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Foundations of Finance Practice 2
nd
Midterm
Foundations of Finance COR1-GB.2311
Practice 2
nd
Midterm Exam
Prof. Anthony Lynch
First Name: _________________
Last Name: ____________________________
Student ID: _________________________
Stern Honor Code : “I pledge my honor that I have not violated the Stern Honor Code in the
completion of this examination.”
Signature: __________________________________________________
Instructions
: 80 minutes. Open Book, but while taking the exam, you cannot communicate with
anyone registered for the course or anyone else, via phone or electronically (which includes
email, text message, Twitter, and Facebook).
You must keep your video camera switched on for
the entire time you are taking the exam.
You are permitted use of Excel or a financial or
scientific calculator.
You must delete any electronic copies of the exam questions and destroy
any hard copies of the exam questions once you have completed the exam.
The exam consists of 15 multiple choice questions which will be graded on a correct/incorrect
basis. Answer
all
questions on NYU Classes.
Each question is worth 1 point so the maximum
number of points you can earn is 15.
If you get stuck on a question, guess, move on, and come
back at the end if you have time.
Good luck!
1
Foundations of Finance Practice 2
nd
Midterm
1.
The expected rate of return on the market portfolio is 13%, and the standard deviation of
market’s return is 10%.
The riskless rate is 5%. Consider two assets, Q and V, for which
you (correctly) estimated that σ[R
Q
] = 6%, β
QM
= 0.6, E[R
Q
] = 9%, σ[R
V
] = 8%, β
VM
=
0.4, E[R
V
] = 9%. Compared to the implications of the CAPM,
A
asset Q is overpriced, asset V is underpriced
B
asset Q is underpriced, asset V is overpriced
C
both are fairly priced
D
both are overpriced
E
both are underpriced
2
Foundations of Finance Practice 2
nd
Midterm
2.
In a world where the CAPM assumptions hold (“CAPM world”), the expected rate of
return on the market portfolio is 14%, and the standard deviation of market’s return is
10%.
The riskless rate is 8%. Consider two assets, QVP and VLM in this economy, for
which
σ[R
QVP
]= 6%, β
QVP.M
= 0.6, E[R
QVP
] = 11.6%,
σ[R
VLM
] = 12%, β
VLM,M
= 0.6, E[R
VLM
] = 11.6%.
Investors in this economy could hold as their entire portfolio
A
asset QVP, but not asset VLM
B
asset VLM, but not asset QVP
C
either QVP or VLM
D
neither QVP nor VLM
E
cannot answer without specifying investors’ risk aversion
3
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Foundations of Finance Practice 2
nd
Midterm
3.
In a world where the CAPM assumptions hold (“CAPM world”), the expected rate of
return on the market portfolio is 14%, and the standard deviation of market’s return is
10%.
The riskless rate is 8%. Consider two assets, QVP and VLM in this economy, for
which
σ[R
QVP
]= 6%, β
QVP.M
= 0.6, E[R
QVP
] = 11.6%,
σ[R
VLM
] = 12%, β
VLM,M
= 0.6, E[R
VLM
] = 11.6%.
Regarding the comovements of asset QVP’s return and asset VLM’s return with the
market, as measured by the correlation with the market’s return,
A
asset QVP has a lower correlation than asset VLM with the market
B
asset VLM has a lower correlation than asset QVP with the market
C
both have same correlations with the market
D
both are independent of the market
E
cannot analyze correlation with the market without determining
overpricing/underpricing
4
Foundations of Finance Practice 2
nd
Midterm
4.
In a world where the CAPM assumptions hold (“CAPM world”), you meet an investor
who holds asset Z as his total portfolio, where E[R
z
] = 12%, σ[R
z
] = 8%. R
f
is 6%, and
E[R
M
] = 15%.
Asset Y has β
YM
=0.5 and σ[R
Y
] = 8%.
The correlation between asset’s Y
return and the market return is
A
0.75
B
1.00
C
1.25
D
0.25
E
–0.25
5
Foundations of Finance Practice 2
nd
Midterm
5.
A T-bill has a face value of $100 and is selling for $98. If the T-bill matures in 80 days,
what is its bond equivalent yield?
A
9.31%
B
2.04%
C
9.18%
D
9.66%
E
9.00%
6
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Foundations of Finance Practice 2
nd
Midterm
6.
Today is Feb 17, 2006 and the yield to maturity (expressed as an APR with semi-annual
compounding) of a 10% Feb 2011 Treasury note with a par value of $100 is 8%.
What
is the price of this note today given that the Feb 2006 coupon has just been paid?
A
100.00
B
148.67
C
107.99
D
108.11
E
92.42
7
Foundations of Finance Practice 2
nd
Midterm
7.
Today is the 17
th
February 2006 and the prices of ½-year, 1-year and 1½-year Treasury
strips (all $100 face value) are $97, $89 and $88 respectively.
These prices imply yields
(expressed as APRs with semi-annual compounding) of 6.186%, 12.000% and 8.706%
respectively.
