Finance with Dr. John Elder
LE#7
Before starting these exercises, be sure to work through the examples in the notes and from the chapter!
Chapt 6 # 2, 3, 5a(i,iii), 5b(i,iii), 6-10, 11.
Complete problem #6, which requires calculation of an efficient
frontier, in a spreadsheet. In particular, use the spreadsheet
template that you used for the previous homework to plot a CAL.
If you entered the formulas for E(rp) and SD(rp)
correctly, you should only need to change the expected return and
standard deviation on the individual assets (stocks and bonds) and the
correlation to the values given in the problem. Again, the
efficient frontier can be plotted by a "scatterplot" of the values in
the columns for the E(rp) and SD(rp).
(Note: In order to change the x and y axes on the
scatterplot, right click on the background, then click "edit".
Submit your spreadsheet table and
scatterplot of the
efficient frontier by printing both on a page to turn in during class.
I should be able to modify and the correlation and std dev and
change the shape of the efficient frontier.
OTIS: Make the necessary trades
to diversify your portfolio so that the Morningstar X-ray is consistent
with your objectives and risk tolerance and print out the X-ray of your
updated portfolio. In a few sentences, describe the trades you
conducted to rebalance your portfolio and why they were appropriate.
Hints:
(2) This requires some thought on diversification. Give it your best shot.
(5ai) Verify E(rp) = 0.728% per month
(5aiii) Verify SD(rp) = 2.267% per month
(5bi) E(rp) = 0.645% per month
(5biii) SD(rp) = 2.133% per month
(6) Do this problem in your spreadsheet, as described
above. Since you are doing this in a spreadsheet, you should
easily be able to do increments of 10% (rather than the 20% described
in the problem). The minimum variance portfolio has 31.4% in
stocks. If you plug that value into your spreadsheet, you should
be able find the expected return (10.9%) and std deviation (19.9%) on
the minimum variance portfolio.
(7) You can simply draw the tangent by hand, if you wish. The
tangency portfolio has 64.7% in stocks and 35.3% in bonds.
(I have given you the actual values for the minimum variance and
tangency portfolios because I don't want you to be concerned with the
"formulas" required to explicitly identify them.) You should be
able to verify in your spreadsheet that the expected return on the
tangency portfolio is 12.88%. Find the std deviation of the
tangency portfolio on your own.
(8) Verify that the slope of the best CAL is 0.316.
(9) Calculate the portfolio weights that give the desired return,
using the tangency portfolio and T-bills as the two assets. We
did this in the last chapter using the expression for the expected
return on a portfolio: E(rp) = wE(ri) + (1-w)E(rj). Then find the std deviation of the portfolio.
(10) Calculate the portfolio weights that give the desired
return, use the stock and bonds funds as the two assets. Again,
use the expression for the expected return on a portfolio: E(rp) = wE(ri) + (1-w)E(rj).
(11) try on your own.