Theorie de Portefeuille

Le Formules pour 2 Titres

Exercice 7.8

An investor has decided to form a portfolio by putting 25% of his money into McDonald’s stock and 75% into Cisco Systems stock. The investor assumes that the expected returns will be 8% and 15%, respectively, and that the standard deviations will be 12% and 22%, respectively.

1. Find the expected return on the portfolio.

library(formattable)

Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio

percent(0.25*0.08+0.75*0.15)

[1] 13.25%

w=c(0.25, 0.75)
er=c(0.08,0.15)
percent(w%*%er)

     [,1]  
[1,] 13.25%

Vp=0.25^2*0.12^2+0.75^2*0.22^2+2*0.25*0.75*1*0.12*0.22
sqrt(Vp)

[1] 0.195

2. Compute the standard deviation of the returns on the portfolio assuming that

1. the two stocks’ returns are perfectly positively correlated. r = 1

r=1
V=c(.12^2,r*.12*.22,r*.12*.22,.22^2)
V=matrix(V,nrow = 2,ncol = 2)
w%*%V%*%w

         [,1]
[1,] 0.038025

2. the coefficient of correlation is .5. r = .5

r=.5
V=c(.12^2,r*.12*.22,r*.12*.22,.22^2)
V=matrix(V,nrow = 2,ncol = 2)
w%*%V%*%w

         [,1]
[1,] 0.033075

3. the two stocks’ returns are uncorrelated. r = 0

r=0
V=c(.12^2,r*.12*.22,r*.12*.22,.22^2)
V=matrix(V,nrow = 2,ncol = 2)
w%*%V%*%w

         [,1]
[1,] 0.028125

Le Formules pour multiples Titres

Exercice de Investissement 4 Titres

w=c(0.25,0.25,0.25,0.25)
n=c(0.00881,0.00562,0.01253,0.02834)

v=matrix(c(0.00235,0.00141,0.00184,0.00167,0.00141,0.00434,-0.00058,0.00182,0.00184,-0.00058,0.01174,-0.00170,0.00167,0.00182,-0.00170, 0.02020),nrow = 4, ncol = 4)

w%*%n
w%*%v%*%w

Exercice 7.62

A portfolio is composed of two stocks. The proportion of each stock, their expected values, and standard deviations are listed next. Stock 1 2 Proportion of portfolio .30 .70 Mean .12 .25 Standard deviation .02 .15 For each of the following coefficients of correlation calculate the expected value and standard deviation of the portfolio. a.   .5 b.   .2