Problem $12-18$ Portfolio Risk and Return $($LO$2)$

Suppose that the S&P $500,$ with a beta of $1\mathrm{.}0,$ has an expected return of $13\%$ and T$-$bills provide a risk$-$free return of $4\%.$

a$.$ What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P $500$ of $(1)0$ ; $(2)0\mathrm{.}25$ ; $(3)0\mathrm{.}50$ ; $(4)0\mathrm{.}75$ ; $(5)1\mathrm{.}0?$

Note: Leave no cells blank $-$ be certain to enter $"$O$"$ wherever required. Do not round intermediate calculations. Enter the value of Expected return as a percentage rounded to $2$ decimal places and value of Beta rounded to $2$ decimal places.

$\backslash$table$[[,$Expected Return,Beta,$],[(1)0,4\mathrm{.}00,\%,0\mathrm{.}00],[(2)0\mathrm{.}25,6\mathrm{.}25,\%,0\mathrm{.}25],[(3)0\mathrm{.}50,8\mathrm{.}50,\%,0\mathrm{.}50],[(4)0\mathrm{.}75,10\mathrm{.}75,\%,0\mathrm{.}75],[(5)1\mathrm{.}0,13\mathrm{.}00,\%,1\mathrm{.}00]]$

b$.$ How does the expected return vary with beta?

Note: Do not round intermediate calculations.

$\backslash$table$[[$The expected return,increases $(,$by$,8$ for a one unit increase in$],[$beta$.,,,]]$n