# ::Free Statistics and Forecasting Software::

v1.1.23-r7
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### :: Investment Diversification - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

The word risk is misused in financial circles since it is usually considered to be synonymous with variability, whereas the more common meaning of the word in lay circles is probability of loss. This demo takes a simple company scenario which is endowed with a high variability, but still has a positive expectation, and shows that if a portfolio of such companies were invested in, and if there were some independence in the experience of these companies (i.e diversification), then the probability of loss for the portfolio is negligible. Use risky() to see the result for one year with a portfolio of n=25 companies, and risky(100) for 100 simulations of this portfolio, showing the slim chance of a loss. The technical point of this program (and several others) is that sample means have an SD that is (1/sqrt(n)) times the SD of the population sampled. The practical implications of this are sometimes under-appreciated.

 Send output to: Browser Blue - Charts White Browser Black/White CSV MS Excel MS Word number of companies number of simulations Chart options Width: Height:

 Source code of R module n <- as.numeric(par1) m <- as.numeric(par2) my.dotplot <- function (x, at=.44, cex=1,...) { min=min(x) max=max(x) z=(x-mean(x))/sd(x) z=(round(10*z)/10) x=z*sd(x)+mean(x) edge=(max-min)/10 stripchart(x, method="stack",xlim=c( min-edge, max+edge), ylab="Frequency", at=at, cex=cex,...) } my.dotplot.lims <- function (x, at=.44, cex=1, x.min=x.min, x.max=x.max, scale=10, ...) { z=(x-mean(x))/sd(x) z=(round(scale*z)/scale) x=z*sd(x)+mean(x) edge=(x.max-x.min)/10 stripchart(x,method="stack",xlim=c(x.min-edge, x.max+edge),ylab="Frequency",at=at,cex=cex,...) } risky <- function (m=1,n=25) { cum=1:m a=matrix(nrow=n,ncol=m) return=c(-1,-.5,0,3) for (i in 1:m) { a[,i]=sample(return,n,T,c(.25,.25,.25,.25)) cum[i]=mean(a[,i]) } if (m ==1) { bitmap(file="mypicture.png") plot(table(a), xlab="net returns", ylab="frequency", col="purple", main="Returns Distribution") dev.off() bitmap(file="mypicture1.png") b=diffinv(a) plot(b, type="l", xlab="company ID", col="purple", ylab="cumulative net return", lwd=2, main="Cumulation of Profits") text(.20*n,max(b)-1,"Profit=",cex=2) text(.45*n,max(b)-1,100*mean(a),cex=2) text(.60*n,max(b)-1,"%",cex=2) dev.off() } if (m >1) { bitmap(file="mypicture2.png") min=min(cum)-0.1 max=max(cum)+0.1 my.dotplot.lims(cum[cum>0], main="Avg. Profit per \$1 Invested", col="blue", x.min=min, x.max=max) my.dotplot(cum[cum<0], col="red", add=TRUE) dev.off() } } risky(m,n)
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 Cite this software as: Weldon L., (2012), Investment Diversification (v1.0.2) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/rwasp_risky.wasp/ The R code is based on : Weldon Larry, R Programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/Programs Weldon Larry, Instructions for using R programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/instructions.doc
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 To cite Wessa.net in publications use:Wessa, P. (2013), Free Statistics Software, Office for Research Development and Education, version 1.1.23-r7, URL http://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.1.23-r7Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net