02 Jun Question Portfolio construction and analysis I.I
Question
Portfolio construction and analysis
I.I
50 pt
Construct a portfolio (Oct 1, 2012 – Sep 14,2014)
1. Give a short summary about the following stocks
6 pt
a.
BHP,NKE,RIO,PFE,PEG,SP500
2. Download the last year daily close prices for SP500 index from yahoo finance
a. http://finance.yahoo.com/q?s=%5EGSPC
3. Download the last 2 year daily close prices for the stocks named in #1 5 pt
4. Import daily close values and betas into excel and compute
18 pt
a. Log return
b. Expected return
c. Variance – VAR function
d. Standard Deviation
e. Covariance matrix
f. Correlation matrix
5. Create a portfolio composed of RIO with each of the other stocks
12pt
a. stock 1 weight = .65, find stock 2 weight
b. find the return on the portfolio with stock weights found in a.
c. find the portfolio variance using the correlation coefficient
d. find the portfolio standard deviation
6. Portfolio Analysis
9 pt
a. State the portfolio with the lowest risk and highest return
b. Look at the correlation coefficient for each pair of RIO,stock 2 and find the lowest
c. Is the lowest risk portfolio ( found in 6.a) also the portfolio with the lowest correlation
coefficient?
II
Efficient Frontier and the Minimum Variance Portfolio
II.I
Portfolio: RIO, NKE
1. Efficient Frontier
a.
b.
c.
d.
e.
f.
II.II
24 pt
12 pt
Input the ER,Variance, sd and CORREL(RIO,NKE) into table
Find the portfolio return for the varying stock weights (see excel template)
Find the portfolio variance
Find the portfolio sd
plot the Efficient Frontier ( x axis is the sd , y axis is the return )
Highlight the lowest risk (?P) combination
2. Find the MVP
12 pt
Using the equations for XA , XB, rP and ?2P on Lecture 4 slide 19
a. Find XA and XB
b. Find rP , ?2P and ?P
c. Compare the lowest risk,return combo in II.I f to the ?P, rP in the MVP, which is lower
risk?
III
CAPM
26 pt
II.I
1. Estimate Beta
8 pt
Using return data calculated in Part I
a. Estimate Beta with formula
and compare with the Beta given from yahoo
finance.
( To estimate beta , our market portfolio is the SP500)
2. CAPM
9 pt
a. find the 3 month US T bill rate as of 10/1/14 , input the value into the rf cell
http://www.treasury.gov/resource-center/data-chart-center/interestrates/Pages/TextView.aspx?data=yield
Note: the values on this page are in percentage already
i.e if the value stated is 0.05 it is 0.05% or 0.0005
b. input the expected return for the SP500 in the ERM cell (calculated in Part 1 4b)
c. input the Estimated betas you found in III #1 into the Beta row
d. Find the CAPM for each stock using the equation:
3. SML
9 pt
If we vary RIO stock beta from 0 to 2.5 by increments of .5
a. Find the CAPM for each given beta
b. plot the SML ( x axis is risk(beta), y axis is CAPM)
c. Compare the CAPM value of RIO with beta 1.28 to the expected return calculated in
Part 1 4b. Is RIO expected return above ( undervalued) or below (overvalued) the CAPM
required rate of return according to our beta calculations? Explain.
Extra – Arbitrage Pricing Theory
5 pt
Explain how APT differs from CAPM ( 2 pt )
Suppose that two factors have been identified for the U.S. economy: the growth rate of GNP,
GNP, and the inflation rate, IR. GNP is expected to be 5% and IR is expected to be 7%. A stock
with a beta of 0.3 on GNP and with a beta of 0.9 on IR currently is expected to return 22%. If
GNP actually grows by 7% and IR by 10%, what is the revised estimate of the return on the
stock? (3 pt)
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