#### Generating Correlated Random Values in Excel

```Hi Mike,

Thanks so much for your advice.  I think that I have it figured out,
but can you confirm this for me?  I can't afford to screw this up.

If  mean(inflation) = .031
stdev(inflation) = .047
mean(stock return) = .106
stdev(stock return) = .204

A     B       C          D
1      Z1    Z2   Inflation   Stock Return

Data Generation Formulas

A2 =NORMINV(RAND(),0,1)
B2 =NORMINV(RAND(),0,1)
C2 =0.031+0.047*A2
D2 =0.106+0.204*(A2*rho+B2*(1-rho^2)^0.5)

Are these formulas correct to generate the random data?  Particularly
cell D2.  Does this give me a complete value that takes into
consideration both the correlated part of the value and the
uncorrelated part?  It looks like it does.  I copied this down many
rows and ran a histogram and it looks good to me, but I just wanted to
confirm before I ran with it.

Thank you again, Mike.

Randy Eastland

+++++++++++++++++++++++++

Randy Eastland  -

I don't know where data is available, but you can get correlated random
values as follows:

If Z1 and Z2 are each independent standard normal random variables,
i.e., each is NORMINV(RAND(),0,1), then to get X and Y with correlation
rho, use

X = MeanX + StDevX*Z1

Y = MeanY + StDevY*(Z1*rho + Z2*(1-rho^2)^0.5)

Alternatively, search google groups for "excel correlated normal" or
similar keywords, without the quotes.

of my university web site, and use its RandBiNormal function, which is
described in RiskSim's built-in Help.

-  Mike Middleton

+++++++++++++++++++++++++

At 14:41 2005-01-05, you wrote:

Hello Mike,

A few weeks ago, you responded to a post that I had placed on an Excel
VBA message board when I was struggling with the ATPVBAEN.XLA!Random
wondered it I could ask you another question.

Actually, 2 questions:

1.  I'm looking for correlation coefficients between the general rate
of inflation, overall stock market returns, and overall bond market
returns. Do you know of a resource where I might find these values?

2.  In building my table of randomly generated inflation rates, stock
market returns, and bond market returns, I am currently using the
formula that you suggested on the message board
(=NORMINV(RAND(),Mean,StDev)).  This formula works excellently, but it
does not consider the fact that these values might be correlated (thus
the first question).  Assuming that I can find r-squared values for a)
inflation with stock returns, and b) inflation with bond
returns, can you offer any advice as to how I might alter this formula
to take correlation into consideration?

Boiled down, my table is basically three columns.  A = inflation rate,
B = stock market returns, and C = bond market returns.  My thought is
to keep your formula intact for inflation, letting this value be
randomly generated around a mean and standard deviation.  B and C then
need to take into consideration that there is at least some correlation
with the inflation rate.  My knowledge of stats began and pretty much
ended back in college.  I have poured through some stats books that I
was able to gather, but I can't
figure out how to do this reliably.  Can you help?

Thank you very much, Mike.  I'm sorry to bother you.  If this is too

Randy Eastland

```
 0
1/12/2005 10:57:51 PM
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```Randy  -

Two things to check:

(1) Your formulas seem OK. But you'll need to either (a) replace "rho" with
a numerical value (between -1 and +1) or a reference to a cell containing a
value or (b) define a name "rho" similarly.

(2) A histogram is useful for checking each variable separately. But you
should also use an XY (Scatter) chart to check the results for a hundred or
so pairs of Inflation and Stock Return.

-  Mike

www.mikemiddleton.com

++++++++++++++++++++++++++

"Randy" <john.public1@comcast.net> wrote in message
> Hi Mike,
>
> Thanks so much for your advice.  I think that I have it figured out,
> but can you confirm this for me?  I can't afford to screw this up.
>
> If  mean(inflation) = .031
> stdev(inflation) = .047
> mean(stock return) = .106
> stdev(stock return) = .204
>
> A     B       C          D
> 1      Z1    Z2   Inflation   Stock Return
>
> Data Generation Formulas
>
> A2 =NORMINV(RAND(),0,1)
> B2 =NORMINV(RAND(),0,1)
> C2 =0.031+0.047*A2
> D2 =0.106+0.204*(A2*rho+B2*(1-rho^2)^0.5)
>
> Are these formulas correct to generate the random data?  Particularly
> cell D2.  Does this give me a complete value that takes into
> consideration both the correlated part of the value and the
> uncorrelated part?  It looks like it does.  I copied this down many
> rows and ran a histogram and it looks good to me, but I just wanted to
> confirm before I ran with it.
>
> Thank you again, Mike.
>
> Randy Eastland
>
> +++++++++++++++++++++++++
>
> Randy Eastland  -
>
> I don't know where data is available, but you can get correlated random
> values as follows:
>
> If Z1 and Z2 are each independent standard normal random variables,
> i.e., each is NORMINV(RAND(),0,1), then to get X and Y with correlation
> rho, use
>
> X = MeanX + StDevX*Z1
>
> Y = MeanY + StDevY*(Z1*rho + Z2*(1-rho^2)^0.5)
>
> Alternatively, search google groups for "excel correlated normal" or
> similar keywords, without the quotes.
>
> of my university web site, and use its RandBiNormal function, which is
> described in RiskSim's built-in Help.
>
> -  Mike Middleton
>
> +++++++++++++++++++++++++
>
> At 14:41 2005-01-05, you wrote:
>
> Hello Mike,
>
> A few weeks ago, you responded to a post that I had placed on an Excel
> VBA message board when I was struggling with the ATPVBAEN.XLA!Random
> function. Your advice was excellent and has help me considerably.  I
> wondered it I could ask you another question.
>
> Actually, 2 questions:
>
> 1.  I'm looking for correlation coefficients between the general rate
> of inflation, overall stock market returns, and overall bond market
> returns. Do you know of a resource where I might find these values?
>
> 2.  In building my table of randomly generated inflation rates, stock
> market returns, and bond market returns, I am currently using the
> formula that you suggested on the message board
> (=NORMINV(RAND(),Mean,StDev)).  This formula works excellently, but it
> does not consider the fact that these values might be correlated (thus
> the first question).  Assuming that I can find r-squared values for a)
> inflation with stock returns, and b) inflation with bond
> returns, can you offer any advice as to how I might alter this formula
> to take correlation into consideration?
>
> Boiled down, my table is basically three columns.  A = inflation rate,
> B = stock market returns, and C = bond market returns.  My thought is
> to keep your formula intact for inflation, letting this value be
> randomly generated around a mean and standard deviation.  B and C then
> need to take into consideration that there is at least some correlation
> with the inflation rate.  My knowledge of stats began and pretty much
> ended back in college.  I have poured through some stats books that I
> was able to gather, but I can't
> figure out how to do this reliably.  Can you help?
>
> Thank you very much, Mike.  I'm sorry to bother you.  If this is too
> much to ask, I understand.
>
> Randy Eastland
>

```
 0
middleton (61)
1/15/2005 12:44:25 AM
```Thanks, Mike.  I appreciate all of your help with this.

