Application 16 - 21 Flashcards
practice equations
TTMAR Hedge Fund has a 1.5 management fee and 30 incentive fee
arrangement, with no hurdle rate and a NAV of $200 million at the start of the
year. At the end of the year, before fees, the NAV is $253 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
Annual Fee = Management Fee + (Max (0, Incentive fee x (Gross Return above HWM - Management Fee-Hurdle Rate))
management fee:
NAV start x management fee %
200 x 0.015 = 3
incentive fee: NAV end - management fee - NAV start x incentive fee % 253 - 3 - 200 x 0.30 = 15
ending NAV:
NAV end - MF - IF
253 - 3 - 15 = 235
TTMAR Hedge Fund has a 2 management fee and 20 incentive fee
arrangement, with no hurdle rate and a NAV of $200 million at the start of the
year. At the end of the year, before fees, the NAV is $250 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
management fee:
200 x 0.02 = 4
incentive fee:
250 - 4 - 200
46 x 0.2 = 9.2
NAV end:
250 - 4 - 9.2
= 236.80
TTMAR Hedge Fund has a 1.5 management fee and 20 incentive fee
arrangement, with no hurdle rate and a NAV of $300 million at the start of the
year. At the end of the year, before fees, the NAV is $400 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
?
TTMAR Hedge Fund has a 1.5 management fee and 15 incentive fee
arrangement, with no hurdle rate and a NAV of $250 million at the start of the
year. At the end of the year, before fees, the NAV is $450 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
?
TTMAR Hedge Fund has a 2 management fee and 30 incentive fee
arrangement, with no hurdle rate and a NAV of $100 million at the start of the
year. At the end of the year, before fees, the NAV is $250 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
?
TTMAR Hedge Fund has a 1 management fee and 30 incentive fee
arrangement, with no hurdle rate and a NAV of $100 million at the start of the
year. At the end of the year, before fees, the NAV is $101 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
?
TTMAR Hedge Fund has a 2 management fee and 15 incentive fee
arrangement, with no hurdle rate and a NAV of $100 million at the start of the
year. At the end of the year, before fees, the NAV is $105 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
after fees, assuming no redemptions or subscriptions.
?
VVMAR Hedge Fund has a 1.5 and 30 fee
arrangement, with no hurdle rate and a NAV of $200 million at the start of the
year. At the end of the year, after fees, the NAV is $270 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 30% of the total profits and so represents the proportion 30%/70% to
the net profits to limited partners.
management fee:
NAV(0) x management fee % 200 x 0.015 = 3
incentive fee: NAV(1) - NAV(0) 270 - 200 = 70 x incentive fee % 70 x 0.30 = 21
1 - 0.3 (other side of incentive fee)
= 0.7
21 / 0.7 = 30
ending NAV:
200 + 3 + 70 + 30 = 303
VVMAR Hedge Fund has a 2 and 20 fee
arrangement, with no hurdle rate and a NAV of $100 million at the start of the
year. At the end of the year, after fees, the NAV is $300 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 20% of the total profits and so represents the proportion 20%/80% to
the net profits to limited partners.
management fee:
100 x 0.02 = 2
incentive fee:
300 - 100 = 200
x 0.2 = 40
1 - 0.2 = 0.8
40 / 0.8 = 50
100 + 2 + 200 + 50 = 352
VVMAR Hedge Fund has a 1.5 and 25 fee
arrangement, with no hurdle rate and a NAV of $150 million at the start of the
year. At the end of the year, after fees, the NAV is $450 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 25% of the total profits and so represents the proportion 25%/75% to
the net profits to limited partners.
?
VVMAR Hedge Fund has a 3 and 15 fee
arrangement, with no hurdle rate and a NAV of $200 million at the start of the
year. At the end of the year, after fees, the NAV is $500 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 15% of the total profits and so represents the proportion 15%/85% to
the net profits to limited partners.
?
