You are trying to determine who is a better market player between your two friends Barbara and Oliver $-$ who are aspiring to be professional investment portfolio managers.Your research into their online brokerage trades has turned up the following performance information: Benchmark PortfolioBarbaras PortfolioOlivers Portfolio WeightReturn WeightReturn WeightReturnStocks$0\mathrm{.}6-5\mathrm{.}00\%$Stocks$0\mathrm{.}5-4\mathrm{.}00\%$Stocks$0\mathrm{.}3-5\mathrm{.}00\%$Bonds$0\mathrm{.}33\mathrm{.}50\%$Bonds$0\mathrm{.}22\mathrm{.}50\%$Bonds$0\mathrm{.}43\mathrm{.}50\%$T$-$Bills$0\mathrm{.}11\mathrm{.}00\%$Cash$0\mathrm{.}31\mathrm{.}00\%$Cash$0\mathrm{.}31\mathrm{.}00\%$ The risk$-$free rate is $1\%$ and the standard deviation for the Benchmark portfolio is $3\mathrm{.}50\%,$ Barbaras portfolio is $5\mathrm{.}00\%,$ and Olivers portfolio is $3\mathrm{.}00\%.$

$1.$ Compare Barbara and Olivers performance relative to the benchmark in terms of portfolio returns.

$2.$ If they are beating the market, determine the sources of their success in terms of security selection and asset allocation.

a$.$ Who is superior in security selection?

b$.$ Who is superior in asset allocation?