Question $2$ Yield Curve $(15$ Marks$)$

Steven is a fixed$-$income portfolio manager who works with large institutional clients. As an

intern working under Steven, you are required to assist him with analysing the yield curve. You

have obtained the following information regarding the current treasury yield curve:

Maturity $($Years$)$ Yield to Maturity $($YTM$)$

$15\mathrm{.}50\%$

$26\mathrm{.}60\%$

$37\mathrm{.}70\%$

$48\mathrm{.}80\%$

Required:

$2\mathrm{.}1.$ Identify the four common shapes of the yield curve and provide a short discussion of the

relationship between the YTM and maturity suggested by each curve. $(8$ marks$)$

$2\mathrm{.}2.$ Determine the forward rates in one year$$s time for the one$-$ and two$-$year maturing bonds.

$(6$ marks$)$

$2\mathrm{.}3.$ Identify the shape of the yield curve based on your findings in $2\mathrm{.}2.$ above. $(1$ mark$)$

Question $3$ Bond Duration and Convexity $(20$ Marks$)$

Steven has a $4-$year maturity bond with a coupon rate of $2\mathrm{.}5\%$ per annum and a par value of

R$1000.$ The bond has a yield to maturity of $3\mathrm{.}6\%$ per annum and a convexity of $125\mathrm{.}50.$ Steven

is expecting the interest rate to increase by $125$ basis points $(1\mathrm{.}25\%),$ and he would like to know

the expected new price for his bond. Using the duration with convexity rule, estimate the

predicted new price for Steven$$s bond.

$(20$ marks$)$