VVMAR Hedge Fund has a 2 and 20 fee
arrangement, with no hurdle rate and a NAV of $50 million at the start of the
year. At the end of the year, after fees, the NAV is $150 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 20% of the total profits and so represents the proportion 20%/80% to
the net profits to limited partners.
?
VVMAR Hedge Fund has a 1.5 and 15 fee
arrangement, with no hurdle rate and a NAV of $75 million at the start of the
year. At the end of the year, after fees, the NAV is $200 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 15% of the total profits and so represents the proportion 15%/85% to
the net profits to limited partners.
?
VVMAR Hedge Fund has a 1 and 15 fee
arrangement, with no hurdle rate and a NAV of $100 million at the start of the
year. At the end of the year, after fees, the NAV is $250 million. Assuming that
management fees are computed on start-of-year NAVs and are distributed
annually, find the annual management fee, the incentive fee, and the ending NAV
before fees, assuming no redemptions or subscriptions. The incentive fee
represents 15% of the total profits and so represents the proportion 15%/85% to
the net profits to limited partners.
?
Consider a $1 billion hedge fund with a 20%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatilities of 10%, 20%, and 30% using the at-the-money incentive
fee approximation formula?
incentive fee call option value: i x 40% x NAV x SD x (square root) T
10% annual asset volatility:
20% x 40% x 1,000,000,000 x incentive fee (volatility) x (square root) Time
0.2 x 0.4 x 1,000,000,000 x 0.10 x (square root) 1
= 8,000,000
20% annual asset volatility:
0.2 x 0.4 x 1,000,000,000 x 0.2 x square root (1) = 16,000,000
30% annual asset volatility:
0.2 x 0.4 x 1,000,000,000 x 0.3 x square root (1) = 24,000,000
Consider a $500 million hedge fund with a 20%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatility of 20%, and using the at-the-money incentive
fee approximation formula?
?
Consider a $250 million hedge fund with a 20%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatilitiy of 30% using the at-the-money incentive
fee approximation formula?
?
Consider a $1 billion hedge fund with a 15%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatilitiy of 40% using the at-the-money incentive
fee approximation formula?
?
Consider a $1 billion hedge fund with a 5%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatility of 35% using the at-the-money incentive
fee approximation formula?
?
Consider a $500 million hedge fund with a 10%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatility of 50% using the at-the-money incentive
fee approximation formula?
?
Consider a $150 million hedge fund with a 25%
incentive fee at the start of a new incentive fee computation period. If the hedge
fund computes incentive fees annually and begins the year very near its highwater
mark, what would be the value of the incentive fee over the next year for
annual asset volatility of 40% using the at-the-money incentive
fee approximation formula?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 100, 102, 99, 97, 95,
100, 109, 103, 103, and 106. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
find the 3-day simple moving average on day 0:
106 + 103 + 103
/3 = 104
find the 3-day simple moving average on day -1:
103 + 103 + 109
/3 = 105
find the 3-day moving average on day -2:
103 + 109 + 100
/ 3 = 104
find the 10-day simple moving average on day 0:
106 + 103 + 103 + 109 + 100 + 95 + 97 + 99 + 102 + 100
/ 10 = 101.4
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 50, 51, 52, 50, 49, 47, 55, 53, 51, and 52. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 30, 31, 35, 36, 36, 37 34, 33, 35, 36 and 37. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 20, 21, 23, 19, 18, 17, 20, 21, 22, and 23. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 45, 47, 48, 46, 45, 44, 45, 44, 45, 47, 48, and 49. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 35, 33, 32, 31, 30, 29, 28, 27, 30 and 21. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 10, 9, 10, 11, 12, 14, 15, 17, 18, and 21. What are the simple (arithmetic) moving average
prices on day 0 using 3-day and 10-day moving averages, as well as the 3-day
moving average for days –2 and –1?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 100, 102, 99, 97, 95,
100, 109, 103, 103, and 106. What are the five-day weighted moving average
prices on days –1 and 0?
