1) What is the standard deviation of the returns for each stock? (Note: while theoretically you
should use excess returns to calculate standard deviation as mentioned in class, it is a pretty
good approximation to just take standard deviation of the returns, so do not worry about this.)
2) What is the covariance and correlation of returns between JPMorgan and Apple? (The same
note applies as above, do not worry about using excess returns.)
3) Calculate the portfolios consisting of JPMorgan and Apple with weights on JPMorgan
ranging from -100% to +200% in increments of 5%, i.e. w=-1,-0.95,-0.9…1.9,1.95,2. You
should have 61 portfolios. Calculate the expected return and standard deviation (s) for all of
them. What is the expected return and standard deviation of the portfolio with 50%
JPMorgan and 50% Apple?
!
HPRJan 2011
=
Padj. close, Jan 2011
" Padj. close, Dec 2010
Padj. close, Dec 2010FE445: Project Assignment #1
2
Use the portfolios calculated in question 3 to answer questions 4-7.
4) Using the standard deviation and expected return for each alternative investment portfolio,
draw a graph with the investment opportunity set for the two stocks: plot the expected return
(on the y-axis) as a function of the standard deviation (on the x-axis) for the above 61
portfolios using the “scatter” chart in Excel.
5) Which of the above portfolios is the minimum variance portfolio? What are the weights and
what is the standard deviation? Just choose from the above portfolios, no need to find the
exact minimum variance portfolio weights.
From here on assume that the monthly return on the risk-free asset is rf=0.01%.
6) Calculate the reward to variability ratio for each portfolio. Which is the mean-variance
efficient portfolio (optimal or tangency portfolio) among the 61 portfolios?
In order to answer questions 7-9, use the tangency portfolio identified in question 6 as the risky
portfolio.
7) Calculate the expected return and standard deviation for the complete portfolios using
weights on the tangency portfolio ranging from 0% to 200% in increments of 5%. You
should have 41 complete portfolios. Plot the CAL (Capital Allocation Line) and identify the
slope.
In questions 8-9, assume that you are investing $100,000.
8) Assume you want a monthly standard deviation of 15%, what is the most efficient way to
achieve this if you are creating a portfolio with JPMorgan and Apple and the risk-free asset?
Calculate the portfolio weights exactly (i.e. do not just choose one of the above 41 complete
portfolios). Specify the dollar amounts invested in each asset.
9) Calculate the utility over the above 41 complete portfolios on the CAL for two investors with
mean-variance utility, one with risk aversion of A=3 and another with A=6. Which of the
above complete portfolios is their optimal portfolio allocation (in dollar terms)?
In questions 10-12, use the S&P 500 index as the market return.
10) Graph a scatterplot of the 60 monthly stock returns vs. the market returns for both stocks
separately. The x axis should be the market return, the y axis the return on the given stock.
11)What is the alpha and beta of Apple and JPMorgan?
12) Using the above estimate of beta what is the expected monthly return on the two stocks
according to the CAPM (i.e. alpha zero) if you expect the market return (the S&P 500 index)
to be 1% a month? Do you necessarily agree with these expected returns or would you want
to make subjective adjustments? (this last question is subjective)