MFIN 6666 Saint Mary’s University Investments and Portfolio Management Exam

MFIN 6666 – Investments & Portfolio Management -Final Exam
Saturday February 26, 2022, 1:00 PM – 4:00 PM (including submission time)
Name: _ _ _ _ _ _ _ _ _ _
A#: _ _ _ _ _ _ _ _ _
Q1. The board of directors of Suncost Inc. declared dividends of 35 cents per share payable on March
24, 2022 to shareholders of record as of Tuesday February 22, 2022, (the day the Family day (Feb 21,
2022), a stock market holiday).
A. When is the ex-dividend day?
B. Carter buys the stock on February 17, 2022, will he receive the dividends?
Yes / NO
MCQ3. Suppose you have an economy with only two risky assets X and Y. You are given the
following information:
Security
E(R)
Sigma
X
9.168%
0.096
Y
12%
0.10
COV (X,Y)
-0.00905
Suppose you have a risk-free asset (T-bill) that pays 5% and that the proportions to invest in each risky
security to form the optimal portfolio (P*) [in other words, the portfolio forming the tangency point
between the CAL with highest slope and the efficient frontier are: w*X = 0.5075 and wY* = 0.4925 . If you
want to achieve a rate of return 14% using P* and the T-bill, how much will you invest in the T-Bills?
A. -0.6178
B. 1.6178
C. -1.62
D. 6.17
MCQ4. Commercial paper is a: (1 mark)
A. short-term unsecured loan issued by only the most creditworthy corporations and the
government.
B. secured loan issued by firms and government.
C. short-term unsecured loan that is offered by nearly all corporations.
D. daily or weekly newspaper that focuses on business news.
MCQ5. You want to purchase XYZ stock at $60 from your broker using as little of your own money
as possible. If initial margin is 50% and you have $3000 to invest, how many shares can you buy?
A)
100 shares
B)
500 shares
B)
200 shares
C)
50 shares
1
MCQ6. Mirage Corporation has 1,000,000 shares outstanding. It wishes to issue 250,000 new shares
using rights issue. If the current stock price is $50 and the subscription price is $45/share, calculate
the value of a right. (1 mark)
A.
B.
C.
D.
$5.00/right
$1.00/right
$2.50/right
$0.25/right
MCQ7. The quoted yield is 3% for 30-day commercial paper and 3.5% for 91-day commercial paper
(as per the bond equivalent quotation). Sophia wants to invest in this money market instrument in 30
days and for 31 days. What is the ‘quoted’ expected 31-day commercial paper rate 30 days from now
(chose the closest answer)?
A.
B.
C.
A.
3.96%
7.31%
7.09%
None of the above
MCQ8. Meghan’s endowed with m0 = $1000 the current period (t=0) and m1 = $50 in the next period
(t=1). Suppose the risk-free interest rate is 10%. Her current bundle of consumption is : C0=549 and
C1=514. However, her desired (optimal) consumption in the next period is 531. She now discovers
three investment opportunities. Project A is a risk-free project that needs initial investment of $1000
and it generates $1150 in the next period. Project B is another risk-free project that needs initial
investment of $500 and it generates $530 in the next period. Project C is a risk-free project that needs
initial investment of $225 and it generates $230 in the next period. Can Meghan improve her
consumption in the current period? What is her optimal consumption path now? (choose the closest
answer)
A.
B.
C.
D.
Yes she can, C0=567 and C1=531.
Yes she can, C0=608.18 and C1=531.
No, her consumption bundle remains unchanged C0=549 and C1=514.
Yes she can, C0=608.18 and C1=45.45.
MCQ9. Connor Corp (CC) Inc. offers 40,000 shares of common stock to the public in an initial
public offering (IPO). The underwriters agree to provide their services in a best efforts underwriting.
The offering price is set at $28. The gross spread per share is $3. After completing their sales efforts
the underwriters determine that they were able to sell a total of 36,750 shares. How much cash did
Connor Corp receive from their IPO?
A.
B.
C.
D.
880,000
918,750
1,029,000
1,120,000
MCQ10. In the APT model, what is the nonsystematic standard deviation of an equally-weighted
portfolio that has an average value of σ(ei) equal to 25% and 50 securities?
A.
B.
C.
D.
12.5%
3.54%
0.5%
0.0%
2
MCQ11. Carter is a mean variance optimizer with a risk aversion coefficient of 3. For the coming year,
he has the choice of investing his nest egg of $2000 in one of two risky mutual funds, A and B. A has
an expected return of 9% and a standard deviation of 20%, whereas B has an expected return of 10%