five-day weighted moving average on day 0:
(106 x 5) + (103 x 4) + (103 x 3) + (109 x 2) + (100 x 1) / 15 = 104.6
five-day moving average on day-1:
(103 x 5) + (103 x 4) + (109 x 3) + (100 x 2) + (95 x 1)
/ 15 = 103.27
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 50, 51, 52, 50, 49, 47, 55, 53, 51, and 52. What are the five-day weighted moving average
prices on days –1 and 0?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 30, 31, 35, 36, 36, 37 34, 33, 35, 36 and 37. What are the five-day weighted moving average prices on days - 1 and 0?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 20, 21, 23, 19, 18, 17, 20, 21, 22, and 23. What are the five-day weighted moving average prices on days - 1 and 0?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 45, 47, 48, 46, 45, 44, 45, 44, 45, 47, 48, and 49. What are the five-day weighted moving average prices on days - 1 and 0?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 35, 33, 32, 31, 30, 29, 28, 27, 30 and 21. What are the five-day weighted moving average prices on days - 1 and 0?
?
A stock price experiences the following 10
consecutive daily prices corresponding to days –10 to –1: 10, 9, 10, 11, 12, 14, 15, 17, 18, and 21. What are the five-day weighted moving average prices on days - 1 and 0?
?
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 100, 109, 103, 103, and
106. What are the exponential moving average prices on days –1 and 0 using
λ = 0.25?
Assume that the exponential moving average up to and including the
price on day –3 was 100.
EMA(λ) = λP(t-1) + λ(1-λ) P(t-2) + λ(1-λ)(^2) P (t-3) + λ(1-λ)(^3) P(t-4)
find the 5-day exponential moving average on day -1:
(0.25 x 103) + (1-0.25) 100
25.75 + 75 = 100.75
find the 5-day exponential moving average on day 0:
(106 x 0.25) + (1-0.25) 100.75 (day - 1 exponential moving average)
26.5 + 75.5625
= 102.0625
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 47, 55, 53, 51, and 52. What are the exponential moving average prices on days –1 and 0 using
λ = 0.30?
Assume that the exponential moving average up to and including the
price on day –3 was 100.
what are the exponential moving average -1:
0.3 x 51 = 15.3
1-0.3 x 50 = 35
15.3 + 35 = 50.3
what are the exponential moving average 0:
52 x 0.3 = 15.6
1-0.3 x 50 = 35
15.6 + 35 = 50.6
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 34, 33, 35, 36, and 37. What are the exponential moving average prices on days –1 and 0 using
λ = 0.35?
Assume that the exponential moving average up to and including the
price on day –3 was 33.
?
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 17, 20, 21, 22, and 23. What are the exponential moving average prices on days –1 and 0 using
λ = 0.15?
Assume that the exponential moving average up to and including the
price on day –3 was 20.
?
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 44, 45, 47, 48, 49. What are the exponential moving average prices on days –1 and 0 using
λ = 0.10?
Assume that the exponential moving average up to and including the
price on day –3 was 43.
?
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 29, 28, 27, 30, and 21. What are the exponential moving average prices on days –1 and 0 using
λ = 0.40?
Assume that the exponential moving average up to and including the
price on day –3 was 25.
?
A stock price experiences the following five
consecutive daily prices corresponding to days –5 to –1: 14, 15, 17, 18, and 21. What are the exponential moving average prices on days –1 and 0 using
λ = 0.25?
Assume that the exponential moving average up to and including the
price on day –3 was 15.
?
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 100, 102, 99, 98,
99, 104, 102, 103, 104, and 100. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
UpperBound = 105 LowerBound = 97
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 50, 51, 52, 50, 49, 47, 55, 53, 51, and 52. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
?
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 30, 31, 35, 36, 37, 34, 33, 35, 36, and 37. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
?
