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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...

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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
Investment Value
(inclusive of
withdrawals and
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
fund, HGLB.
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-
Answered Same Day Jun 18, 2021


Ayush answered on Jun 19 2021
131 Votes
Problem 1
A. Following table lists the calculations for Sharpe, Treynor, and Jensen Measure for 3 US ETFs. For more detailed refer Excel.
    First Trust Large Cap Alphadex
    First Trust Total US Alphadex
    First Trust Cloud Computing ETF
    Market Return
    Risk free
    Risk free
    Avg. Return %
    Avg. Risk %
    Sharpe Ratio
    Treynor Ratio
    Jensen Alpha
We explain the Calculations for FEX ETF.
Similar calculations were performed for TUSA, and SKYY ETFs
Monthly Average Return % = Portfolio Return of ETF%
= Average of Monthly Return of ETF for months 1 – 60
Monthly Average Risk % = Portfolio Risk of ETF %
= Standard Deviation of Monthly Return of ETF for months 1 – 60
elation = Co
elation (Monthly return of ETF for months 1 – 60, Monthly Market Return for months 1 –60)
Using formulas, we calculate the 3 measures for FEX ETF,
Sharpe Ratio = = = 0.17
Beta =
= = 1.03
Treynor Ratio = = = 0.006
Jensen Alpha = Portfolio Return% - (Rf % + Beta*(Market Return% - Rf %))
     = 0.72% - (0.08%+1.03*(0.88%-0.08%)) = -0.19%
We evaluate the 3 ETFs based on of Sharpe ratio, Treynor Ratio, and Jensen Alpha. Of the three funds, namely FEX, TUSA, and SKYY, we eliminate TUSA fund since it has not performed well. Its performance as per 3 measures is the worst and even Market Portfolio does good job as compared to it. Thus, we choose FEX and SKYY. However, I will prefer SKYY as it has outperformed the market by 0.48% per month. Also, it has performed in terms of Sharpe ratio (0.31) and Treynor ratio (0.013), giving highest performance among the 3 funds.
    First Trust Large Cap Alphadex
    First Trust Total US Alphadex
    First Trust Cloud Computing ETF
    Market Return
    Risk free
    Risk free
    Adj. Return
Again calculating for the FEX ETF,    
M2 = Sharpe Ratio*Market Risk% + Risk-free% = 0.17*3.51% + 0.08% = 0.69%
T2 = Adjusted Portfolio Return% - Market Return %
Wrp = = = = 97%, Wrf = 1 – Wrp = 3%
Adjusted Portfolio Return% = Wrp*Portfolio Return of FEX%+ Wrf*Risk-free
             = 97%*0.72%+3%*0.08% = 0.70%
T2 = 0.70%-0.88% = -0.18%
We do this process for the other 2 funds. M2 and T2 are risk-adjusted performance measures. The Sharpe Ratio and Treynor ratio are difficult to interpret. M2 and T2 are in percentage return unit which can be interpreted instantly. The M2 (1.16%) and T2 (0.47%) of SKYY tell us that how other funds and market have fared vis-à-vis SKYY. It also enhances our decision to invest in SKYY.
    First Trust Large Cap Alphadex
    First Trust Total US Alphadex
    First Trust Cloud Computing ETF
    Market Return
    Tracking E
    Information Ratio
As we know, Information Ratio is used to assess the skill of the Fund Manager. The higher the Information Ratio, the higher the active return. Therefore, Information Ratio of SKYY is highest of 10.03. This means that for a given amount of risk taken, the fund manager has performed better in comparison to other 2 funds relative to the index.
No, it is not justifiable to charge 1.57% for annual expenses because the fund has performed worse than market portfolio. The charge translates to a monthly charge of 0.131% (1.57%/12). The Jensen Alpha for TUSA is -0.30%. If it will be charged, it will lead to a worsening of performance.
Problem 2
A. Arithmetic average time-weighted annual rate of return
Following Table gives the calculation done for Time-Weighted Return for each year. For more detailed calculation, please refer Excel.
    End of year price ($)
    Dividend paid at
end of year...

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