Consider a stock with a current price of $100 that will be worth either $125 or $80 in 1 year. Assume rf=2% (annual compounding). You have invented a new derivative security called a "square", whose payoff in 1 year is the square of the stock price, i.e., payoff = P₁². a. What are the payoffs to this security in the two states of the world at time 1? (1 point each) b. What portfolio of stock (number of shares) and borrowing (dollar value of initial position, with positive numbers indicating borrowing) will replicate these payoffs? (2 points each) c. What is the current value of this security, i.e., the value of this replicating portfolio? (2 points)

Answers

Answer 1

The current value of the "square" security is $11,012.50.The payoffs to the "square" security in the two states of the world are $125² = $15,625 and $80² = $6,400. To replicate these payoffs, we need to find a portfolio of the stock and borrowing.

In this case, we can determine the number of shares of stock and the dollar value of borrowing that will result in the same payoffs. Finally, the current value of the security is the value of the replicating portfolio, which can be calculated using the present value formula.

a. The payoffs to the "square" security in the two states of the world are $125² = $15,625 and $80² = $6,400.

b. To replicate these payoffs, we need to find a portfolio of the stock and borrowing. Let's denote the number of shares of stock as S and the dollar value of borrowing as B. In the first state, the value of the portfolio would be S(125) - B, and in the second state, it would be S(80) - B. By setting up two equations using these values and the payoffs, we can solve for S and B.

$15,625 = S(125) - B

$6,400 = S(80) - B

Solving these equations, we find S = 100 and B = 6,250.

c. The current value of the "square" security is the value of the replicating portfolio. We can calculate this using the present value formula:

Value = (Payoff in State 1 * Probability of State 1) + (Payoff in State 2 * Probability of State 2)

Value = ($15,625 * 0.5) + ($6,400 * 0.5)

Value = $11,012.50

Therefore, the current value of the "square" security is $11,012.50.

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Related Questions

What type of economy is an economic system in which private businesses can operate freely with minimal state control?Henry lives in a country where the government gives many incentives to produce military goods and few incentives to produce consumer goods. Henry knows a more efficient way to finish his task at work and feels like sharing it with his boss. However, he has no incentive to share it. Which type of economy does Henry most likely live in?

Answers

Answer:

Private business freedom : Capitalist or Market Economy. Henry is more likely in Socialist Economy.

Explanation:

Economy type in which private sector has full freedom, un-intervened by government or state control is Capitalist or Market Economy. Profit maximisation motive & high consumer choice, sovereignity such economy's main features.

Henry's country which gives incentives to reallocate production choice 'what to produce' (from consumer goods to military goods). He has more efficient idea for work implementation, but lacks incentive (probably due to lack of creative & innovative ideas reward). These features characterise a Socialist Economy, in which government or state has supreme power over central economic decisions. Social welfare is considered priority, government monopoly curbs innovation & creativity, there is less consumer choice, sovereignity.

which of the following should be pracited among all co workers in the workplace
a.bullying
b.discrimination
c.stereotyping
d.tolerance

Answers

Answer:

c

Explanation:

Answer:

D. Tolerance

Explanation:

Because what, you souldnt do any of the others, dude, teachers sometimes

After adjusting your seat, your _____ should be as close as possible to the backrest.
A. hands
B. arms
C. bottom
D. legs

Answers

Answer:

C. Bottom is the answer

Explanation:

My parents would always yell at me to scooch backwards in the car if I was leaning too far forward. I don't need to know how to drive to know this.

This is a question about driving right? Lol, cause if it's not, sorry.

Help me please ASAP.

Answers

your answer is D because i took the test a couple of days back

All of the following are career pathways in the Architecture and Construction
Career Cluster except.
A. Design/Pre-Construction.
B. Construction.
C. Power, Structural, and Technical Systems.
D. Maintenance/Operations.

Answers

C. Power, Structural, and Technical Systems.

correct me if im wrong

Answer:

The answer is C.

Explanation:

I took the test. Hope this helps! ;) <3

To satisfy demands for withdrawals, banks keep:
A. discount rates.
B. monetary policies.
C. balance sheets.
D. fractional reserves.​

Answers

C. balance sheets

explanation:

Max works at Pizza Palace 20 hours each week at a rate of $10 per hour. He is paid every two week. Calculate his gross and net pay. (Social Security 6.2%, Medicare 1.45%, and Federal and State Tax 10%)

Answers

Answer:

$329.4

Explanation:

Max earns $10 per hour. If he works for 20 hours each week, his weekly pay will be $10  times 20 hours

=$10 x 20 hours

=$200

He is paid every two weeks. His gross pay is $400. ($200 x 2)

Net pay would be gross pay -deductions

Deductions.

Social security

= 6.2% x  $400

=$24.8

medicare

=1.45% x $400

=$5.8

Federal and State Tax

=10% x $400

=$40

Total deductions = $24.8 +$5.8 +$40=$70.6

Net pay =$400 -$70.6

=  $329.4  

Which of the following is true of small business owners?
A. the work business owners do requires little physical stamina.
B. the business owner starts with a business plan.
C. the business owner need to know little about management and finance. D. it's easy for most business owners to find a marketable idea.

Answers

Answer:

B

Explanation:

I mean, hopefully, they made a business plan lol. If you don't plan out your business right, you'll have a hard time making it become successful without a good plan.

if i post by business page will you guys follow it ?

Answers

Answer:

Yassss queeeennnn

Explanation:

jdnskakana

Explanation:

Yes i will definately follow it

Which of the following vehicles would have a lower insurance premium?
O A brand new SUV
O A used town car

Answers

Answer:

A used town ca

Explanation:

Because its used and that insures that it works so it makes the insurance go down

The correct answer is option B.