What is the price today of a 10% Feb 2007 Treasury note
($100 par)?
A
$97.90
B
$98.17
C
$103.64
D
$98.30
E
Not enough information is available
8
Foundations of Finance Practice 2
nd
Midterm
8.
Today is the 17
th
February 2006 and the prices of ½-year, 1-year and 1½-year Treasury
strips (all $100 face value) are $97, $89 and $88 respectively.
These prices imply yields
(expressed as APRs with semi-annual compounding) of 6.186%, 12.000% and 8.706%
respectively. What is the ½-year interest rate I can lock in today for the ½-year period
starting in 1 year expressed as an APR with semiannual compounding?
A
1.14%
B
2.27%
C
8.71%
D
12.00%
E
Not enough information is available
9
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Foundations of Finance Practice 2
nd
Midterm
9.
Today is the 17
th
February 2006 and the prices of ½-year, 1-year and 1½-year Treasury
strips (all $100 face value) are $97, $89 and $88 respectively.
These prices imply yields
(expressed as APRs with semi-annual compounding) of 6.186%, 12.000% and 8.706%
respectively. What return will I earn expressed as an APR with semiannual compounding
if I buy ½-year Treasury strips today, roll them into ½-year Treasury strips in a half year
from today and then roll those into ½-year Treasury strips in one year from today?
A
8.950%
B
8.964%
C
8.706%
D
6.186%
E
Not enough information is available
10
Foundations of Finance Practice 2
nd
Midterm
10.
Suppose investors care about E[R
p
], σ[R
p
] and σ[R
p
, EI] where EI is a macroeconomic
indicator and R
p
is portfolio return and a 2 factor model holds for the economy such that
the two factors are r
M
, the excess return on the market portfolio, and r
EI
, the excess return
on the portfolio maximally correlated with EI. Which of the following is true?
A
Two assets with the same CAPM betas must have different expected returns.
B
Two assets with different CAPM betas might have the same expected returns.
C
Two assets with the same CAPM betas must have the same expected returns.
D
Both A and B are true.
E
None are true
11
Foundations of Finance Practice 2
nd
Midterm
11.
Let GIP(Jan) be the growth in industrial production in January and let R
M
(Jan) be the
January return on the market portfolio.
Suppose each individual cares about
{E[R
p
(Jan)], σ[R
p
(Jan)], σ[R
p
(Jan), GIP(Jan)]} when forming his/her portfolio p for
January and a two-factor model holds for January with GIP(Jan) the only state variable.
Let R
GIP
(Jan) be the return on the portfolio maximally correlated with GIP(Jan) and R
M
be the market portfolio’s return. R
f
, the riskless rate, is 0.7%. The following additional
information is available:
i
β*
i,M
β*
i,GIP
LZ
0.9
0.1
where β*
i,M
and β*
i,GIP
are regression coefficients from a multiple regression (time-series)
of (R
i
(t)-R
f
) on (R
M
(t)-R
f
) and (R
GIP
(t)-R
f
):
R
i
(t)-R
f
= φ
i,0
+ β*
i,M
( R
M
(t) - R
f
) + β*
i,GIP
(R
GIP
(t) - R
f
) + e
i
(t).
Also know that E[R
M
(Jan)] = 2% and E[R
GIP
(Jan)] = 1.7%.
What is E[R
LZ
(Jan)]?
A
1.97%
B
1.87%
C
2.67%
D
2.04%
E
Not enough information.
12
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Foundations of Finance Practice 2
nd
Midterm
12.
Which of these investors could possibly care about more than expected return on her
portfolio and the standard deviation of return on her portfolio?
A
A single-period investor with access to risky assets whose returns are normally
distributed.
B
A multiperiod investor whose labor income moves with the business cycle.
C
An investor in a CAPM world.
D
Both A and B.
E
None of the above.
13
Foundations of Finance Practice 2
nd
Midterm
13.
If the (positive) yield to maturity on a discount bond is constant from one year to the
next, the price of the discount bond over the next year will
A
Increase
B
Decrease
C
Remain the same
D
You cannot tell
E
Sometimes increase and sometimes decrease depending on the shape of the yield
curve
14
Foundations of Finance Practice 2
nd
Midterm
14.
Assuming you hold a U.S. treasury coupon bond to maturity, its holding period return
(expressed as an APR with semi-annual compounding) is equal to
A
the coupon rate if you can and do reinvest at the coupon rate
B
the coupon rate if you don’t reinvest
C
the YTM if you can and do reinvest at the YTM
D
the YTM if you can and do reinvest at the coupon rate
E
none of the above
15
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Foundations of Finance Practice 2
nd
Midterm
15.
The yield curve is u-shaped.
The current spot rate (the current yield on a ½-year strip)
expressed as an APR with ½-year compounding is 5%, while the yield on a 25-year strip
expressed as an APR with ½-year compounding is 8% . The minimum yield expressed as
an APR with ½-year compounding is 3% for the 10-year strip. Suppose the expectations
hypothesis holds.
Which of the following is true?