and a standard deviation of 25%. In addition to being able to invest in one of funds A and B, he can also
invest in a short-term money market fund that invests in U.S. Treasury bills, which yield 6% currently.
The money market fund also allows good clients like Carter to short sell the money market fund with
minimal transactions costs. The following additional information is available on the two funds. Which
mutual fund should Carter choose?
A. Mutual fund A
B. A and B are equally preferred
C. Mutual fund B
D. None of the above
MCQ12. Consider the following investment alternatives. First, a risky portfolio A that pays a 15
percent rate of return with a probability of 60% or a 5 percent return with a probability of 40%.
Second, another risky portfolio B that has an expected return of 13.5% and a standard deviation of
12.64%. Kyle S. is a risk-averse investor with an utility function of U = E ( R) − A  2 . What should be
2
the risk aversion coefficient of the investor so he indifferent between the two risky portfolios A
and B? (T-bill that pays 6 percent)
A. 3.8
B. 432.87
C. 3.68
D. 4
MCQ13. Lu Sang is investing in an economy with ONLY TWO stocks: A and B. The market the
capitalization of A is twice that of B. The standard deviations of A and B are: SigmaA = 30% and
SigmaB = 50%. Their correlation coefficient is between A and B = 70%. What is the beta of stock A?
A. 1
B. 0.5
C. 0.83
D. 0.89
?
MCQ14. Consider the following regression: ??+1 = ? + ? (?? ) + ??+1, where ??+1 is the return on
??
?
stock in t+1, the regressor (? ) is the earnings-price ratio for period t and ??+1 is the error term in t+1,
?
under what conditions you would conclude that the finding of this model is consistent with the value
investment style of buying and holding value stocks?
A)
the slope “?” -for one given stock- is positive and significant
B)
the slope “?” -for one given stock- is negative and insignifcant
C)
the slopes “?” -for large number of stocks- are positive and significant
D) the slopes “?” -for large number of stocks- are negative and insignificant
MCQ15. Pascal’s utility function is U(W)=ln(W). His current wealth is $5,000. He is now given a
chance to buy a futures contract on Nickel that gives him 75% chance of winning $5,000, and 25%
chance of losing $4,000. What is his, Julius’ certainty equivalent for holding the futures contract?
A. 2126.58
B. 8.563756
C. 5623.41
D. 8.517193
3
Question 1. (2 marks) Consider a portfolio of four stocks as displayed in the following table:
stock
weight
beta
1
0.1
1.2
2
0.2
1.4
3
0.5
1
4
0.2
?
The expected return of the portfolio is 0.12, the annual effective risk-free rate is 0.04, and the market
risk premium is 0.06. Assuming the Capital Asset Pricing Model, calculate βeta of stock 4?
Question 2. (2 marks) Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor
and portfolio B has a beta of 2.0 on the factor. The expected return of A is ?? = 11% and the
expected return of B is ?? = 17%. Assume a risk free rate of ?? = 6%. Assume RedOne M. wants
to take advantage of any arbitrage opportunity and is willing to take a short position of $100,000. He
approaches you to help him figuring out whether there is an arbitrage opportunity or not? If yes,
exhibit it and calculate RedOne’s dollar return?
4
Question 3. (2 marks) The shareholding of Busayo Fund is given below:
– large capital growth (LCG): 49%
large capital value (LCV): 51%
– Small capital growth (SCG): 0%
Small capital value (SCV): 0%
Locate the style of Busayo Fund in the “style graph” below (use the diamond symbol: )? Comment?
100%
Large
growth
Large
Value
Small
Growth
Small
Value
0%
-100%
-100%
0%
100%
Question 4. (2 marks) In a market, the risk-free interest rate is given to be 0.04. Consider an
investment I in this market, whose Sharpe ratio is 0.4. You construct a portfolio where you put a third
of your wealth in the investment I and the remainder of your wealth in the risk-free asset. The
expected return of this (existing) portfolio is 0.08. You decide to rebalance your portfolio so that four
fifths of your wealth gets invested in the investment I and the remainder is invested in the risk-free
asset. What is the volatility of this (new) portfolio?
5
Short Problem I: (5 points) USE the information below for all 5 questions of this problem. ALL
questions are independent. Assume that a three-factor APT describes the returns of all well-diversified
portfolios, and that the three factors are unexpected changes in production (factor 1), a default spread
