APS 502 Financial Engineering I March. 23, 2017
Instructions: Closed book and closed notes except for one side of a 3 by 5 inch
notecard. Only a simple scienti…c non-…nancial calculator with no programming
capability is allowed. Please write neatly as this will aid in providing maximum
partial credit. IMPORTANT: Interpretation of the exam questions is
part of the exam and so no questions will be taken DURING the
exam that ask for clari…cation of the question. You MUST turn in
this question sheet with your answer booklet or else your exam will
NOT be marked.
Problem 1 (10 points)
A friend needs to borrow $100,000 from you. She promises to pay you
back over 10 years in the form of equal monthly payments. You decide that
a fair interest rate is 8% compounded annually. What should be the monthly
payment?
Solution:
Problem 2 (12 points)
Consider the following equation that relates spot rates si ; sj and the forward
rate fi;j (assume i < j)
(1 + si )i (1 + fi;j )j i
= (1 + sj )j
Suppose that the left hand side of the equation is larger than the right
hand side of the equation. Give a sequence of …nancial operations (lending and
borrowing) that will enable you to make a riskless pro…t without investing any
amount of your own money. Excessive long answers will result in the loss marks.
Solution: If (1 + si )i (1 + fi;j )j i > (1 + sj )j , then we can borrow
money (for example $1) for j periods at the spot rate sj and then
immediately lend $1 at the spot rate si for i periods and then lend
the amount at time i at the rate fi;j for the next j i periods to get
(1+si )i (1+fi;j )j i at time j and then pay back the loan at time j which
is (1 + sj )j and then you have (1 + si )i (1 + fi;j )j i (1 + sj )j > 0 dollars
left over.
Problem 3 (15 points)
You have the following information for 3 bonds:
1
This study source was downloaded by 100000855420558 from CourseHero.com on 10-28-2022 15:02:14 GMT -05:00
https://www.coursehero.com/file/36501256/midterm-winter-2017-solutionspdf/
Instructions: Closed book and closed notes except for one side of a 3 by 5 inch
notecard. Only a simple scienti…c non-…nancial calculator with no programming
capability is allowed. Please write neatly as this will aid in providing maximum
partial credit. IMPORTANT: Interpretation of the exam questions is
part of the exam and so no questions will be taken DURING the
exam that ask for clari…cation of the question. You MUST turn in
this question sheet with your answer booklet or else your exam will
NOT be marked.
Problem 1 (10 points)
A friend needs to borrow $100,000 from you. She promises to pay you
back over 10 years in the form of equal monthly payments. You decide that
a fair interest rate is 8% compounded annually. What should be the monthly
payment?
Solution:
Problem 2 (12 points)
Consider the following equation that relates spot rates si ; sj and the forward
rate fi;j (assume i < j)
(1 + si )i (1 + fi;j )j i
= (1 + sj )j
Suppose that the left hand side of the equation is larger than the right
hand side of the equation. Give a sequence of …nancial operations (lending and
borrowing) that will enable you to make a riskless pro…t without investing any
amount of your own money. Excessive long answers will result in the loss marks.
Solution: If (1 + si )i (1 + fi;j )j i > (1 + sj )j , then we can borrow
money (for example $1) for j periods at the spot rate sj and then
immediately lend $1 at the spot rate si for i periods and then lend
the amount at time i at the rate fi;j for the next j i periods to get
(1+si )i (1+fi;j )j i at time j and then pay back the loan at time j which
is (1 + sj )j and then you have (1 + si )i (1 + fi;j )j i (1 + sj )j > 0 dollars
left over.
Problem 3 (15 points)
You have the following information for 3 bonds:
1
This study source was downloaded by 100000855420558 from CourseHero.com on 10-28-2022 15:02:14 GMT -05:00
https://www.coursehero.com/file/36501256/midterm-winter-2017-solutionspdf/
