Download Chapter 011 Risk and Return

Lecture 7 Portfolios
ADMN 3116
Instructor Anton Miglo
Lecture 7 Introduction to portfolios and diversification
Handouts
Part 1
1. A portfolio is a(n):
a. all securities issued by a firm.
b. a number of assets held by an investor.
2. The percentage of a portfolio's value that is represented by a single security is referred to as
the portfolio weight.
3. The concept of investing in a variety of diverse assets to reduce risk is diversification.
4. The efficient set of portfolios contains all portfolios:
A) with maximal expected return
B) with minimal variance
C) which provide maximal expected return for any given value of variance
D) which have securities with highest betas for any given value of variance
5. If the goal is to reduce overall risk you should invest in stocks with returns that are
positively correlated
Part 2
1. Suppose you are looking at investing in either stock A or stock B. You have the following
information about the rates of return:
Scenario
1
2
Probability
0.2
0.8
Stock A
0%
20.0%
Stock B
10.0%
5.0%
a. Calculate the mean, variance, and the standard deviation of return for each stock.
b. Suppose you have a choice between the three following strategies: 1) to invest 50
percent in each stock; 2) to invest 70 percent in stock A and 30 percent in stock B; 3) to
invest 10 percent in stock B and 90 percent in Canadian treasury bonds with risk-free
interest rate of 10 percent. Find the mean, variance, and standard deviation of return for
each portfolio.
c. Which portfolio is the best if you are risk-neutral?
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Lecture 7 Portfolios
2. Assume that you have been provided with the following information about two
stocks, RIM2 and Microsoft+:
Return on RIM2 Return on Microsoft+
Mean
Variance
0.12
0.036
0.15
0.058
The correlation coefficient between the two stocks equals 0.9. There are 4 investment
alternatives.
Alternative
Investment
1
100% in RIM2
2
50% in RIM2 and 50% in Microsoft+
3
30% in RIM2 and 70% in Microsoft+
4
100% in Microsoft+
a. If you are risk-neutral, which alternative is the best?
b. Now, suppose that you are risk-averse and that you are maximizing the following
function: 𝐸(𝑊) − 2𝑉𝑎𝑟(𝑊), where 𝑊 is the portfolio return. Which portfolio is the
best?
3. Project (Excel).
1) Choose 12 stocks from Yahoo! Finance web site.
2) Collect historical price information for each stock from Yahoo! Finance
(finance.yahoo.com) for the last five years. Collect information in an Excel file.
3) Calculate monthly returns as the percentage change in the monthly prices.
4) Compute the mean monthly returns and standard deviations for the monthly returns of each
of the stocks. Compute annual statistics.
5) Calculate the monthly return to an equally weighted portfolio of these 12 stocks. Compute
the mean and standard deviation of monthly returns for the equally weighted portfolio.
6) Create an Excel plot with standard deviation (volatility) on the x-axis and average return on
the y-axis.
7) Compare the volatilities of the individual stocks with the volatility of the equally weighted
portfolio.
8) Create a histogram of monthly portfolio returns. Describe the shape of probability
distribution of the returns.
Part 3
1. Explain “Home bias” phenomenon.
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