factor (factor 2), and a Treasury term-spread factor (factor 3). Because of recent adverse events, over the
next year, the market expects production to grow only by 1.5%, default spread to be 3.0%, and the term
spread to be 1.8%. The pricing relationships for all well diversified portfolios are given by:
E (rA ) = 0.05 +  i1 * 0.07 +  i 2 * 0.05 −  i 3 * 0.04
All investors can borrow or lend at the risk free rate of 5%. Sigma(factor 1) = Sigma (factor2) = Sigma
(factor3) = 0.15. For simplicity, assume that the coefficient of correlation between any two factors is 0.
The return process for portfolio A (which is well diversified) over the next year is:
rA = E (rA ) + 1.2 f1 + 0.5 f 2 − 0.5 f 3 .
5.a. What is the expected return portfolio A? (1 point)
PLEASE REPORT YOUR
ANSWER HERE
expected return portfolio A
5.b. What is the standard deviation of portfolio A? (1 point)
PLEASE REPORT
YOUR ANSWER
HERE
Standard deviation of
portfolio A
5.c. If production grows by 3% over the next year, the default spread falls to 2.75%, and the term spread
does exactly what the market expects, what will be the return on the portfolio A? (1 point)
PLEASE REPORT
YOUR ANSWER HERE
return on the portfolio A
5.d. Assume you are using the same original factors (i.e. same economy). You are considering investing
in an actively managed fund ChigaBiga. The residual standard deviation eChigabiga : σ(e)= 11%. The real
return-generating
process
for
rChigaBiga = 0.08 + 2 f1,Chigabiga + f 2,Chigabiga − 0.4 f 3,Chigabiga + eChigabiga
ChigaBiga
is:
What’s the equilibrium expected return for ChigaBiga based on its risk exposure? (1 point)
PLEASE REPORT YOUR
ANSWER HERE
expected return of ChigaBiga
5.e. According to your calculation in 5.d., you should: (1 point)
A. Buy ChigaBiga because it is overpriced
B. Sell ChigaBiga because it is overpriced
C. Buy ChigaBiga because it is underpriced
D. Sell ChigaBiga because it is underpriced
6
Short Problem II: (2 marks) Narinder is using four major indexes derived from MSCI (Morgan
Stanley Capital International) database. The four different countries are U.S., Canada, France and
Germany. The index in each country (whether value or growth) includes the stocks with the largest
market capitalization. The sample period includes monthly total returns for the period January 1985
through December 2011 (324 months). All returns are in U.S. dollars, and assume no transaction costs.
For each market (i.e. index), Narinder, classifies stocks as value or growth based upon price-to-book
ratio (P/E). Narinder is using a dataset free from survivorship bias as he retains data for firms that
disappear from the index. Thus, portfolio returns are computed for firms that were actually present in
the MSCI database for each country. The portfolio returns are computed as value-weighted average
return for all stocks included each month. For each country the rebalancing is made January of each
year. Narinder decides to examine the value-growth spread (?? − ?? ), which is equivalent to a long
position in the value index and a short position in the growth index, in equal dollar amount, rebalanced
monthly (with no transaction costs). He runs the following regression:
?? − ?? = ?? + ?? (?? − ?? ) + ?? (?????? − ???? ) + ?? ? + ??
where ?? and ?? represent the monthly return on value-weighted value and growth portfolios
(indexes), ?? − ?? is the value-growth spread, ?? is world market monthly return and is the sixmonth ?? U.S. T-Bill. J is a dummy variable that represents the month of January (i.e. equal 1 for the
month January and 0 otherwise), Small-Big Spread is a proxy for firm size.
Country
Panel C:
?? − ?? = ?? + ?? (?? − ?? ) + ?? (?????? − ???? ) + ?? ? + ??
??
??
??
??
0.06
-0.13*
0.65*
1.24*
(0.45)
(-4.30)
(8.08)
(2.63)
Canada
0.21
-0.16*
0.83*
0.29
(1.11)
(-3.29)
(5.94)
(0.24)
France
0.20
0.03
0.52*
1.02
(1.19)
(0.72)
(4.77)
(1.59)
Germany
0.25
-0.02
0.29*
-0.36
(1.58)
(-0.49)
(3.10)
(-0.65)
Consider the 5% level or less is the conventional level of statistical significance (i.e. the absolute
value of t-stat is larger than 1.95).
U.S.
A. Based on results of Panel C, what can you conclude about the size effect (across the four
countries)? Do you have any reservation?
B. Do you think that buying value and selling growth stocks can provide superior performance
as an investment strategy?
7
Formula
10000 − P  360
Banker’ s Discount yield (U.S.) = RBDY = 