A
The market is expecting future spot rates (future yields on a ½-year strips) to be
higher than the current spot rate.
B
The market is expecting future spot rates to be lower than the current spot rate.
C
The market is expecting future spot rates in the near future to be lower than the
current spot rate and is expecting future spot rates in the distant future to be
higher than the current spot rate.
D
The market is expecting future spot rates in the near future to be higher than the
current spot rate and is expecting future spot rates in the distant future to be lower
than the current spot rate.
E
None are true.
16
Foundations of Finance Practice 2
nd
Midterm
Foundations of Finance Practice 2
nd
Midterm Exam Solution
1.
The expected rate of return on the market portfolio is 13%, and the standard deviation of
market’s return is 10%.
The riskless rate is 5%. Consider two assets, Q and V, for which
you (correctly) estimated that σ[R
Q
] = 6%, β
QM
= 0.6, E[R
Q
] = 9%, σ[R
V
] = 8%, β
VM
=
0.4, E[R
V
] = 9%. Compared to the implications of the CAPM,
A
asset Q is overpriced, asset V is underpriced
B
asset Q is underpriced, asset V is overpriced
C
both are fairly priced
D
both are overpriced
E
both are underpriced
A.
Calculate Jensen’s alpha for both.
Asset i:
α
i,M
= E[r
i
]
- β
j,M
E[r
M
]
where r
i
= R
i
- R
f
is the excess return on asset i; and,
r
M
= R
M
- R
f
is the excess return on the market portfolio.
Q
:
α
Q,M
= E[r
Q
]
- β
Q,M
E[r
M
] = (9 - 5) - 0.6 × (13 – 5) = -0.8 < 0
V
:
α
V,M
= E[r
V
]
- β
V,M
E[r
M
] = (9 - 5) - 0.4 × (13 – 5) =
0.8 > 0
Q
lies below the SML and so is overpriced relative to the CAPM.
V
lies above the SML and so is underpriced relative to the CAPM.
0
1
.)))))))))))))))))))))))))))))))))))-
P
0
E[ D
1
]
17
Foundations of Finance Practice 2
nd
Midterm
2.
In a world where the CAPM assumptions hold (“CAPM world”), the expected rate of
return on the market portfolio is 14%, and the standard deviation of market’s return is
10%.
The riskless rate is 8%. Consider two assets, QVP and VLM in this economy, for
which
σ[R
QVP
]= 6%, β
QVP.M
= 0.6, E[R
QVP
] = 11.6%,
σ[R
VLM
] = 12%, β
VLM,M
= 0.6, E[R
VLM
] = 11.6%.
Investors in this economy could hold as their entire portfolio
A
asset QVP, but not asset VLM
B
asset VLM, but not asset QVP
C
either QVP or VLM
D
neither QVP nor VLM
E
cannot answer without specifying investors’ risk aversion
A.
Investors in a CAPM world hold efficient portfolios that lie on the CML as their entire portfolio.
CML:
.
CML for QVP =
= 11.6
=
11.6 = E[R
QVP
]
QVP lies on the CML and so an efficient portfolio, which means that investors could hold VLM as their entire
portfolio in a CAPM world.
CML for VLM =
= 15.2
>
11.6 = E[R
VLM
]
VLM does not lie on the CML and so is not an efficient portfolio, which means that investors could not hold VLM as
their entire portfolio in a CAPM world.
18
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Foundations of Finance Practice 2
nd
Midterm
3.
In a world where the CAPM assumptions hold (“CAPM world”), the expected rate of
return on the market portfolio is 14%, and the standard deviation of market’s return is
10%.
The riskless rate is 8%. Consider two assets, QVP and VLM in this economy, for
which
σ[R
QVP
]= 6%, β
QVP.M
= 0.6, E[R
QVP
] = 11.6%,
σ[R
VLM
] = 12%, β
VLM,M
= 0.6, E[R
VLM
] = 11.6%.
Regarding the comovements of asset QVP’s return and asset VLM’s return with the
market, as measured by the correlation with the market’s return,
A
asset QVP has a lower correlation than asset VLM with the market
B
asset VLM has a lower correlation than asset QVP with the market
C
both have same correlations with the market
D
both are independent of the market
E
cannot analyze correlation with the market without determining
overpricing/underpricing
B.
Know:
.
So:
which is greater than
.
19
Foundations of Finance Practice 2
nd
Midterm
4.
In a world where the CAPM assumptions hold (“CAPM world”), you meet an investor
who holds asset Z as his total portfolio, where E[R
z
] = 12%, σ[R
z
] = 8%. R
f
is 6%, and
E[R
M
] = 15%.
Asset Y has β
YM
=0.5 and σ[R
Y
] = 8%.
The correlation between asset’s Y
return and the market return is
A
0.75
B
1.00
C
1.25
D
0.25
E
–0.25
A.
The example on pages 16-18 of
Lecture 5: CAPM
has a question asking for the correlation between asset H and the
market.
The answer for the question uses the following formula:
.
When we try to applying this formula to the current question, we see that the standard deviation of the market σ[R
M
]
is not given in the question:
.
