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 $.$$ $76.56$ ii $.$$ $76.92$ iii. $ $77.67$ iv $.$$ $80.00$ b $.$A $6\%$coupon bond with semiannual coupons has a convexity $($ in years $)$of $120,$sells for $80\%$of par, and is priced at a yield to maturity of $8\%.$If the YTM increases to $9.5\%,$the predicted contribution to the percentage change in price, due to convexity, would be: i $.1.08\%$ ii $.1.35\%$ iii. $2.48\%$ iv $.7.35\%$ c $.$Which statement is true for the Macaulay duration of a zero $-$ coupon bond? The Macaulay duration of a zero $-$ coupon bond : i $.$Is equal to the bond $$ 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 $.8.18$ ii $.8.33$ iii. $9.78$ 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.