Answer to Question #238316 in Macroeconomics for Comfort

Question

QUESTION FOUR (20 Marks)
Two year ago, you acquired a 10 year $1000 par value bond at 12% YTM. Recently you sold this bond at 8% YTM. Using semi-annual compounding, compute the
annualised horizon return for this
investment. (10 Marks)

Answer 1

Calcuate the bond price at the time of purchasing (beginning value)

$Bond\space price=Coupon\times(\frac{1-(\frac{1}{(1+r)^n})}{r})+\frac{Face\space value}{(1+r)^n}$

Here,

"r" is the rate

"n" is the number of compounding period

Substitute the values in the formula

$Bond\space price=0\times(\frac{1-(\frac{1}{(1+\frac{0.12}{2})^{10\times2}})}{\frac{0.12}{2}}) +\frac{\$1,000}{(1+\frac{0.12}{2})^{10\times2}}=\$311.80$

Calculate the current bond price (ending wealth value)

Here,

the number of years to maturity will be 8 years (i.e. 10 years-8 years)

$Bond\space price=0\times(\frac{1-(\frac{1}{(1+\frac{0.08}{2})^{8\times2}})}{\frac{0.08}{2}}) +\frac{\$1,000}{(1+\frac{0.08}{2})^{8\times2}}=\$533.91$

Calculate the annualized horizon yield

$\$311.80=\displaystyle\sum_{t=1}^{2\times 2}\frac{\frac{0}{2}}{(1+\frac{i}{2})^{2\times 2}}$

$\$311.80=\frac{\$533.91}{(1+\frac{1}{2})}$

$(1+\frac{i}{2})^4=\frac{\$533.91}{\$311.80}$

$(1+\frac{i}{2})=\sqrt[4]{\frac{\$533.91}{\$311.80}}$

$1+\frac{i}{2}=\sqrt[4]{1.712348}$

$i=(1.1439-1)\times2\\=0.2879\space or\space 28.79\%$