A stock will provide a rate of return of either $-31\%$ or $34\%.$ If both possibilities are equally likely, calculate the stock's expected return and standard deviation.

Consider the following scenario analysis:

$\backslash$table$[[,,$Rate of Retun$],[$Scenario$,$Probability,Stock,Bond,$],[$Recession$,0\mathrm{.}2,-0\mathrm{.}09,0\mathrm{.}2,],[$Normal$,0\mathrm{.}5,0\mathrm{.}21,0\mathrm{.}08,],[$Boom$,0\mathrm{.}3,0\mathrm{.}31,0\mathrm{.}08,]]$

a$.$ Is it reasonable to assume that bonds will provide higher returns in recessions than in booms?

b$.$ Calculate the expected rate of return and standard deviation for each investment.

c$.$ Which investment would you prefer and why?

$3.$ In a recent $5-$year period, mutual fund manager Ali Ayberk produced the following percentage rates of return for the Mesozoic Fund that she manages. Rates of return on the market index are given for comparison.