Microsoft Word - FINA 6223 Summer 2020 PS1
Chapters 1, 2, & 3 problem set.
Deadline to submit through Blackboard: 5pm Friday May 29, 2020.
Instructions: Answer completely each of the assigned questions and include all necessary
supporting work. Students may work in groups of up to three total students. All group
members’ names should be clearly identified at the top of the submitted assignment. Each
group must work independently of other groups.
Assignments shall be submitted through Blackboard. Please designate only one student to
submit the group’s assignment. Late assignments will not be accepted. Failure to follow
instructions will result in a reduced grade.
Problem 1: Index Construction [35 points]
a. [3 points] ** initially only stocks 1 through 5 are in the index ** Day 0 is the first day of
the index (refe
ed to as index inception date). Assume the index is market-capitalization
weighted and compute the index divisor such that the index level is 100 on Day 0.
. [3 points] Use the above information to compute the return to the index on Day 1
assuming it is market-capitalization weighted. Report the new index level and the index
eturn.
c. [3 points] At the end of Day 1, the index committee removes stock #3 and replaces it with
stock #6. Using the above information, compute the new index divisor after the
eplacement.
d. [3 points] Compute the Day 2 return to the index. Report the new index level and the
index return.
e. [3 points] Now assume Stock 1 splits 2-for-1 at the end of Day 2 and at the new price is
2.75 and shares outstanding are 160 million. What is the new index divisor at the end of
Day 2?
f. [15 points] Repeat a. to e. for a price-weighted version of the index.
Stock Price Shares
Outstanding
Price Shares
Outstanding
Price Shares
Outstanding
1 5 80,000, XXXXXXXXXX,000, XXXXXXXXXX,000,000
2 150 1,500, XXXXXXXXXX,500, XXXXXXXXXX,500,000
XXXXXXXXXX, XXXXXXXXXX500, XXXXXXXXXX500,000
4 75 10,000, XXXXXXXXXX,000, XXXXXXXXXX,000,000
5 60 5,000, XXXXXXXXXX,000, XXXXXXXXXX,000,000
6 99 2,500, XXXXXXXXXX,500, XXXXXXXXXX,500,000
Day 0 Day 1 Day 2
g. [5 points] Compute the Day 1 return to a version of this index that is equally weighted. At the
end of Day 1, assuming no rebalancing since Day 0, what will be the new weights? If the index
were to be rebalanced to restore equal weights at the end of Day 1, indicate the necessary
adjustments in terms of the percentage of the portfolio that must be traded to restore equal
weights.
Problem 2: Buying on Margin [20 points]
An investor recently opened a
okerage account with $400,000 of cash. They decide to purchase shares
of NewCorp (NEWC). Prescribing to the philosophy of “go big or go home,” the investor decides to
utilize the full margin bo
owing capacity available through their
oker. The investor may bo
ow from
their
oker at 8% per year and must have an initial margin of at least 50%. The maintenance margin is
25%. The cu
ent market price of NEWC is $160.00.
a. [4] Assume the investor utilizes their maximum margin potential. How many shares of
NEWC can the investor purchase?
. [4] Below what stock price will the investor receive a margin call?
c. [4] If the investor holds this position for 3 months and then sells the shares and repays the
loan, what is the percentage profit (loss) if the market price of NEWC is $210.00 after 3
months?
d. [4] If the investor holds this position for 3 months and then sells the shares and repays the
loan, what is the percentage profit (loss) if the market price of NEWC is $110 after 3 months?
e. [4] Compare your answers in C. and D. to the profit (loss) if the investor did not use the
margin account and instead only purchased $400,000 worth of NEWC shares. Discuss the
effect of leverage on returns.
Problem 3: Equivalent Taxable Yields [8 points]
a. [4 points] Consider a tax exempt municipal bond with an annual yield of 2%. Find the
equivalent taxable yield for investors with each of the following tax
ackets: 0%; 15%;
25%, 35%.
a. [4 points] Fairfax County, a AAA-rated municipality, issued tax exempt municipal bonds
that yield 1% and mature in 5 years. Otherwise identical corporate bonds that are AAA-
ated and mature in 5 years but are taxable yield 1.4%. What is the implied tax rate?
Problem 4: Asset Allocation [12 points]
Assume you have a consulting client that is a non-profit organization with a $100 million reserve
account invested in U.S. stocks. The client has hired you to help them implement their strategic
asset allocation (SAA) using passive index funds. You can select among mutual funds that track
major US stock market indexes. For example, if you select the CRSP Mega Cap US stock index,
there is a Vanguard mutual fund available to track that index. For this question, you don’t have
to wo
y about finding specific mutual funds, just in selecting which indexes you want the
mutual funds to track.
The client’s SAA is: 60% Large Cap US Stocks, 20% Mid Cap US Stocks, and 20% Small Cap
US Stocks.
Use the following snapshot to help answer the following questions. Consider only the families
of indexes highlighted in the picture (Russell, MSCI, S&P, and CRSP). The snapshot came
from:
http:
www.crsp.com/indexes-pages/key-concept-4-crsp-approach-combining-size-benchmarks
a. [4] Given your client’s SAA, which family of indexes’ design do you think best suits
your client’s investment policy? State very concisely the reason for your choice. There
is not necessarily a co
ect answer – I want you to think about the question and justify
your choice as opposed to picking the co
ect index family.
. [4] How does the definition of “Mid-cap” vary across the 4 index providers summarized in the
figure?
c. [4] How does the definition of “Small-cap” vary across the 4 index providers summarized in the
figure?