$$ Question Set $4>$

Over the past $10$ years, a bank has experienced the following loan losses on its C&I loans, consumer loans, and total loan portfolio.

$\backslash$table$[[,$CeI Loans,Consumer Loans,Total Loans$],[$Year$,0\mathrm{.}0080,0\mathrm{.}0165,0\mathrm{.}0075],[2018,0\mathrm{.}0088,0\mathrm{.}0183,0\mathrm{.}0085],[2017,0\mathrm{.}0100,0\mathrm{.}0210,0\mathrm{.}0100],[2016,0\mathrm{.}0120,0\mathrm{.}0255,0\mathrm{.}0125],[2015,0\mathrm{.}0104,0\mathrm{.}0219,0\mathrm{.}0105],[2014,0\mathrm{.}0084,0\mathrm{.}0174,0\mathrm{.}0080],[2013,0\mathrm{.}0072,0\mathrm{.}0147,0\mathrm{.}0065],[2012,0\mathrm{.}0080,0\mathrm{.}0165,0\mathrm{.}0075],[2011,0\mathrm{.}0096,0\mathrm{.}0201,0\mathrm{.}0095],[2010,0\mathrm{.}0144,0\mathrm{.}0309,0\mathrm{.}0155],[2009,,,]]$

Using regression analysis on these historical loan losses, the bank has estimated the following:

$x_C=0\mathrm{.}002+0\mathrm{.}8x_L,$ and $,x_h=0\mathrm{.}003+1\mathrm{.}8x_L$

$,$ where $x_C=$ loss rate in the commercial sector, $x_h=$ loss rate in the consumer $($household$)$ sector, and $x_L=$ loss rate for its total loan portfolio.

$(1)$ If the bank's total loan loss rates increase to $10$ percent, what are the expected loss rates in the commercial and consumer sectors$?$

Commercial Sector $=18\mathrm{.}3\%$; Consumer Sector $=8\mathrm{.}2\%$

Commercial Sector $=8\mathrm{.}0\%$; Consumer Sector $=18\mathrm{.}0\%$

Commercial Sector $=8\mathrm{.}2\%$; Consumer Sector $=18\mathrm{.}3\%$

Commercial Sector $=18\mathrm{.}0\%$; Consumer Sector $=8\mathrm{.}0\%$

Question $15$

$1$ pts

Assume the same information as in the previous question $$ Question Set $4>.$

$(2)$ In which sector should the bank limit its loans and why?

Commercial Sector; The loss rates are systematically higher than the loss rates for the total loan portfolio.

Consumer Sector; The loss rates are systematically higher than the loss rates for the total loan portfolio.

None of the options.

Consumer Sector; The loss rates are systematically lower than the loss rates for the total loan portfolio.