Microsoft Word - FINA 6223 Summer 2020 PS2
Problem Set #2.
Problem 1: Calculating Returns [21 points]
The SPDR S&P Biotech ETF’s investment objective is to produce returns that match those of the
S&P Biotechnology Select Industry Index. There also exist leverage and inverse leveraged ETFs
having investment objectives that are multiples of that index. Specifically, these are the
Direxion Daily S&P Biotech Bull 3x shares (ticker LABU) that aims to return +3 times the daily
index return and the Daily S&P Biotech Bear 3x Shares (ticker LABD) that aims to return -3
times the daily index return. The spreadsheet data_PS_2.xlsx accompanies this problem set.
There you will find daily prices and distribution amounts for these 3 ETFs. Use that data to
answer the following questions.
A. [4 points] Use the daily prices and distributions to compute the daily returns to each ETF for
the time period July XXXXXXXXXXto June XXXXXXXXXXNote, the dividends appear on the ex-date, so
the seller of the stock receives the dividend, not the buyer.
B. [3 points] Compute the arithmetic average daily returns to each of the funds.
C. [3 points] Compute the geometric average daily returns to each of the funds.
D. [2 points] Why does the geometric average return differ from the arithmetic average? To
what is that difference proportional?
E. [3 points] Compute the holding period return (across the full holding period) for each of the
funds.
F. [6 points] Assume that on June 30, 2016, you invested $100,000 in equal amounts of LABU
and LABD (i.e. use $50,000 to buy LABU shares at the 06/30/2016 closing price, and
$50,000 to do the same with LABD).
i. What would that portfolio be worth at the end of June 30, 2018?
ii. What would be the weights of LABU and LABD in the portfolio as of June 30, 2018?
iii. One might think since LABU and LABD return +3 and -3 times the daily returns to
the same index that the portfolio return would be 0%. Why is this not the case?
Problem 2: The Efficient Frontier and the CAL [18 points]
Consider the case of 2 risky assets. Asset 1 has an expected return of 9.00% and a standard deviation of
20.00%. Asset 2 has an expected return of 5.00% and a standard deviation of 7.00%. The co
elation
coefficient for the two assets is XXXXXXXXXXThe return on the risk-free asset is 0.25%.
1. [8 points] What are the expected return and standard deviations of the following portfolios?
a. 80% stocks, 20% bonds
. 60% stocks, 40% bonds
c. 40% stocks, 60% bonds
d. 20% stocks, 80% bonds
2. [2 points] What are the expected return and standard deviation from allocating our wealth 20% to
the risk-free asset and 80% to the (40,60) (stock,bond) portfolio?
3. [2 points] What is the slope of the line formed by all possible combinations of the risk-free asset
and the (40,60) portfolio?
4. [2 points] What portfolio (selected from all the possible combinations of stocks and bonds) forms
the best possible Capital Allocation Line? The co
ect answer will define the portfolio according
to the weights, e.g. (w1,w2) = (50,50).
5. [2 points] What is the slope of the Capital Market Line (CML)?
6. [2 points] What are the expected return and standard deviation of a portfolio that invests -25% in
the risk-free asset and the remainder of the portfolio in the optimal portfolio found in Step #4?
Problem 3: 3 risky assets [10 points]
Consider three risky assets with the following properties. Use this information to answer the following
questions.
Expected
Return
Standard
Deviation
Asset XXXXXXXXXX% 12.00%
Asset XXXXXXXXXX% 25.00%
Asset XXXXXXXXXX% 20.00%
Covariances:
σ1,2 = XXXXXXXXXX
σ1,3 = XXXXXXXXXX
σ2,3 = XXXXXXXXXX
1. [3 points] What are the co
elation coefficients for assets (1 & 2), (1 & 3), (2 & 3)?
2. [3 points] What is the expected return for the portfolio that invests 30% in Asset 1, 30% in Asset
2, and 40% in Asset 3?
3. [4 points] Compute the standard deviation for the portfolio that invests 30% in Asset 1, 30% in
Asset 2, and 40% in Asset 3?