Suppose you are considering two possible investment opportunities: a $12-$year Treasury bond and a $7-$year, A$-$rated corporate bond. The current real risk$-$free rate is $3\%,$ and inflation is expected to be $2\%$ for the next $2$ years, $3\%$ for the following $4$ years, and $4\%$ thereafter. The maturity risk premium is estimated by this formula: MRP $=0\mathrm{.}01($t $-1)\%.$ The liquidity premium $($LP$)$ for the corporate bond is estimated to be $0\mathrm{.}2\%.$ You may determine the default risk premium $($DRP$),$ given the company's bond rating, from the following table. Remember to subtract the bond's LP from the corporate spread given in the table to arrive at the bond's DRP$.$

Corporate Bond Yield

Rate Spread $=$ DRP $+$ LP

U$.$S$.$ Treasury $0\mathrm{.}73\%$

AAA corporate $0\mathrm{.}830\mathrm{.}10\%$

AA corporate $1\mathrm{.}250\mathrm{.}52$

A corporate $1\mathrm{.}690\mathrm{.}96$

What yield would you predict for each of these two investments? Round your answers to three decimal places.

$12-$year Treasury yield: fill in the blank $7$

$\%$

$7-$year Corporate yield: fill in the blank $8$

$\%$

Given the following Treasury bond yield information, construct a graph of the yield curve.

Maturity Yield

$1$ year $5\mathrm{.}42\%$

$2$ years $5\mathrm{.}52$

$3$ years $5\mathrm{.}69$

$4$ years $5\mathrm{.}74$

$5$ years $5\mathrm{.}67$

$10$ years $5\mathrm{.}76$

$20$ years $6\mathrm{.}40$

$30$ years $5\mathrm{.}92$

Choose the correct graph.

The correct graph is

graph B

$.$

A$.$

B$.$

C$.$

D$.$

Based on the information about the corporate bond provided in part b$,$ calculate yields and then construct a new yield curve graph that shows both the Treasury and the corporate bonds. Round your answers to two decimal places.

Years Treasury yield A$-$corporate yield

$15\mathrm{.}42\%$ fill in the blank $10$

$\%$

$25\mathrm{.}52\%$ fill in the blank $11$

$\%$

$35\mathrm{.}69\%$ fill in the blank $12$

$\%$

$45\mathrm{.}74\%$ fill in the blank $13$

$\%$

$55\mathrm{.}67\%$ fill in the blank $14$

$\%$

$105\mathrm{.}76\%$ fill in the blank $15$

$\%$

$206\mathrm{.}40\%$ fill in the blank $16$

$\%$

$305\mathrm{.}92\%$ fill in the blank $17$

$\%$

Choose the correct graph.

The correct graph is

graph C

$.$

A$.$

B$.$

C$.$

D$.$

Which part of the yield curve $($the left side or right side$)$ is likely to be most volatile over time?

Short$-$term rates are

more

volatile than longer$-$term rates; therefore, the

left

side of the yield curve would be most volatile over time.

Using the Treasury yield information in part c$,$ calculate the following rates using geometric averages $($round your answers to three decimal places$)$:

The $1-$year rate, $1$ year from now

fill in the blank $21$

$\%$

The $5-$year rate, $5$ years from now

fill in the blank $22$

$\%$

The $10-$year rate, $10$ years from now

fill in the blank $23$

$\%$

The $10-$year rate, $20$ years from now

fill in the blank $24$

$\%$