PROBLEMS

$1.$ Considering the world economic outlook for the coming year and estimates of sales and earnings in the pharmaceutical industry, you expect the rate of return for Lauren Labs common stock to range between $-20$ percent and $+40$ percent with the following probabilities:

Probability

$0\mathrm{.}10$

$0\mathrm{.}15$

$0\mathrm{.}20$

$0\mathrm{.}25$

$0\mathrm{.}20$

$0\mathrm{.}10$

Possible Returns

$\backslash (-0\mathrm{.}20\backslash )$

$\backslash (-0\mathrm{.}05\backslash )$

$0\mathrm{.}10$

$0\mathrm{.}15$

$0\mathrm{.}20$

$0\mathrm{.}40$

Compute the expected rate of return $\backslash ($ E$\backslash$left$($R$\_\{$i$\}\backslash$right$)\backslash )$ for Lauren Labs.

$2.$ Given the following market values of stocks in your portfolio and their forecasted rates of return, what is the expected rate of return for your common stock portfolio?

$3.$ The following are the monthly rates of return for Madison Cookies and for Sophie Electric during a six$-$month period.

Compute the following:

a$.$ Average monthly rate of return, $\backslash (\backslash$bar$\{$R$\}\_\{$i$\}\backslash ),$ for each stock

b$.$ Standard deviation of returns for each stock

c$.$ Covariance between the rates of return

d$.$ The correlation coefficient between the rates of return

What level of correlation would you have expected before performing your calculations? How did your expectations compare with the computed correlation? Would these two stocks be good choices for diversification? Why or why not?