So need to calculate σ[R
M
] using other information provided in the question.
Know that all investors hold total
portfolios which lie on the CML.
Since Z is held by an investor as a total portfolio,
Z
must lie on the CML.
Formula for the CML:
.
So applying the formula for the CML to Z gives:
which implies σ[R
M
] = 12%.
Then can calculate
ρ[R
Y
, R
M
] by plugging this value for σ[R
M
] into the formula for ρ[R
Y
, R
M
] given above:
.
.
20
Foundations of Finance Practice 2
nd
Midterm
5.
T-bill has a face value of $100 and is selling for $98. If the T-bill matures in 80 days,
what is its bond equivalent yield?
A
9.31%
B
2.04%
C
9.18%
D
9.66%
E
9.00%
A.
0
n = 80
.))))))))))))))))))))))))))))))))))))))))-
Price
100
Need to first calculate the holding period return using the following formula on page 4 of
Lecture 7-8: Debt
Instruments - Definitions and Markets
:
Then can calculate the bond equivalent yield which is the return on the bill expressed as an APR with a compounding
period equal to maturity of the bill (here 80/365 years) using the following formula on page 4 of
Lecture 7-8: Debt
Instruments - Definitions and Markets
:
21
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Foundations of Finance Practice 2
nd
Midterm
6.
Today is Feb 17, 2006 and the yield to maturity (expressed as an APR with semi-annual
compounding) of a 10% Feb 2011 Treasury note with a par value of $100 is 8%.
What
is the price of this note today given that the Feb 2006 coupon has just been paid?
A
100.00
B
148.67
C
107.99
D
108.11
E
92.42
D.
Need to use the following formula that calculates the price of a Treasury note or bond given that you know the yield
to maturity expressed as an APR with ½ year compounding
(YTM) on page 9 of
Lecture 7-8: Debt Instruments -
Definitions and Markets
:
P(0) = C x PVAF
YTM/2,N
+ 100 x PVIF
YTM/2,N
where C is the coupon paid on an 100 par, N is the number of coupon payments to maturity and P(0) is the invoice
price today.
The coupon on 100 par is always half the coupon rate, so here the coupon C is 10/2 = 5.
The maturity date for the
note is Feb 2011, today is Feb2006 and the Feb 2006 coupon has just been paid, so N = 10.
2/06
8/06
2/07
8/10
2/11
0
½
1
4½
5
.)))))))))))))))))))))))))2)))))))))))))))))))))))))2)
...
))2)))))))))))))))))))))))))-
5
5
5
5 + 100
Using the formula:
22
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Foundations of Finance Practice 2
nd
Midterm
7.
Today is the 17
th
February 2006 and the prices of ½-year, 1-year and 1½-year Treasury
strips (all $100 face value) are $97, $89 and $88 respectively.
These prices imply yields
(expressed as APRs with semi-annual compounding) of 6.186%, 12.000% and 8.706%
respectively.
What is the price today of a 10% Feb 2007 Treasury note
($100 par)?
A
$97.90
B
$98.17
C
$103.64
D
$98.30
E
Not enough information is available
D.
Need to use the formula used on page 11 of
Lecture 8: Bond Pricing and Forward Rates
that calculates prices of
Treasury notes using prices of Treasury strips and a no-arbitrage condition.
Today is 2/17/06 and so a 10% Feb 2007 note with 100 par pays a coupon of 10/2 = 5
in ½ a year and a coupon of 5
plus 100 par in 1 year.
2/06
8/06
2/07
0
½
1
.))))))))))))))))))))))))))))))2))))))))))))))))))))))))))))))-
-P
10% Feb 07
(0)
10/2
100 + 10/2
The price of a ½-year strip with a face value of $100 is $97, so the ½-year discount factor d
½
(0) is 0.97.
The price of
a 1-year strip with a face value of $100 is $89, so the 1-year discount factor d
1
(0) is 0.89.
So applying the formula:
P
10%Feb 07
(0)
= 5 x d
½
(0) + 105 x d
1
(0) = 98.3
= 5 x 0.97 + 105 x 0.89 = 98.3
23
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Foundations of Finance Practice 2
nd
Midterm
8.
Today is the 17
th
February 2006 and the prices of ½-year, 1-year and 1½-year Treasury
strips (all $100 face value) are $97, $89 and $88 respectively.
These prices imply yields
(expressed as APRs with semi-annual compounding) of 6.186%, 12.000% and 8.706%
respectively. What is the ½-year interest rate I can lock in today for the ½-year period
starting in 1 year expressed as an APR with semiannual compounding?
A
1.14%
B
2.27%
C
8.71%
D
12.00%
E
Not enough information is available
B.
0
1
1½
.))))))))))))))))))))))))))
2
))))))))))))))))))))))))))
2)))))))))))))))))))))))))))-
12 × 18 FRA
- 1
One Approach
The question gives you strip yields so could use the approach implemented in the example on page 31 of
Lecture 8:
Bond Pricing and Forward Rates
that uses the prices of the strips that mature at the start and the end of the forward
rate period to calculate the forward rate.
