Suppose that we live in a market where we have the following bonds:

Given the three bonds, the spot rates in this economy are: $r_1=4\%,r_2=6\%,$ and

$r_3=9\%$

Suppose that security D is also available for trading and has the following $($expected$)$

future cash flows:

$($a$)(")$ Given the term structure of interest rates in this economy, what is the fair market

value of security $D,V_D?$

$($Use at least three decimals for intermediate calculations. Write your final answers in

dollars and round to two decimals: for instance, if the answer is $$450\mathrm{.}355$ or $$450\mathrm{.}359,$

write $450\mathrm{.}36$ without the dollar sign; if the answer is $$450\mathrm{.}354$ or $$450\mathrm{.}351,$ write $450\mathrm{.}35.)$

The value of security $D{V}_D$ is:

$($b$)(")$ How would you replicate the cashflows of security D by trading only in the three

bonds? Give an explicit description of how many of each bond you need to buy or sell to

form the replicating portfolio, where $b_A$ denotes the number of Bond $A,b_B$ denotes the

number of Bond $B,$ and $b_C$ denotes the number of $B$ ond $C.$

$($Use at least three decimals for intermediate calculations. Write your final answers as

positive numbers if you want to buy, and as negative numbers if you want to sell a given

bond. Also, round your final answers to two decimals: for instance, if the number of

bonds to buy is $3\mathrm{.}855$ or $3\mathrm{.}859,$ write $3\mathrm{.}86$ ; if the number of bonds to sell is $3\mathrm{.}854$ or

$3\mathrm{.}851,$ write $-3\mathrm{.}85.)$

The number of Bond $A{b}_A$ is:

The number of Bond $B{b}_B$ is:

The number of Bond $C{b}_C$ is:

$($c$)(")$ If someone was willing to trade security D for $$444\mathrm{.}95($bid price$)$ and $$445\mathrm{.}05$

$($ask price$),$ can you create an arbitrage trading strategy by buying or selling one unit of

security $D$ and trading the number of bonds that you wish, $(b_A,b_B,b_C)?$ What is the

profit of your strategy today?

$($Use at least three decimals for intermediate calculations. Write your final answers as

positive numbers if you want to buy, and as negative numbers if you want to sell a given

bond. Also, round your final answers to two decimals: for instance, if the number of

bonds to buy is $3\mathrm{.}855$ or $3\mathrm{.}859,$ write $3\mathrm{.}86$ ; if the number of bonds to sell is $3\mathrm{.}854$ or

$3\mathrm{.}851,$ write $-3\mathrm{.}85.)$

Do you buy or sell one unit of security D$?$

$($write "buy" or "sell"$)$

The number of Bond $A{b}_A$ is

The number of Bond $B{b}_B$ is:

The number of Bond $C{b}_C$ is:

The profit today is: $