
• Date: Sun, 25 Oct 92 11:37 EDT

```October 25, 1992

Dear Mathematica support:

This is a not-especially intelligent query about (I think)
writing a vector-dependent program in Mma.

I'm trying to write a small program to do portfolio problems in
finance.  I want to both manipulate numbers and do analytics.
Here's part of the program:

Clear[S,X,Y,x,n,ER,ERp,Varp,Var,V]
n=4;
X=Array[x,n]; (* portfolio proportions *)
Y=Array[ER,n]; (* vector of expected asset returns *)
S=Array[V,{n,n}]; (* variance/covariance matrix *)
ERp=X.Y; (* expected portfolio return *)
Varp=X.S.X; (* portfolio variance *)
D[ERp,x]
D[Varp,x]

This program produces the correct output:  I.e., the last two
lines produce the derviative of ERp wrt x and the derivative
of Varp wrt x.

Now suppose I try to put numerical values in for X, Y, and S.
For instance, the next cell of this program has the following:

Y={6,7,8,9};
S = {{10,2,4,5},{2,20,4,1},{4,4,40,10},{5,1,10,60}};
X = {0.4919379941,0.2998194609,0.1116229845,0.0966195605};
ERp

I would have thought that this cell should produce a numerical
answer.  However, it only produces the following:

ER x + ER x + ER x + ER x

Can anyone tell me what I'm doing wrong?

Simon Benninga
Finance Department
Wharton School
University of Pennsylvania
BENNINGA at WHARTON.UPENN.EDU

FAX:  215-898-6200
TEL:  215-898-9466

P.S.  As you can see, I'm new to Mma.  I'm using version 2.1 for
MS-DOS Windows.  If anyone out there is doing finance with Mma,
I'd be interested in making contact.

```

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