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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.

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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)

Cite this software as:

Weldon L., (2017), Investment Diversification (v1.0.3) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://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

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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