You are the owner of a well$-$diversified portfolio valued at $$3,630,000,$ and you have an additional $$370,000$ to

invest. You want to purchase shares of Kroger $($KR$),$ Tesla $($TSLA$),$ and Bank of America $($BAC$).$

Of your additional investment of $$370,000,$ you wish to put $15\%$ in KR$,55\%$ in TSLA, and $30\%$ in BAC.

A single$-$factor analysis yields the following results for the three stocks:

$KR$: ${}_{KR}=-0\mathrm{.}45,{}_{KR}=0\mathrm{.}90$

TSLA: ${}_{\text{T}\text{S}\text{L}\text{A}}=+0\mathrm{.}25,{}_{\text{T}\text{S}\text{L}\text{A}}=1\mathrm{.}80$

BAC:,${}_{\text{B}\text{A}\text{C}}=+0\mathrm{.}10,{}_{\text{B}\text{A}\text{C}}=1\mathrm{.}20$

a$)$ What is the combined beta of these stocks using the weights given above?

b$)$ Before purchasing these three additional stocks, your portfolio beta is ${}_P=0\mathrm{.}890.$ What will be the new

value of beta after you have added the stocks to your portfolio?

c$)$ Is the updated portfolio going to be more or less risky? Explain, considering both market and firm$-$specific

risk.