INVESTMENT SCIENCE HW 1 SOLUTIONS
JOHN C. MILLER
1. Chapter 2, Exercise 2: The 72 rule
Find n such that (1 + r)n = 2: Taking logs, n ln(1 + r) = ln 2. So for small r,
r ln(1 + r) =
ln 2
0.69
.
n
n
Thus,
n
0.69
69
69
=
=
r
100r
i
where i = 100r.
We have th

INVESTMENT SCIENCE PRACTICE PROBLEMS (NOVEMBER 2015) SOLUTIONS
JOHN C. MILLER
1. Optimal hedge ratio
You are long X dollars of an asset (stock or portfolio) A with standard deviation of returns
A . You would like to short Y dollars of asset B, with standa

INVESTMENT SCIENCE MORE PRACTICE PROBLEMS (DECEMBER
2015) - SOLUTIONS
JOHN C. MILLER
Please find these additional practice problems that cover the material in Sections 9.1, 9.2
and 18.2 of the second edition of the text.
1. Is this stocks alpha statistica

INVESTMENT SCIENCE PRACTICE PROBLEMS (NOVEMBER 2015)
JOHN C. MILLER
1. Optimal hedge ratio
You are long X dollars of an asset (stock or portfolio) A with standard deviation of returns
A . You would like to short Y dollars of asset B, with standard deviati

INVESTMENT SCIENCE MORE PRACTICE PROBLEMS (DECEMBER
2015) - SOLUTIONS
JOHN C. MILLER
Please find these additional practice problems that cover the material in Sections 9.1, 9.2
and 18.2 of the second edition of the text.
1. Is this stocks alpha statistica

ANJLJE J
AMS 550.442: Investment Science
Midterm Exam, October 13, 2015
The full score of exam is equal to 100 points.
Multiple choice questions (circle clearly appropriate answer). 3 points each.
1. The Treasury will sell $20 billion in Tbills. There are

INVESTMENT SCIENCE HW 3 PROBLEMS - FALL 2016
JOHN C. MILLER
1. Textbook Chapter 3 - Exercise 11 - Bond market
We have 3 bonds of all maturity 10 years and $1000 face:
1. A bond with 4% fixed coupon and $950 market price.
2. A bond with 4% plus current sho

INVESTMENT SCIENCE 2016 HW 8
JOHN C. MILLER
1. Textbook Chapter 6 - Exercise 2 - Dice Product
Two dice are rolled and the two resulting values are multiplied together to form the quantity
Z. What are the expected value and the variance of the random varia

INVESTMENT SCIENCE 2016 HW 9
JOHN C. MILLER
1. Chapter 7 - Question 2 - A small world
Consider a world in which there are only two risky assets, A and B, and a risk-free asset F .
The two risky assets are in equal supply in the market; that is, M = 12 (A

INVESTMENT SCIENCE 2016 HW 10
JOHN C. MILLER
1. Chapter 7 - Question 8 - Wizards
Electron Wizards, Inc. (EWI) has a new idea for producing TV sets, and it is planning
to enter the development stage. Once the product is developed (which will be at the end

INVESTMENT SCIENCE PRACTICE PROBLEMS (NOVEMBER 2015)
JOHN C. MILLER
1. Optimal hedge ratio
You are long X dollars of an asset (stock or portfolio) A with standard deviation of returns
A . You would like to short Y dollars of asset B, with standard deviati

AMS 550.442: Investment Science
Practice Questions
PROBLEM 1. Consider a 10 year 4% Treasury note, with face
$100.
(a) Given yield y, what is the equation for the price of the bond?
(b) If y = 5%, what is the price?
(c) What is dP/dy evaluated at 5%?
(d)

INVESTMENT SCIENCE HW 7 SOLUTIONS
JOHN C. MILLER
1. Chapter 7 - Question 7 - Zero-beta assets
Let w0 be the portfolio (weights) of risky assets corresponding to the minimum-variance
point in the feasible region. Let w1 be any other portfolio on the effici

INVESTMENT SCIENCE HW8 SOLUTIONS
JOHN C. MILLER
1. Chapter 8 - Question 2 - APT factors
Two stocks are believed to satisfy the two-factor model
r1 = a1 + 2f1 + f2
r2 = a2 + 3f1 + 4f2 .
In addition, there is a risk-free asset with a rate of return of 10%.

INVESTMENT SCIENCE HW 2 SOLUTIONS
JOHN C. MILLER
1. Textbook Chapter 3 - Exercise 1 - Amortization
A debt of $25,000 is to be amortized over 7 years at 7% interest. What value of monthly
payments will achieve this?
First we need to know the monthly rate.

INVESTMENT SCIENCE HW 5 SOLUTIONS
JOHN C. MILLER
1. Homework question assigned in class: Consumption smoothing and
precautionary saving
Suppose you have no income in the first period, and your income Y in the second period
is a random variable with a 50%

INVESTMENT SCIENCE HW 6 SOLUTIONS
JOHN C. MILLER
1. Chapter 6 - Question 6 - Wild cats
Suppose there are n assets which are uncorrelated. You may invest in any one, or in any
combination of them. The mean rate of return r is the same for each asset, but t

INVESTMENT SCIENCE HW 3 SOLUTIONS
JOHN C. MILLER
1. Proof of Equation 3.3
Proposition (Macaulay duration formula). The Macaulay duration for a bond with a coupon
rate c per period, yield y per period, m periods per year, and exactly n periods remaining is

INVESTMENT SCIENCE HW 4 SOLUTIONS
JOHN C. MILLER
1. Textbook Chapter 4 - Exercise 2 - Spot update
Given the (yearly) spot rate curves s = (5.0, 5.3, 5.6, 5.8, 6.0, 6.1) find the spot rate curve
for next year. Here the implicit assumption of the exercise i

AMS 550.442: Investment Science
Practice Questions
PROBLEM 1. Consider a 10 year 4% Treasury note, with face $100.
(a) Given yield y, what is the equation for the price of the bond?
(b) If y = 5%, what is the price?
(c) What is dP/dy evaluated at 5%?
(d)

INVESTMENT SCIENCE SUPPLMENTARY NOTES
JOHN C. MILLER
Note - these lecture notes do not include any diagrams. As I add new sections I will release
updated copies. The emphasis will be on material that is not covered in much detail in the
text.
1. Repos
Let

Chapter
The
2
Basic
Theory
of
Interest
1. (A nice inheritance) Use the "72 rule". Years = 1994-1776 = 218 years.
(a) i = 3.3%. Years required for inheritance to double = Zf = 8 :'=!21.8. Times
doubled= Hi = 10 times. $1 invested in 1776 is worth 210 :'=!$