The general formula is on page 27 of
Lecture 8: Bond Pricing and
Forward Rates
where t is the start of the forward rate period, here 1, and t+α is the end of the forward rate period, here 1½.
So
applying the formula here:
which implies
f
1,1½
(0) =
2.27%.
24
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Foundations of Finance Practice 2
nd
Midterm
0
1
1½
.))))))))))))))))))))))))))
2
))))))))))))))))))))))))))
2)))))))))))))))))))))))))))-
12 × 18 FRA
1
Another Approach
The question gives you strip prices so could use the approach implemented in the example on page 32 of
Lecture 8:
Bond Pricing and Forward Rates
that uses the prices of the strips that mature at the start and the end of the forward
rate period to calculate the forward rate.
Question asks for the ½-year interest rate I can lock in today for the ½-year period starting in 1 year expressed as an
APR with semiannual compounding.
So the start of the forward rate period is 1 year from today and the end of the
forward rate period is 1½ years from today.
The price of a 1-year strip with a face value of $100 is $89, so the 1-year
discount factor d
1
(0) is 0.89. The price of a 1½-year strip with a face value of $100 is $88, so the 1½-year discount
factor d
1½
(0) is 0.88.
Now use the general formula on page 27 of
Lecture 8: Bond Pricing and Forward Rates
:
d
t+α
(0)
=
d
t
(0)
d
t,t+α
(0)
where t is the start of the forward rate period, here 1, and t+α is the end of the forward rate period, here 1½.
So
applying the formula here:
d
1½
(0)
=
d
1
(0)
d
1,1½
(0)
which gives
d
1,1½
(0) = 0.88/0.89 = 0.988764.
25
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Foundations of Finance Practice 2
nd
Midterm
The forward rate (expressed as an APR with ½-year compounding) can be calculated from the forward rate discount
factor in the same way that the yield on a strip can be calculated from strip prices (see the calculations on page 32 of
Lecture 8-9: Bond Pricing and Forward Rates
).
The forward rate period here starts 1 year from today and ends 1½
years from today, so the forward rate period is ½ a year.
The forward rate discount factor tells how much you would
need to agree to invest at the start of the forward rate period to get $1 back at the end of the forward rate period.
Hence:
1 + the effective ½-year rate offered by the forward contract = 1/d
1,1½
= 1/0.988764.
To express the forward rate as an APR with ½-year compounding, need to multiply the effective ½-year rate offered
by the forward contract by 2.
It follows that the forward rate expressed as an APR with ½-year compounding is given
by:
0
1
1½
.))))))))))))))))))))))))))
2
))))))))))))))))))))))))))
2)))))))))))))))))))))))))))-
12 × 18 FRA
1
Return formula:
effective
½-year rate
=
r
n
= (1+r)
n
- 1
n = 1
APR with
½-year
f
1,1½
(0) =
2 ×
= 2.27%.
compounding
1 + hold-to-maturity return
= 1 + effective ½-year rate
m = 2
effective ½-year rate
26
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Foundations of Finance Practice 2
nd
Midterm
9.
Today is the 17th February 2006 and the prices of ½-year, 1-year and 1½-year Treasury
strips (all $100 face value) are $97, $89 and $88 respectively.
These prices imply yields
(expressed as APRs with semi-annual compounding) of 6.186%, 12.000% and 8.706%
respectively. What return will I earn expressed as an APR with semiannual compounding
if I buy ½-year Treasury strips today, roll them into ½-year Treasury strips in a half year
from today and then roll those into ½-year Treasury strips in one year from today?
A
8.950%
B
8.964%
C
8.706%
D
6.186%
E
Not enough information is available
E.
Future yields on ½-year Treasury strips are uncertain today because the position of the yield curve in the future is
incertain today.
27
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Foundations of Finance Practice 2
nd
Midterm
10.
Suppose investors care about E[R
p
], σ[R
p
] and σ[R
p
, EI] where EI is a macroeconomic
indicator and R
p
is portfolio return and a 2 factor model holds for the economy such that
the two factors are r
M
, the excess return on the market portfolio, and r
EI
, the excess return
on the portfolio maximally correlated with EI. Which of the following is true?
A
Two assets with the same CAPM betas must have different expected returns.
B
Two assets with different CAPM betas might have the same expected returns.
C
Two assets with the same CAPM betas must have the same expected returns.
D
Both A and B are true.
E
None are true
B.
Since a two-factor model holds for the economy, assets don’t have to lie on the SML any more.
Instead all assets
satisfy (see page 5 of
Lecture 6-7: Multifactor Asset Pricing Models and Empirical Evidence
):
E[r
i
] = β
*
i,M
λ
*
M
+ β
*
i,EI
λ
*
EI
where:
λ
*
M
and λ
*
EI
are risk premia that are the same for all assets and portfolios.
r
i
=
R
i
-R
f
, r
M
=
R
M
-R
f
and r
EI
=
R
EI
-R
f
.
