$1.$ An investor buys a $20-$year semiannual bond with a coupon rate of $5\%$ for $$950.$ He plans to hold the bond for $8$ years and then sell it$.$ The investor expects to reinvest the first $6$ coupon payments at $4\mathrm{.}5\%$ and the next $10$ payments at $5\mathrm{.}5\%.$ He also expects the bond$$s YTM at the end of the holding period to be $6\%.$ Find annualized total return.

$2.$ At which tax rate will investors prefer a corporate bond with a pre$-$tax yield$-$to$-$maturity of $12\%$ and municipal security with a pre$-$tax yield$-$to$-$maturity of $9\%?$

Question #$6$

a$.$ A $6\%$ coupon bond paying interest annually has a modified duration of $10$ years, sells for $$800,$ and

is priced at a yield to maturity of $8\%.$ If the YTM increases to $9\%,$ the predicted change in price, using the

duration concept, decreases by:

i$.$ $$76\mathrm{.}56$

ii$.$ $$76\mathrm{.}92$

iii. $$77\mathrm{.}67$

iv$.$ $$80\mathrm{.}00$

b$.$ A $6\%$ coupon bond with semiannual coupons has a convexity $($in years$)$ of $120,$ sells for $80\%$ of par,

and is priced at a yield to maturity of $8\%.$ If the YTM increases to $9\mathrm{.}5\%,$ the predicted contribution to the

percentage change in price, due to convexity, would be:

i$.1\mathrm{.}08\%$

ii$.1\mathrm{.}35\%$

iii. $2\mathrm{.}48\%$

iv$.7\mathrm{.}35\%$

c$.$ Which statement is true for the Macaulay duration of a zero$-$coupon bond? The Macaulay duration

of a zero$-$coupon bond :

i$.$ Is equal to the bond$$s maturity in years

ii$.$ Is equal to one$-$half the bond$$s maturity in years

iii. Is equal to the bond$$s maturity in years divided by its yield to maturity

iv$.$ Cannot be calculated because of the lack of coupons.

d$.$ A bond with an annual coupon payment has a coupon rate of $8\%,$ YTM of $10\%,$ and a Macaulay

duration of $9.$ The bond$$s modified duration is:

i$.8\mathrm{.}18$

ii$.8\mathrm{.}33$

iii. $9\mathrm{.}78$

iv$.10$

e$.$ The interest rate risk of a bond normally is:

i$.$ Greater for shorter maturities

ii$.$ Lower for a longer duration

iii. Lower for higher coupons

iv$.$ None of the above

f$.$ When interest rates decline, the duration of a $30-$year bond selling at a premium:

i$.$ Increases

ii$.$ Decreases

iii. Remains the same

iv$.$ Increases at first, then declines

g$.$ Which bond has the longest duration?

i$.8-$year maturity, $6\%$ coupon

ii$.8-$year maturity, $11\%$ coupon

iii. $15-$year maturity, $6\%$ coupon

iv$.15-$year maturity, $11\%$ coupon

Question $7$

You are managing a portfolio of $$1$ mm$.$ Your target duration is $10$ years, and you can choose from two bonds: a zero$-$ coupon bond with a maturity of $5$ years, and perpetuity, each currently yielding $5\%.$

a$.$ How much of each bond will you hold in your portfolio?

b$.$ How will these fractions change next year if the target duration is now nine years?

Question #$8$

a$.$ Explain the impact on the offering yield of adding a call feature to a proposed bond issue.

b$.$ Explain the impact on both bond duration and convexity of adding a call feature to a proposed bond issue

Answer all these questionsand show working on how you got your answers.