Please provide with solutions and answers for 2questions Use the table for the q
ID: 2614760 • Letter: P
Question
Please provide with solutions and answers for 2questions
Use the table for the question(s) below.
Market Price
Cash Flow in One Year
Security
Today
Poor Economy
Good Economy
A
200
840
0
B
600
0
840
C
???
840
4200
3) Suppose that security C had a risk premium of 30%, describe what arbitrage opportunity exists (if any) and how you would exploit it.
4) Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period is 115. There are 183 days in the coupon period. Suppose that this bond has a coupon rate of 7.4% and there are 10 semiannual coupon payments remaining.
a) Assuming that the par value is $100, what is the “clean price” for this bond if a 5.6% discount rate is used?
) What is the accrued interest for this bond?
C) What is the “dirty price?” (i.e., invoice price)
Market Price
Cash Flow in One Year
Security
Today
Poor Economy
Good Economy
A
200
840
0
B
600
0
840
C
???
840
4200
Explanation / Answer
a). Step 1 : Determine the risk free rate
We can construct the risk-free asset by forming a portfolio of A and B. This portfolio has a certain payoff of $840.
The price for this portfolio is $800.
We know that,
$800 = $840/(1+i)
1+i = 840/800
i = 1.05 – 1
i = 0.05 or 5%
Step 2 : Determine the price using the expected return
Since the risk premium is 30% and the risk –free rate is 5%, then the expected return is 35%.
The average payoff of security C = (840+4200)/2 = $2,520
The Price of C = 2,520/1.35 = $1,867
However, Security C has the same payoff as a portfolio consisting of 1 unit of security A and 5 units of security B. herefore, under the law of one price, the value must be (1 x $200) + (5 x $600) = $3,200.
Since, these two prices are not the same, there must be an arbitrage opportunity. Here, we can buy security C for $1,867 and sell the portfolio of A and B for $3,200 yielding an arbitrage profit of $1,333.
b). When a bond is purchased between coupon periods, the buyer pays a price that includes accrued interest (full/dirty price). Calculate the fractional period between the settlement date and the next coupon date.
W = (days between settlement date and next coupon payment date)/(days in coupon period)
= 115/183 = 0.6284
Clean price = full price – accrued interest
PV(t) = 3.7/(1.028^0.6284) + 3.7/(1.028^1.6284) + 3.7/(1.028^2.6284) + 3.7/(1.028^3.6284) + 3.7/(1.028^4.6284) + 3.7/(1.028^5.6284) + 3.7/(1.028^6.6284) + 3.7/(1.028^7.6284) + 3.7/(1.028^8.6284) + 3.7/(1.028^9.6284)
= 3.6363 + 3.5373 + 3.4410 + 3.3472 + 3.2561 + 3.1674 + 3.0811 + 2.9972 + 2.9155 + 79.4885
= $108.8676 (dirty/full price)
(ii) AI = semi-annual coupon payment x (1-w)
= $3.7 x (1 – 0.6284) = $1.3749
= $108.8676 - $1.3749
= $107.4927
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