λ
*
M
= E[r
M
] and λ
*
EI
= E[r
EI
].
β
*
i,M
and β
*
i,EI
are regression coefficients from a time-series regression of r
i
on r
M
and r
EI
:
r
i
= a
i,EI
+ β
*
i,M
r
M
+ β
*
i,EI
r
EI
+ e
i
where:
r
M
and r
M I
are the two factors.
β
*
i,EI
and β
*
i,M
are referred to as risk loadings and vary across assets; they measure the sensitivity of
asset i to the 2 risks that individuals care about.
So two assets with the same CAPM betas might have different expected returns or the same expected returns
depending on their risk loadings with respect to the second factor, and two assets with different CAPM betas might
have the same expected returns depending on their risk loadings with respect to the second factor.
So both A and C
are false and only B is true.
28
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Foundations of Finance Practice 2
nd
Midterm
11.
Let GIP(Jan) be the growth in industrial production in January and let R
M
(Jan) be the
January return on the market portfolio.
Suppose each individual cares about
{E[R
p
(Jan)], σ[R
p
(Jan)], σ[R
p
(Jan), GIP(Jan)]} when forming his/her portfolio p for
January and a two-factor model holds for January with GIP(Jan) the only state variable.
Let R
GIP
(Jan) be the return on the portfolio maximally correlated with GIP(Jan) and R
M
be the market portfolio’s return. R
f
, the riskless rate, is 0.7%. The following additional
information is available:
i
β*
i,M
β*
i,GIP
LZ
0.9
0.1
where β*
i,M
and β*
i,GIP
are regression coefficients from a multiple regression (time-series)
of (R
i
(t)-R
f
) on (R
M
(t)-R
f
) and (R
GIP
(t)-R
f
):
R
i
(t)-R
f
= φ
i,0
+ β*
i,M
( R
M
(t) - R
f
) + β*
i,GIP
(R
GIP
(t) - R
f
) + e
i
(t).
Also know that E[R
M
(Jan)] = 2% and E[R
GIP
(Jan)] = 1.7%.
What is E[R
LZ
(Jan)]?
A
1.97%
B
1.87%
C
2.67%
D
2.04%
E
Not enough information.
A.
Know a two-factor model holds with GIP(Jan) as the state variable: (R
M
(Jan)-R
f
) and (R
GIP
(Jan)-R
f
) are the two
factors. So from page 5 of
Lecture 6-7: Multifactor Asset Pricing Models and Empirical Evidence
:
E[R
i
(Jan)] = R
f
+ β*
i,M
λ*
M
+ β*
i,GIP
λ*
GIP
where λ*
M
= E[R
M
(Jan)] - R
f
and λ*
GIP
= E[R
GIP
(Jan)] - R
f
.
So E[R
LZ
(Jan)] = 0.7 + 0.9 x (2 -0.7) + 0.1 (1.7 - 0.7) = 1.97.
29
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Foundations of Finance Practice 2
nd
Midterm
12.
Which of these investors could possibly care about more than expected return on her
portfolio and the standard deviation of return on her portfolio?
A
A single-period investor with access to risky assets whose returns are normally
distributed.
B
A multiperiod investor whose labor income moves with the business cycle.
C
An investor in a CAPM world.
D
Both A and B.
E
None of the above.
B.
By assumption, all investors in a CAPM world only care about the expected return on their portfolios and the standard
deviation of the return on their portfolios (see page 2 of
Lecture 5: CAPM
).
So C is not the correct answer.
A single-period investor with access to risky assets whose returns are normally distributed only cares about the
expected return on her portfolio and the standard deviation of the return on her portfolio (see page 27 of
Lecture 3-4:
Portfolio Management-A Risky and a Riskless Asset
). So A is not the correct answer.
A multiperiod investor whose labor income moves with the business cycle could possibly care about the covariance of
her portfolio return with a macroeconomic indicator in addition to the expected return on her portfolio and the
standard deviation of the return on her portfolio (see page 2 of
Lecture 6-7: Multifactor Asset Pricing Models and
Empirical Evidence
). So B is the correct answer.
30
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Foundations of Finance Practice 2
nd
Midterm
13.
If the (positive) yield to maturity on a discount bond is constant from one year to the
next, the price of the discount bond over the next year will
A
Increase
B
Decrease
C
Remain the same
D
You cannot tell
E
Sometimes increase and sometimes decrease depending on the shape of the yield
curve
A.
Price of a strip with $1 of face value (see page 4 of
Lecture 8: Bond Pricing and Forward Rates
):
.
where y
T
is the yield to maturity on the strip expressed as an APR with ½-year compounding.
For fixed y
T
, as T
decreases, d
T
(0) increases.
0
½
1
9½
10
.)))))))))))))))))))))))))2)))))))))))))))))))))))))2)
...
))2)))))))))))))))))))))))))-
P(0)
P(1)
100
The price of a strip with par of $100 at time 0 that matures at time 10 and has a yield to maturity expressed as an APR
with ½-year compounding of y > 0 is given by:
.