Randy

Michael R Middleton wrote:
> Randy  -
>
> Two things to check:
>
> (1) Your formulas seem OK. But you'll need to either (a) replace
"rho" with
> a numerical value (between -1 and +1) or a reference to a cell
containing a
> value or (b) define a name "rho" similarly.
>
> (2) A histogram is useful for checking each variable separately. But
you
> should also use an XY (Scatter) chart to check the results for a
hundred or
> so pairs of Inflation and Stock Return.
>
> -  Mike
>
> www.mikemiddleton.com
>
> ++++++++++++++++++++++++++
>
> "Randy" <john.public1@comcast.net> wrote in message
> > Hi Mike,
> >
> > Thanks so much for your advice.  I think that I have it figured
out,
> > but can you confirm this for me?  I can't afford to screw this up.
> >
> > If  mean(inflation) = .031
> > stdev(inflation) = .047
> > mean(stock return) = .106
> > stdev(stock return) = .204
> >
> > A     B       C          D
> > 1      Z1    Z2   Inflation   Stock Return
> >
> > Data Generation Formulas
> >
> > A2 =NORMINV(RAND(),0,1)
> > B2 =NORMINV(RAND(),0,1)
> > C2 =0.031+0.047*A2
> > D2 =0.106+0.204*(A2*rho+B2*(1-rho^2)^0.5)
> >
> > Are these formulas correct to generate the random data?
Particularly
> > cell D2.  Does this give me a complete value that takes into
> > consideration both the correlated part of the value and the
> > uncorrelated part?  It looks like it does.  I copied this down many
> > rows and ran a histogram and it looks good to me, but I just wanted
to
> > confirm before I ran with it.
> >
> > Thank you again, Mike.
> >
> > Randy Eastland
> >
> > +++++++++++++++++++++++++
> >
> > Randy Eastland  -
> >
> > I don't know where data is available, but you can get correlated
random
> > values as follows:
> >
> > If Z1 and Z2 are each independent standard normal random variables,
> > i.e., each is NORMINV(RAND(),0,1), then to get X and Y with
correlation
> > rho, use
> >
> > X = MeanX + StDevX*Z1
> >
> > Y = MeanY + StDevY*(Z1*rho + Z2*(1-rho^2)^0.5)
> >
> > Alternatively, search google groups for "excel correlated normal"
or
> > similar keywords, without the quotes.
> >
page
> > of my university web site, and use its RandBiNormal function, which
is
> > described in RiskSim's built-in Help.
> >
> > -  Mike Middleton
> >
> > +++++++++++++++++++++++++
> >
> > At 14:41 2005-01-05, you wrote:
> >
> > Hello Mike,
> >
> > A few weeks ago, you responded to a post that I had placed on an
Excel
> > VBA message board when I was struggling with the
ATPVBAEN.XLA!Random
> > function. Your advice was excellent and has help me considerably.
I
> > wondered it I could ask you another question.
> >
> > Actually, 2 questions:
> >
> > 1.  I'm looking for correlation coefficients between the general
rate
> > of inflation, overall stock market returns, and overall bond market
> > returns. Do you know of a resource where I might find these values?
> >
> > 2.  In building my table of randomly generated inflation rates,
stock
> > market returns, and bond market returns, I am currently using the
> > formula that you suggested on the message board
> > (=NORMINV(RAND(),Mean,StDev)).  This formula works excellently, but
it
> > does not consider the fact that these values might be correlated
(thus
> > the first question).  Assuming that I can find r-squared values for
a)
> > inflation with stock returns, and b) inflation with bond
> > returns, can you offer any advice as to how I might alter this
formula
> > to take correlation into consideration?
> >
> > Boiled down, my table is basically three columns.  A = inflation
rate,
> > B = stock market returns, and C = bond market returns.  My thought
is
> > to keep your formula intact for inflation, letting this value be
> > randomly generated around a mean and standard deviation.  B and C
then
> > need to take into consideration that there is at least some
correlation
> > with the inflation rate.  My knowledge of stats began and pretty
much
> > ended back in college.  I have poured through some stats books that
I
> > was able to gather, but I can't
> > figure out how to do this reliably.  Can you help?
> >
> > Thank you very much, Mike.  I'm sorry to bother you.  If this is
too
> > much to ask, I understand.
> >
> > Randy Eastland
> >

```
 0
1/16/2005 9:50:02 PM

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