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 20, 21, 23, 19, 18, 17, 20, 21, 22, and 23. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
?
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 45, 47, 48, 46, 45, 44, 45, 47, 48, and 49. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
?
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 35, 33, 32, 31, 30, 29, 28, 27, 30 and 21. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
?
A stock price experiences the following 10
consecutive daily high prices corresponding to days –10 to –1: 10, 9, 10, 11, 12, 14, 15, 17, 18, and 21. What is the day 0 price level that signals a
breakout and possibly a long position, using these 10 days of data as
representative of a trading range?
?
ABC Corp. has offered to purchase DEF Corp.
for $25 per share. Immediately before the merger proposal announcement, DEF
was trading at $18 per share. Immediately after the announcement, DEF is
trading at $23 per share. Assuming that the share price of DEF would fall to $16
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
share price if merger fails 16 and 25 if the merger occurs
Long binary call max: $9
Short binary put min: -$9
ABC Corp. has offered to purchase DEF Corp.
for $15 per share. Immediately before the merger proposal announcement, DEF
was trading at $7 per share. Immediately after the announcement, DEF is
trading at $13 per share. Assuming that the share price of DEF would fall to $5
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
?
ABC Corp. has offered to purchase DEF Corp.
for $24 per share. Immediately before the merger proposal announcement, DEF
was trading at $59 per share. Immediately after the announcement, DEF is
trading at $22 per share. Assuming that the share price of DEF would fall to $57
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
?
ABC Corp. has offered to purchase DEF Corp.
for $18 per share. Immediately before the merger proposal announcement, DEF
was trading at $17 per share. Immediately after the announcement, DEF is
trading at $16 per share. Assuming that the share price of DEF would fall to $15
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
?
ABC Corp. has offered to purchase DEF Corp.
for $27 per share. Immediately before the merger proposal announcement, DEF
was trading at $19 per share. Immediately after the announcement, DEF is
trading at $25 per share. Assuming that the share price of DEF would fall to $17
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
?
ABC Corp. has offered to purchase DEF Corp.
for $23 per share. Immediately before the merger proposal announcement, DEF
was trading at $12 per share. Immediately after the announcement, DEF is
trading at $21 per share. Assuming that the share price of DEF would fall to $10
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
?
ABC Corp. has offered to purchase DEF Corp.
for $22 per share. Immediately before the merger proposal announcement, DEF
was trading at $14 per share. Immediately after the announcement, DEF is
trading at $20 per share. Assuming that the share price of DEF would fall to $12
if the deal fails and that the riskless interest rate is 0%, describe a long position in
DEF taken by an event-driven hedge fund both as a combination of positions in a
risk-free bond and a binary call option and as a combination of positions including
a binary put option.
?
Prior to a merger announcement, MegaStock,
trading at $102, plans to offer one share of MegaStock for 3.5 shares of
MiniStock, trading at $20. After the announcement, MegaStock trades at $100,
MiniStock jumps to $25, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their pre-announcement levels?
if the deal goes through: (number of shares x the jump in the ministock - what the megastock trades after announced) 3.5 x 25 = 87.50 100-87.5 = 12.50
if the deal fails:
3.5 x 25 = 87.50
3.5 x 20 = 70
100 - 87.50 + 70 - 102
= -19.50
Prior to a merger announcement, MegaStock,
trading at $50, plans to offer one share of MegaStock for 1 shares of
MiniStock, trading at $40. After the announcement, MegaStock trades at $48,
MiniStock jumps to $42, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their preannouncement levels?
ministock jump x number of trades 1 x 42 = 42 megastock tades - minstock jump 48 - 42 = 6
ministock jump
42
ministock trading x 1
40 x 1 = 40
mega stock trade - ministock jump + ministock trading - mega stock original plan to trade
48 - 42 + 40 - 50
= -4
Prior to a merger announcement, MegaStock,
trading at $200, plans to offer one share of MegaStock for 2 shares of
MiniStock, trading at $90. After the announcement, MegaStock trades at $196,
MiniStock jumps to $95, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their preannouncement levels?