If the yield to maturity expressed as an APR with ½-year compounding remains equal to y, then its price at time 1 is
given by:
.
P(1) > P(0) since the $100 is discounted back 20 ½-year periods at (y/2) to get P(0), but is only discounted back 18
½-year periods at (y/2) to get P(1).
31
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Foundations of Finance Practice 2
nd
Midterm
14.
Assuming you hold a U.S. treasury coupon bond to maturity, its holding period return
(expressed as an APR with semi-annual compounding) is equal to
A
the coupon rate if you can and do reinvest at the coupon rate
B
the coupon rate if you don’t reinvest
C
the YTM if you can and do reinvest at the YTM
D
the YTM if you can and do reinvest at the coupon rate
E
none of the above
C.
Consider a coupon bond that matures in 5 year time.
0
½
1
4½
5
.)))))))))))))))))))))))))2)))))))))))))))))))))))))2)
...
))2)))))))))))))))))))))))))-
C
C
C
C + 100
The price is the value of the bond’s cash flows at time 0 discounting them back at the yield to maturity on the bond.
So the price of the bond is the single-sum equivalent on the bond’s cash flows when the interest rate is the yield to
maturity on the bond.
If you invest the bond’s cash flows at the bond’s yield to maturity, the amount you will have in
the bank account at the maturity of the bond will be the single-sum equivalent at the bond’s maturity date of the
bond’s cash flows, when the
interest rate is the yield to maturity on the bond.
Thus, the bond’s price and the amount
in the bank account at maturity are equivalent single sums when the interest rate is the yield to maturity on the bond,
and so the amount in the bank account at the bond’s maturity date is given by the future value interest formula as
follows (see the future value interest formula on page 32 of
Lecture 1-2: Time Value of Money
):
where T is the maturity date of the bond in years, y is the yield to maturity, P(0) is the price, and V
T
is
the amount in
the bank account at the bond’s maturity date
It follows that the holding period return expressed as an APR with ½-year compounding from buying the bond at time
0 and investing its cash flows at the yield to maturity until the maturity of the bond is the bond’s yield to maturity.
32
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Foundations of Finance Practice 2
nd
Midterm
15.
The yield curve is u-shaped.
The current spot rate (the current yield on a ½-year strip)
expressed as an APR with ½-year compounding is 5%, while the yield on a 25-year strip
expressed as an APR with ½-year compounding is 8% . The minimum yield expressed as
an APR with ½-year compounding is 3% for the 10-year strip. Suppose the expectations
hypothesis holds.
Which of the following is true?
A
The market is expecting future spot rates (future yields on a ½-year strips) to be
higher than the current spot rate.
B
The market is expecting future spot rates to be lower than the current spot rate.
C
The market is expecting future spot rates in the near future to be lower than the
current spot rate and is expecting future spot rates in the distant future to be
higher than the current spot rate.
D
The market is expecting future spot rates in the near future to be higher than the
current spot rate and is expecting future spot rates in the distant future to be lower
than the current spot rate.
E
None are true.
C
If the expectations hypothesis holds:
(1)
Yield curve having a negative slope at any maturity implies the expected spot rate at
that time in the future is lower than the yield curve at that maturity: so the market is
expecting future spot rates in the near future out to at least 9.5 years to be lower than
the current spot rate because the yield curve is negatively sloped out to at least a
maturity of 9.5 years.
(2)
Yield curve having a positive slope at any maturity implies the expected spot rate at that
time in the future is higher than the yield curve at that maturity: so the market is
expecting future expecting future spot rates in the distant future, at least 25 years or
more in the future, to be higher than the current spot rate.
33
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Additional Practice Questions for Lecture Notes 5-8
1.
According to the CAPM, if a security's beta is negative, then its expected return must be
A
The market rate of return
B
Zero
C
A negative rate of return
D
The risk free rate
E
None of the above
2.
Suppose the expected return on stock ABC is 14%. Suppose R
f
= 3%, E[R
M
] = 10% and
β
ABC, M
= 1.45. Then
the Jensen’s alpha on ABC is
A
0.85
B
-0.50
C
3.85
D
Zero
E
Not enough information to answer
3.
According to CAPM, if the expected return on asset 1, E[R
1
], is greater than the expected return on asset 2,
E[R
2
], then:
A
R
1
must always be greater than R
2
B
σ[R
1
] must be greater than σ[R
2
]
C
β
1,M
must be greater than β
2,M
D
ρ[R
1
, R
M
] must be greater than ρ[R
2,
R
M
]
E
all of the above must be true
4.
In a world where the CAPM assumptions hold for any stock j, (j = 1,…,n), and for any investor (“CAPM
world”), you run the market-model regression using excess returns (returns in excess of the riskless rate):
r
j
= α
j
+ β
jM
r
M
+e
j
.
You find that:
A
α
j
varies across stocks, capturing firm specific variations, and can take any value
B
α
j
varies across stocks, capturing unique as well as systematic variations, and can take any value
C
α
j
is strictly positive for all stocks
D
α
j
is zero for all stocks
E
α
j
is strictly negative for all stocks
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Answers to Additional Practice Questions
1.
