You are a Fixed Income Portfolio Manager and has been approached by a potential investor who is new to the bond market. The potential investor has raised some queries and would like your assistance on the following item as per below:

a$)$ What are the three main characteristics a fixed income investor should be aware when investing in a bond instrument. The potential investor would like to buy Bond X described in the exhibit below, for settlement on $16$ June $2020.$

Annual Coupon $5\%$

Coupon Payment Frequency Semi$-$annual

Interest Payment Dates $10$ April and $10$ October

Maturity Date $10$ October $2022$

Day Count Convention $30/360$

Annual Yield$-$to$-$Maturity $4\%$

a$)$ What is the price that Bond X settled on $16$ June $2020$ is closest to$?$

Assume that the $6\mathrm{.}75\%$ US Treasury bond that matures on $15$ August $2041$ is priced to yield $8\mathrm{.}14\%$ for settlement on $15$ October $2020.$ Coupons are paid semi$-$annually on $15$ February and $15$ August. The yield$-$to$-$maturity is stated on a street$-$convention semi$-$annual bond basis. This settlement date is $61$ days into a $184-$day coupon period, using the actual$/$actual day$-$count convention. Compute the following for this Treasury bond assuming a $100$ bps change in the yield$-$to$-$maturity and investment of USD$1$M$.$

b$)$ approximate modified duration;

c$)$ the approximate Convexity;

d$)$ Assuming the approximate effective duration is $5\mathrm{.}907$ and approximate convexity of $87\mathrm{.}157.$ Calculate the estimated convexity adjusted percentage price change resulting from a $100$ basis points decrease in yield to maturity.

e$)$ Bonds often have embedded optionality with different exercise styles. Distinguish between an American$-$Style Call, European$-$Style Call and Bermuda$-$Style Call bonds and impact of the stated optionality on the yields of the bonds.

f$)$ Critically assess the key risks to which a bond investment is exposed to$?$

g$)$ Differentiate between a passive bond investment strategy to an active bond investment strategy.

h$)$ Critically outline the main sources of profit for an active bond management strategy. Support your response with relevant examples.

i$)$ Outline the two components of interest rate risks for a coupon paying bond.

j$)$ Differentiate between clean price, dirty price and full price

k$)$ For a bond under what conditionals an investor$$s rate of return on a bond investment to equal the bond$$s YTM$?$

l$)$ Assume that the thereare two non$-$callable fixed$-$coupon bonds on the same date with the same coupon rate except that one matures in $5$ years and the other matures in $15$ years. Critically explain the impact on each of the bond for a $0\mathrm{.}5\%$ change in interest rate.