4.two_stocks_example

4.two_stocks_example - University of California Los Angeles...

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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Portfolio possibilities curve Efficient frontier Example using R Means, variances, covariance are given: Suppose two stocks have the following expected return and variance: ¯ R A = 0 . 01 , ¯ R B = 0 . 013 ,σ 2 A = . 061 ,σ 2 B = 0 . 0046, and σ AB = 0 . 00062. The following simple R commands will read these inputs and construct the portfolio possibilities curve with and without short sales allowed. #Read expected returns, variances, and covariances: r1_bar <- 0.01 r2_bar <- 0.013 var1 <- 0.0061 var2 <- 0.0046 cov_12 <- 0.00062 #Short sales NOT allowed: a <- seq(0, 1, 0.01) b <- 1-a rp_bar_ns <- a*r1_bar+b*r2_bar var_p_ns <- a^2*var1+b^2*var2+2*a*b*cov_12 sd_p_ns <- var_p_ns^0.5 #Short sales allowed: a1 <- seq(-2,2, 0.01) b1 <- 1-a1 rp_bar_s <- a1*r1_bar+b1*r2_bar var_p_s <- a1^2*var1+b1^2*var2+2*a1*b1*cov_12 sd_p_s <- var_p_s^0.5 #Plot the two portfolio possibilities curves: #Green: Short sales allowed. #Blue: Short sales not allowed. plot(sd_p_s, rp_bar_s, col="green", xlab="Portfolio standard deviation", ylab="Portfolio expected return") points(sd_p_ns, rp_bar_ns, col="blue") 1 Portfolio possibilities curve: ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●...
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This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.

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4.two_stocks_example - University of California Los Angeles...

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