The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
$\begin{array}{lcll}
\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \
\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \
\
\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \
&&&\text { and on 1 October 20X2 } \begin{array}{l}
\

\end{array} \
\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \
&&&\text { and on 1 October 20X2 }

\end{array}$
The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2.
EXHiBiT 2 Binomial interest Rate Tree
on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
$\begin{array} { l c }
\text { Issue Date: } & 6 \text { December 20X0 } \
\hline \text { Maturity Date: } & 6 \text { December 20X4 } \
\text { Coupon Rate: } & 2 \% \
\text { Issue Price: } & \$ 1,000 \
\text { Conversion Ratio: } & 31\
\hline
\end{array}$
-A fall in interest rates would most likely result in:
A) a decrease in the effective duration of Bond 3.
B) Bond 3 having more upside potential than Bond 2.
C) a change in the effective convexity of Bond 3 from positive to negative.

Question

The following information relates to Questions 1-10
Samuel & Sons is a fixed-income specialty firm that offers advisory services to investment management companies. on 1 october 20X0, Steele ferguson, a senior analyst at Samuel, is reviewing three fixed-rate bonds issued by a local firm, Pro Star, inc. The three bonds, whose characteristics are given in Exhibit 1, carry the highest credit rating.
EXHiBiT 1 fixed-Rate Bonds issued by Pro Star, inc.
 $\begin{array}{lcll}
\text { Bond } & \text { Maturity } & \text { Coupon } &{\text { Type of Bond }} \
\hline \text { Bond 1 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Option-free } \
\
\text { Bond 2 } & 1 \text { October 20X3 } & 4.40 \% \text { annual } & \text { Callable at par on 1 October 20X1 } \
&&&\text { and on 1 October 20X2 } \begin{array}{l}
\

\end{array} \
\text { Bond 3 } & \text { 1 October 20X3 } & 4.40 \% \text { annual } & \text { Putable at par on 1 October 20X1 } \ 
&&&\text { and on 1 October 20X2 }

\end{array}$
 The one-year, two-year, and three-year par rates are 2.250%, 2.750%, and 3.100%, re-spectively. Based on an estimated interest rate volatility of 10%, ferguson constructs the bino-mial interest rate tree shown in Exhibit 2. 
EXHiBiT 2 Binomial interest Rate Tree
  on 19 october 20X0, ferguson analyzes the convertible bond issued by Pro Star given in Exhibit 3. That day, the option-free value of Pro Star's convertible bond is $1,060 and Pro Star's stock price is $37.50.
EXHiBiT 3 Convertible Bond issued by Pro Star, inc.
 $\begin{array} { l c } 
\text { Issue Date: } & 6 \text { December 20X0 } \
\hline \text { Maturity Date: } & 6 \text { December 20X4 } \
\text { Coupon Rate: } & 2 \% \
\text { Issue Price: } & \$ 1,000 \
\text { Conversion Ratio: } & 31\
\hline
\end{array}$
-A fall in interest rates would most likely result in:
A) a decrease in the effective duration of Bond 3. 
B) Bond 3 having more upside potential than Bond 2. 
C) a change in the effective convexity of Bond 3 from positive to negative.

Quizplus · Accepted Answer

A fall in interest rates generally increases the price of bonds, giving bonds with higher duration (like Bond 3, implied to have a longer duration than Bond 2) more upside potential due to their higher sensitivity to interest rate changes. Effective duration and convexity are properties of a bond's price sensitivity to interest rate changes, but a fall in rates does not inherently change the effective duration in a specific direction for all bonds nor does it change the sign of a bond's convexity.

The Following Information Relates to Questions 1-10 Samuel & Sons

The Following Information Relates to Questions 1-10
Samuel & Sons