?
Prior to a merger announcement, MegaStock,
trading at $100, plans to offer one share of MegaStock for 5 shares of
MiniStock, trading at $10. After the announcement, MegaStock trades at $102,
MiniStock jumps to $19, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their preannouncement levels?
?
Prior to a merger announcement, MegaStock,
trading at $50, plans to offer one share of MegaStock for 1 shares of
MiniStock, trading at $30. After the announcement, MegaStock trades at $50,
MiniStock jumps to $40, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their preannouncement levels?
?
Prior to a merger announcement, MegaStock,
trading at $120, plans to offer one share of MegaStock for 6 shares of
MiniStock, trading at $20. After the announcement, MegaStock trades at $123,
MiniStock jumps to $24, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their preannouncement levels?
?
Prior to a merger announcement, MegaStock,
trading at $50, plans to offer one share of MegaStock for 0.5 shares of
MiniStock, trading at $80. After the announcement, MegaStock trades at $50,
MiniStock jumps to $85, and an arbitrageur takes a traditional and hedged
merger arbitrage position. Ignoring transaction costs, interest, and dividends,
how much money would the arbitrageur earn per share of MegaStock if the
merger consummates, and how much money would be lost if the deal fails and
the prices revert to their preannouncement levels?
?
Consider a firm with a borrowing cost of 8% on
unsecured, subordinated straight debt and a current stock price of $40. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 4% by offering a conversion ratio such as 20. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
Bond strike price = bond face value / conversion ratio
= 1000 / 20
= 50
Consider a firm with a borrowing cost of 7.5% on
unsecured, subordinated straight debt and a current stock price of $50. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 5% by offering a conversion ratio such as 15. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
bond strike price = bond face value / conversion ratio
1000 / 15 = $66.67
Consider a firm with a borrowing cost of 8.5% on
unsecured, subordinated straight debt and a current stock price of $65. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 4% by offering a conversion ratio such as 10. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
?
Consider a firm with a borrowing cost of 9% on
unsecured, subordinated straight debt and a current stock price of $55. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 4.5% by offering a conversion ratio such as 25. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
?
Consider a firm with a borrowing cost of 5.5% on
unsecured, subordinated straight debt and a current stock price of $60. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 5.5% by offering a conversion ratio such as 30. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
?
Consider a firm with a borrowing cost of 6% on
unsecured, subordinated straight debt and a current stock price of $45. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 3% by offering a conversion ratio such as 35. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
?
Consider a firm with a borrowing cost of 6.5% on
unsecured, subordinated straight debt and a current stock price of $70. The firm
may be able to issue three-year convertible bonds at an annual coupon rate of
perhaps 3.5% by offering a conversion ratio such as 5. What is the bond’s strike
price, and what does the conversion option allow the bond investors to do? Assuming that the bond’s face value is $1,000.
?
Returning to the previous example of an 8%
unsecured bond rate, a $40 stock price, and a conversion ratio of 20, and
assuming that a three-year European-style call option—given a current stock
price of $40, a strike price of $50, and other parameters, such as volatility and
dividends—is valued at $5.14 per share according to the Black-Scholes option
pricing model, what are the value of the convertible bond, the conversion value,
and the conversion premium?
Convertible bond face value of $1,000.
Find the value of the convertible bond:
2nd CLR TVM
3 > N
8 > I/Y
40 > PMT
1000 > FV
CPT > PV = 8969.92
conversion ratio x value of dividend (call option)
20 x 5.14
= 102.80
102.80 + 8969.92
= 999.72
conversion value:
conversion ratio x current stock price
20 x 40
= 800
conversion premium: convertible bond - conversion value / conversion value 999.72 - 800 / 800 = 0.2496
Returning to the previous example of an 9%
unsecured bond rate, a $45 stock price, and a conversion ratio of 15, and
assuming that a three-year European-style call option—given a current stock
price of $45, a strike price of $50, and other parameters, such as volatility and
dividends—is valued at $2 per share according to the Black-Scholes option
pricing model, what are the value of the convertible bond, the conversion value,
and the conversion premium?
