Question $3$

a$.$ Current market yields on U$.$S$.$ government securities are distributed by maturity as follows:

$3-$month Treasury bills $=1\mathrm{.}90$ percent

$6-$month Treasury bills $=2\mathrm{.}10$ percent

$1-$year Treasury notes $=2\mathrm{.}25$ percent

$2-$year Treasury notes $=2\mathrm{.}51$ percent

$3-$year Treasury notes $=2\mathrm{.}82$ percent

$5-$year Treasury notes $=3\mathrm{.}28$ percent

$7-$year Treasury notes $=3\mathrm{.}56$ percent

$10-$year Treasury bonds $=3\mathrm{.}98$ percent

$20-$year Treasury bonds $=4\mathrm{.}69$ percent

$30-$year Treasury bonds $=5\mathrm{.}25$ percent

i$.$ Draw a yield curve for these securities$.$

ii$.$ What shape does the curve have?

Question $3$

iii. What significance might this yield curve have for an investing institution with $75$ percent of its investment portfolio in $7-$year to $30-$year U$.$S$.$ Treasury bonds and $25$ percent in U$.$S$.$ government bills and notes with maturities under one year?

iv$.$ What would you recommend to management?

b$.$ A bond possesses a duration of $8\mathrm{.}89$ years. Suppose that market interest rates on comparable bonds were $7\mathrm{.}5$ percent this morning, but have now shifted downward to $7\mathrm{.}25$ percent. What percentage change in the bond's value occurred when interest rates decreased by $25$ basis points? What advise will you have for the investor of such bonds?

c$.$ The investments officer for Sillistine Savings is concerned about interest rate risk lowering the value of the institution's bonds. A check of the bond portfolio reveals an average duration of $4\mathrm{.}5$ years. How could this bond portfolio be altered in order to minimize interest rate risk within the next year?