 10000  N
 P − Pt −1 
Rate of Return =  t

 Pt −1 
10000 − P  365
Bond Equivalent Yield (CAN) = RBEY = 
 N
P


 (Adjusted Average Price )t 
 (TMC )t 
PWI t = 
VWI t = 
  IndexBaseYear
  IndexBaseYear
(
(
)
)
Average
TMC
Price
BaseYeart 
BaseYeart



Equity
or
Net
Worth
(net
of
interest)


Margin (on Buy on Margin) = 

Market Value of Assets


 Equity or Net Worth (net of any liability) 
Margin (on short sale) = 

Market Value of Owed Securities


•
P=D/(k-g) ; ROE = Net Income (NI) / Equity ; P/E = Market Price per Share / EPS
NI
EBT
EBIT
Sales
TA




EBT
EBIT
Sales
TA
Eqty
NI
Sales
TA
ROE =


SALES
2
2 TA
2 EQUITY
ROE =
Var (aX + bY + cZ ) = (a X ) + (b Z ) + (c Z ) + 2ab cov( X , Y )
+ 2ac cov( X , Z ) + 2cb cov( Z , Y )
cov( X , Y ) =  X ,Y  X  Y
cov(RA + RB , RC ) =  cov( RA , RC ) +  cov( RB , RC )
•
n
E ( R ) =  pi Ri
•
•
•
n
 p ( R − E ( R)) ;  = Var (R)
= RF + yE ( RP ) − RF ;  C = y P
; Var ( R) =
i =1
1/ 2
2
i =1
E ( RC ) = y( RP ) + (1 − y) RF
cov( R A , R A ) =  A2
i
R
i
; RC = yRP + (1 − y) RF
 E ( RP ) − RF  
 E ( RP ) − RF  
 = RF +  C 

E ( RC ) = RF + y P 
P
P




RP − R f
A
y* =
U = E (r) −  2
2
A 2
CAPM: CAPM:

E (ra ) = r f +  a E (rM ) − r f
, Where 
a
=
cov( ra , rm )
 m2
= am
a
m
SIM: Single Index Model: If Ri = ri – rf and Rm = rm – rf then Ri = i + ßi *Rm + ei

2
i
= 
2
i
2
m
+
 i (e)
 i2 m2
R = =
=
1
−
 i2
 i2
2
2
i (e) ,
2
2
2
COV ( Ri , R j ) = i  j  m
APT (multifactor): E(Ri) – rf = i,F1 [E(RF1) – rf ] +i,F2 [E(RF2) – rf ] +…+ i,Fk [E(RFk) – rf ]
Or E (ri ) = rf + BETAi1 * F1 + BETAi 2 * F2 + BETAi 3 * F3 …
Realized return-generating process: ri = E(Ri) +i,1 f1 +i,2 f2 +…+ i,kfk
8
Treynor measure: ?? =
?̅? −?̅?
??
; Sharpe measure: ?? =
?̅? −?̅?
??
;
Jensen’s alpha: ??? − ??? = ?? + ?? [??? − ??? ] + ??? ; Information ratio or appraisal ratio: ??? =
?̅? −?̅?
???
∑ ??,? (??,? − ??,? ) ∑(??,? − ??,? )??,?
?????? ?????? = ⏟
+⏟
???????? ????????
????? ??????????
′
??
?? ??1
Total Derivative : ?(?0, ?1(?0)) = 0 = ??0 + ??1 ??0
First derivative of xn = n x(n-1) and ln(x) = 1/x
The root (x) of the following quadratic equation ax 2 + bx + c = 0 is
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