Convertible bond face value of $1,000.
convertible bond value: 3 > N 9 > I/Y 45 > PMT FV > 1000 CPT > PV = 886.09
15 x 2 = 30
886.09 + 30
= 916.09
15 x 45 = 675
916.09 - 675
/ 675
= 0.357170 (35.72%)
Returning to the previous example of an 7.5%
unsecured bond rate, a $50 stock price, and a conversion ratio of 15, and
assuming that a three-year European-style call option—given a current stock
price of $50, a strike price of $50, and other parameters, such as volatility and
dividends—is valued at $3 per share according to the Black-Scholes option
pricing model, what are the value of the convertible bond, the conversion value,
and the conversion premium?
Convertible bond face value of $1,000.
?
Suppose that the realized volatility of an asset
has exactly six equally likely outcomes: 1%, 2%, 3%, 4%, 5%, or 6%. The
expected value of the volatility is 3.5%. Now consider the same dispersion
expressed in term of variance:
0.01 + 0.04 + 0.09 + 0.16 + 0.25 + 0.36 / 6 = 0.152 (Variance)
Square root (0.152) = 0.389444048185 (38.94%) Variance approximately
0.152^2 = 0.023104 (2.3%) Expected variance
Given the following five equally-likely volatilities, compute the expected variance
and the expected volatility: 20%, 25%, 30%, 35% and 40%.
?
What would be the short position in a four-year
zero-coupon bond that would form a duration-neutral hedge with a $2 million long
position in a bond with a duration of 2.5?
Long bond duration / short bond duration x long bond position
2.5 / 4
x 2,000,000
= 1,250,000
What would be the short position in a five-year
zero-coupon bond that would form a duration-neutral hedge with a $4 million long
position in a bond with a duration of 3?
long bond duration / short position x long bond position
3 / 5 x 4
$2.40
What would be the short position in a three and half-year
zero-coupon bond that would form a duration-neutral hedge with a $5 million long
position in a bond with a duration of 2?
?
What would be the short position in a one and a half-year
zero-coupon bond that would form a duration-neutral hedge with a $6 million long
position in a bond with a duration of 4.5?
?
What would be the short position in a five and a half-year
zero-coupon bond that would form a duration-neutral hedge with a $7 million long
position in a bond with a duration of 1?
?
What would be the short position in a six and a half-year
zero-coupon bond that would form a duration-neutral hedge with a $4.50 million long
position in a bond with a duration of 3.6?
?
What would be the short position in a two and a half-year
zero-coupon bond that would form a duration-neutral hedge with a $5.50 million long
position in a bond with a duration of 2.5?
?
Holding the information ratio constant at 1.0,
consider what IC would be necessary to maintain this IR when the breadth of
the portfolio is changed in various scenarios:
- One portfolio manager is a market timer who makes one major bet each
quarter on the up-and-down movement of the stock market. Her breadth
per year is 4. Value of information coefficient?
- Next, consider a commodities trader who makes nine forecasts per year on
the movement of crude oil prices. Breadth = 9 and Information ratio constant at 1. Value of information coefficient?
IR = IC x (square root) Breadth
1 = IC x square root (4)
= 0.5
1 = IC x square root (9)
= 0.3333
Holding the information ratio constant at 2.0,
consider what IC would be necessary to maintain this IR when the breadth of
the portfolio is changed in various scenarios:
- One portfolio manager is a market timer who makes one major bet each
quarter on the up-and-down movement of the stock market. Her breadth
per year is 5. Value of information coefficient?
?
