Microsoft Word - FINA 6223 Summer 2020 PS3
Problem #1 [18 points]
On blackboard you will find the data file named FINA_6223_Summer2020_PS3.xlsx. Tab Q1
contains monthly returns data for 3 US ETFs, the market portfolio, and the risk-free return.
A. [6 points] Compute the Sharpe, Treynor, and Jensen measures for the 3 funds and the market
(no Jensen necessary for the market as it would be zero). Evaluate the two funds based on
these ratios. If you select one fund for your entire portfolio, which do you prefer and why?
B. [6 points] Compute the M2 and T2 measures. What information do these measures add to
your performance analysis from Part A?
C. [4 points] Compute the tracking e
or for each fund as the return deviation from the market.
Compute the information ratio for each fund as the ratio of the average tracking e
or to the
standard deviation of that tracking e
or. What do you learn from the information ratio?
D. [2 points] The TUSA charges 1.57% annual expenses to actively re-weight the universe of
US stocks. Based on the performance analysis, is there any evidence that those fees are
Problem 2: Computing returns [12 points]
The following table provides the end of year prices and dividend information for GDUB stock.
At the end of each year 2014 to 2018, an investor purchases 100 shares of GDUB. At the end of 2019,
the investor collects the last dividend and sells all shares.
A. [4 points] What is the arithmetic average time-weighted annual rate of return?
B. [4 points] What is the geometric average time-weighted annual rate of return?
C. [4 points] What is the dollar-weighted annual rate of return? A suggestion is to construct a chart
of all cash flows.
3. Computing more returns [12 points]
A company makes a $50 million investment. At the end of the first 3 quarters, they withdrawal $5
million. Using the information below, answer the following questions:
A. [4 points] Compute the simple Holding Period Return (HPR)
B. [4 points] Compute the annual time-weighted return
C. [4 points] Compute the annual dollar-weighted return
Year End of year price Dividend paid at end of yea
0 50,000,000 50,000,000
0.25 -5,000,000 47,000,000
0.5 -5,000,000 41,000,000
0.75 -5,000,000 35,000,000
1 0 38,000,000
Problem 4: Comparing performance [7 points]
Two investment professionals are comparing their return performance. The first professional managed
portfolios with an average return of 10% and the second professional managed portfolios with a 12% rate
of return. The beta of the first portfolio was 0.8 while the beta of the second was 1.1. The risk-free rate
of return was 2% and the expected market return is 8%.
A. [5 points] Which manager was a better selector of individual stocks, and why?
B. [2 points] Plot both of the portfolios on the security market line.
Problem 5: Closed End Funds [10 points]
See the worksheet named “Closed End Fund” for the prices and NAV of a recently IPO-ed closed end
A. [5 points] For each day, compute the premium (discount) of the price to the NAV. Compute the
average daily premium.
B. [3 points] Plot the premium (discount) through time on a graph.
C. [2 points] Explain if this fund exhibits the same premium(discount) pattern around its IPO and
post-IPO period as the example we discussed in class.
Problem 6: Mutual Fund Returns [15 points]
You are considering investing in a mutual fund’s A share class that has a 3% sales charge (front-end
load) and annual expense ratio of 1.0%. Alternatively, you might invest in that fund’s C shares that
have no load and an annual expense ratio of 1.5%. Assume the fund’s assets return 9% annually.
a. [3 points] For a 2-year holding period, which share class will you prefer?
. [3 points] For a 50-year holding period, which share class will you prefer?
c. [5 points] After how many years will the two mutual fund share classes result in the same
future wealth amounts?
d. [2 points] How does your answer to part c. change if the fund’s assets return 14% per
e. [2 points] What accounts for the greater expenses of the C-shares, compared to the A-