E.
In a CAPM world, all assets lie on the Security Market Line (SML):
SML:
Using the SML:
.
2.
A.
3.
C.
In a CAPM world, all assets lie on the Security Market Line (SML):
SML:
Using the SML:
.
35
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4.
D.
Define r
i
= R
i
- R
f
to be the excess return on asset i; and,
r
M
= R
M
- R
f
to be the excess return on the market portfolio.
Consider the excess return market model for asset i:
r
i
= α
i,M
+ β
i,M
r
M
+ e
i,M
where E[e
i
] = 0.
So
E[r
i
] = α
i
+ β
i,M
E[r
M
].
CAPM states that all assets lie on the SML:
E[r
i
] = β
i,M
E[r
M
].
So in a CAPM world:
α
i,M
= 0
for any asset i.
36
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The comparative balance sheets of Constantine Cavamanlis Inc. at the beginning and the end of the year 2020 are as follows.
CONSTANTINE CAVAMANLIS INC.
BALANCE SHEETS
Dec. 31, 2020
Jan. 1, 2020
Inc./Dec.
Assets
Cash
$ 45,000
$ 13,000
$32,000
Inc.
Accounts receivable
91,000
88,000
3,000
Inc.
Equipment
39,000
22,000
17,000
Inc.
Less: Accumulated Depreciation-Equipment
17,000
11,000
6,000
Inc.
Total
$158,000
$112,000
Liabilities and Stockholders' Equity,
Accounts payable
$ 20,000
$ 15,000
5,000
Inc.
Common stock
100,000
80,000
20,000
Inc.
Retained earnings
38,000
17,000
21,000
Inc.
Total
$158,000
$112,000
Net…
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Calculate the net price factor (as a %) and net price (in $) by using the complement method. Round your answer to the nearest cent.
List Price
Trade Discount Rate
Net Price Factor
Net Price
$3,499.00
35%
$4
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BRECMBC9 7.J1.014.
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Calculate the trade discount (in $) and trade discount rate (as a %). Round your answer to the nearest tenth of a percent.
List Price
Trade Discount Rate
Trade Discount
Net Price
$4,500.00
$3,515.00
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Journalizing Partner's Original Investment
assumed a $57,000 note payable owed by Lin that was used originally to purchase the land.
Xi Lin contributed land, inventory, and $35,000 cash to a partnership. The land had a book value of $79,000 and a market value of $152,000. The inventory had a book value of $53,100 and a market value of $48,900. The partnership also
Required:
Provide the journal entry for Lin's contribution to the partnership. If an amount box does not require an entry, leave it blank.
35,000
53,100 X
152,000
48,900
X
79,000 X
57,000
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Record the assets at their current values, and record the liability at its current value. Lin's Capital…
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E Chapter 5 Homework - FINANCIA X
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Koch Corporation's adjusted trial balance contained the following asset accounts at December 31, 2020: Cash $7,000, Land
$40,000, Patents $12,500, Accounts Receivable $90,000, Prepaid Insurance $5,200, Inventory $30,000, Allowance for Doubtful
Accounts $4,000, and Equity Investments (to be sold in the next quarter) $11,000.
Prepare the current assets section of the balance sheet. (List Current Assets in order of liquidity.)
КОСН СORPORATION
Balance Sheet (Partial)
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nit Activity: Mathematical Models and Consumer Finance
Task 7
Financing Transportation
Respond to each question below in two to three complete sentences. Each question is worth four points.
Space used (includes formatting): 0/15000
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Lydia makes a down payment of $1,600 on a $11,000 car loan. How much of the purchase price will the interest be calculated
on? Explain how you arrived at the final answer.
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king a down payment on a car loan help a car buyer?
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Concord Industries has equivalent units of 7100 for materials and for conversion costs. Total manufacturing costs are $124370. Total
materials costs are $91000. How much is the conversion cost per unit?
O $17.52.
O $4.70.
$12.82.
O $30.33
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18. Using the following information, complete the income statement, statement of retained earnings, and balance sheet for RN Painting for the month of March 2018. The business
began operations on March 1, 2018.
E (Click the icon to view the account balances.)
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Chapter: Recording Business TraNSACTIONS
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6
7
Proble X
P-F:2-30A. Journalizing transactions, posting journal entries to T-
accounts, and preparing a trial balance (Learning Objectives 3, 4)
15
G
New
Ann Simpson started her practice as a design consultant on September 1,
2024. During the first month of operations, the business completed the
following transactions:
3. Prepare the trial balance of Vince York, M.D., as of July 31, 2024.
30
Received $48,000 cash and issued common stock to Simpson.
Purchased office supplies, $1,200, and furniture, $1,300, on account.
Performed services for a law firm and received $1,900 cash.
X
Paid $18,000 cash to acquire land to be used in operations.
Performed services for a hotel and received its promise to pay the $1,200
within one week.
Paid for the furniture purchased on September 4 on account.
Paid assistant's semimonthly salary, $1,500.
Received cash on…
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