Holding the information ratio constant at 3.0,
consider what IC would be necessary to maintain this IR when the breadth of
the portfolio is changed in various scenarios:
- One portfolio manager is a market timer who makes one major bet each
quarter on the up-and-down movement of the stock market. Her breadth
per year is 2. Value of information coefficient?
?
Holding the information ratio constant at 4.0,
consider what IC would be necessary to maintain this IR when the breadth of
the portfolio is changed in various scenarios:
- One portfolio manager is a market timer who makes one major bet each
quarter on the up-and-down movement of the stock market. Her breadth
per year is 3. Value of information coefficient?
?
Holding the information ratio constant at 5.0,
consider what IC would be necessary to maintain this IR when the breadth of
the portfolio is changed in various scenarios:
- One portfolio manager is a market timer who makes one major bet each
quarter on the up-and-down movement of the stock market. Her breadth
per year is 20. Value of information coefficient?
?
Holding the information ratio constant at 10.0,
consider what IC would be necessary to maintain this IR when the breadth of
the portfolio is changed in various scenarios:
- One portfolio manager is a market timer who makes one major bet each
quarter on the up-and-down movement of the stock market. Her breadth
per year is 14. Value of information coefficient?
?
Suppose that a short seller establishes a short
position in one share of XYZ Corporation at $50 per share and that XYZ pays a
dividend of $0.30 per share each calendar quarter. The current rebate on XYZ
share is 1% per year. What would be the dollar return to the short seller if XYZ
rose to $51 at the end of one year?
Looking at all the total losses of a short position:
if the share price rises to $51 the short position loses $1
then if the share has dividends $0.30 (quarterly). 4 x $0.30 = $1.20. So, the short position loses another $1.20.
rebate: is the dividend of the owner of the share (the lender - the person in short position)
the rebate is 1%. $50 x 0.01 = $0.50
rebate - rise of the stock - dividend
$0.50 - $1 - $1.20 = - $1.70
Suppose that a short seller establishes a short
position in 10 shares of XYZ Corporation at $65 per share and that XYZ pays a
dividend of $0.40 per share each calendar quarter. The current rebate on XYZ
share is 1% per year. What would be the dollar return to the short seller if XYZ
rose to $66 at the end of one year?
10 x 1 = -10
0.4 x 4 x 10= -16
65 x 0.01 x 10= 6.5
= -19.5
Suppose that a short seller establishes a short
position in twenty-five shares of XYZ Corporation at $55 per share and that XYZ pays a
dividend of $0.50 per share each calendar quarter. The current rebate on XYZ
share is 1.5% per year. What would be the dollar return to the short seller if XYZ
rose to $65 at the end of one year?
?
Suppose that a short seller establishes a short
position in fifty shares of XYZ Corporation at $70 per share and that XYZ pays a
dividend of $0.10 per share each calendar quarter. The current rebate on XYZ
share is 2% per year. What would be the dollar return to the short seller if XYZ
rose to $70 at the end of one year?
?
Suppose that a short seller establishes a short
position in one hundred shares of XYZ Corporation at $10 per share and that XYZ pays a
dividend of $0.15 per share each calendar quarter. The current rebate on XYZ
share is 1% per year. What would be the dollar return to the short seller if XYZ
rose to $5 at the end of one year?
?
Suppose that a short seller establishes a short
position in 200 shares of XYZ Corporation at $15 per share and that XYZ pays a
dividend of $0.20 per share each calendar quarter. The current rebate on XYZ
share is 1% per year. What would be the dollar return to the short seller if XYZ
rose to $10 at the end of one year?
?
Suppose that a short seller establishes a short
position in three hundred share of XYZ Corporation at $13 per share and that XYZ pays a
dividend of $0.25 per share each calendar quarter. The current rebate on XYZ
share is 2.30% per year. What would be the dollar return to the short seller if XYZ
rose to $15 at the end of one year?
?
