The Chinese University of Hong Kong
FINA 3080-F/G: Investment Analysis and Portfolio Management
2021 – 22 Term 2
Instructor: Prof. Darwin Choi
Team Homework Assignment 1
Due on Friday, February 25, 2022
This is a group assignment and you should work with your teammates. You can find your
teammates’ names on Blackboard. We assign an alphabet to each team and you are welcome
to come up with a more innovative team name that starts with the alphabet (e.g., Group D can
call themselves Group DarwinRocks). Each team should submit two things: 1. your answers
in a document (Word or pdf) and 2. your calculations in Excel (do not worry about the format;
it’s ok as long as your numbers and formulas are there). Please submit everything on
Blackboard before 11:59pm on the due date to receive full credit.
All the data are in Homework 1.xlsx on Blackboard.
Problem 1 – Returns
(You do not have to answer this problem in the write-up. Just calculate everything in Excel.)
In the Excel file, you can find the monthly historical closing prices for the following securities
and indexes from December 31, 2006 to December 31, 2021:
i) HSI (Hang Seng Index)
ii) 0008.HK, listed on the Stock Exchange of Hong Kong
iii) IBM, listed on the New York Stock Exchange
Calculate the holding period return for each index or security i in month t by
𝑟, =
,
,
,
,
where Pi,t is the price of index/security i at the end of month t. You should have 180 months
of returns for each i. (Note: the stock prices are already adjusted for dividends and stock splits,
so you don’t need to worry about them.)
For the remaining problems, use the series of monthly returns you calculate in Problem 1.
1
Problem 2 – The Market Portfolio and Individual Stocks
a) Calculate the arithmetic average return and the standard deviation of return for the Hang
Seng Index.1
b) Your mother is worried that she will make a huge loss in March 2022 by investing in the
Hang Seng Index. Using historical returns (but without assuming that they come a normal
distribution), comfort her by estimating a monthly return x% so that she will make at least
x% with a 95% chance (i.e., only with 5% chance she will make less than x%; x could be
negative).
c) Repeat part a) for 0008.HK and IBM.
d) Your mother is risk-averse and is thinking which index or security she should invest in. If
she can only pick one from HSI, 0008.HK, and IBM, can we advise her which one to pick?
Problem 3 – Buying on Margin
a) Your father argues that he can make more money if he borrows money to invest in the Hang
Seng Index at a margin of 50%. Your father’s utility function is UF = E(r) – ½AFσ2, where
AF = 2. Assume he can borrow at an interest rate of 0.5% per month. Also assume that he
will not face any margin calls. Given your estimates from the historical returns, explain to
him whether buying the Hang Seng Index on a 50% margin or investing in the Hang Seng
Index without borrowing is a better strategy based on his utility function.
b) Can we conclude from the calculation in part (a) that all risk-averse investors would make
the same choice (50% margin or no margin)?
1
Throughout this project, I expect you to calculate the sample standard deviation. But as I said in the lecture, I
treat both sample standard deviation and population standard deviation as correct answers. The difference
between the two is small.
2