Suppose that a set of portfolio managers has a chance p = 50% of beating the market by 10% in a given year and chance 1 - p of underperforming by 10%. Performance from one year to the next is independent and uncorrelated. Returns are simple returns and compounding is ignored. (a) What is the probability that a manager will achieve a five-year track record which beats the market for at least 4 out of 5 years? (b) Suppose that unsuccessful managers get forced out of business as soon they are down overall -30%; that is, as soon as as their record contains 3 more losing years than winning years. What is the probability of failure over a five-year horizon? (c) Among those who survive, what is the expected total return?
Suppose that a set of portfolio managers has a chance p = 50% of beating the market by 10% in a given year and chance 1 - p of underperforming by 10%. Performance from one year to the next is independent and uncorrelated. Returns are simple returns and compounding is ignored. (a) What is the probability that a manager will achieve a five-year track record which beats the market for at least 4 out of 5 years? (b) Suppose that unsuccessful managers get forced out of business as soon they are down overall -30%; that is, as soon as as their record contains 3 more losing years than winning years. What is the probability of failure over a five-year horizon? (c) Among those who survive, what is the expected total return?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:4. Suppose that a set of portfolio managers has a chance p = 50% of beating the market
by 10% in a given year and chance 1 - p of underperforming by 10%. Performance
from one year to the next is independent and uncorrelated. Returns are simple returns
and compounding is ignored.
(a) What is the probability that a manager will achieve a five-year track record which
beats the market for at least 4 out of 5 years?
(b) Suppose that unsuccessful managers get forced out of business as soon they are
down overall -30%; that is, as soon as as their record contains 3 more losing years
than winning years. What is the probability of failure over a five-year horizon?
(c) Among those who survive, what is the expected total return?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