A used town car would have a lower insurance premium.

Insurance premium

An insurance premium is the amount of money an individual or business pays for an insurance policy. Insurance premiums are paid for policies that cover healthcare, auto, home, and life insurance.

What is an example of a premium in insurance?

A premium is the price of the insurance you've chosen, charged by your insurance company. A deductible is an amount you have to pay before your insurance company initiates coverage. For example, if your car insurance premium is $800 per year, you must pay your insurer $800 per year to have the insurance.

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Which is used to trace a check back to the account on which it was written?
Group of answer choices

a valid date

an endorsement

a bank route number

a signature

Answers

Answer:

a bank route number

Explanation:

The routing number is among the three numbers found at the bottom of a check. The routing number is at the bottom left.  It serves as an ' identity ' for your bank. The routing number enables other banks to contact your bank and collect funds from your account every time you write a check.

A routing number is a unique number for every banking institution.  The number proves that the bank is a recognized financial institution with an account with the Federal Reserve.

Which of the following occupations is most responsible for ensuring the quality and safety of the food
supply chain?
O chefs
O farmers
O grocery store owners
O food processors

Answers

I would say farmers because all of they rely on their food producs

Answer: I am pretty sure the answer the answer would be the farmers

Explanation: the food comes form the farmers, including meats, veggies, fruits, well you get the point. And if there is something bad with one of the meat animals, they are in charge of not selling the "bad meat" to any stores or big meat companies

Question 12 When you get a vaccine, it benefits others because you can't get them sick. If left to the free market, the socially optimal amount of vaccines would be produced. vaccines would be underproduced. vaccines would be overproduced.​

Answers

Answer:

yup you are right i think so idrk

Write a question keep it simple

Answers

Answer:

Why do people break up if they love each other?

Explanation:

sorry it's not simple lol

Calculate the 4-day moving average for the following data (Remember that
you're finding 4 different averages)"
1
2
3
4
$182.60
$172.95
$160.08
$175.83
$152.01
$157.89
$148.48
5
6
7
Your answer

Answers

Answer:

116 . 100. 560 . 58

257 . 1100. 342 . 186

Why do you think economists have different belief systems/theories on economics?

Answers

Economists have different belief Systems because Economists also disagree because their methods are not good enough to reveal the whole truth. Economic theory is an attempt to explain and interpret economic data, for example, to determine the causes and effects of economic events.

Answer:The principal disagreement among economists is a matter of economic philosophy. There are two major schools of economic thought: Keynesian economics and free-market, or laissez-faire, economics.

Keynesian economists, named after John Maynard Keynes, who first formulated these ideas into an all-encompassing economic theory in the 1930s, believe that a well-functioning and flourishing economy may be created with a combination of the private sector and government help.

By government help, Keynes meant an active monetary and fiscal policy, which works to control the money supply and adjust Federal Reserve interest rates in accordance with changing economic conditions.

By contrast, the free-market economists advocate a government "hands-off" policy, rejecting the theory that government intervention in the economy is beneficial. Free-market economists—and there are many distinguished advocates of this theory, including Nobel Memorial Prize winner Milton Friedman—prefer to let the marketplace sort out any economic problems. That would mean no government bailouts, no government subsidies of business, no government spending explicitly designed to stimulate the economy, and no other efforts by the government to help what the economists believe is the ability of a free economy to regulate itself.

Explanation:

Simply Imagine wants to grow their company but is hindered by increasing labor costs and import quotas.
Simply Imagine should consider becoming a(n)
(A) countertrader (B) wholly owned subsidiary (C) strategically(D) mulimatiomnal (E) franchiser

Answers

Answer:

multinational

Explanation:

A multinational business operates in at least one other country apart from its home country. The company will have factories/ offices in different countries and its headquarters in the domicile state. The operations of a multinational are coordinated at its headquarters.

By becoming a multinational, simple imagine can expand in countries with relatively cheap labor. It will overcome the import quota challenge by operating from a country without restrictions or from the source state.

he U.S. government's ability to pay for Social Security in the near future is a problem because:

Answers

Answer:

Our country's notional debt

Explanation:

After learning about social media ethics, what 5 things would you tell other high school students positive or negative about social media and how it will potentially affect their high school experience and their potential career?

Answers

1. A positive is meeting and learning from new people 2. social media Can be dangerous to mental health 3 Stay in touch with distant people 4. Learn subjects 5. What you say online can bite you on the butt

It is the idea being transmitted by the sender to the receiver. It includes three aspects — content , structure and style

Answers

Answer:

decodes and feedback.

Explanation:

It is a message since it is written or recorded words or information sharing or ideas conveyed by the sender to the receiver.  It includes information and communication, how important and useful information is, and can be read in order to understand it.  The structure of a message is tone.

The Style includes how the sender composes and writes a message.

Message is the idea being transmitted.

A Message is a form of communication sent to a recipient who is not present physically and its can be in verbal, written or recorded form.

Message is one of the essential elements of communication process. The other process includes Sender, Encoding, Interference, Communication channel, Receiver, Decoding and Feedback

Roughly, there are 3 purposes for passing message

To inform people of certain subject.To persuade others to do one biddingTo builds one's goodwill.

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WILL MARK BRANLIEST!!!!!
Which portion would not be part of an investment portfolio? (Select the best answer.) commodities funds

a savings account

a savings 529 plan

equity investments in a company

Answers

Answer:

a savings 529 plan

Hope this helps plz mark me brainliest

Answer:

A savings account

Explanation:

Took the quiz

Two friends wanted to decide where to go for dinner. Their conversation went like this: "We need to get something to eat. How about Sharky's so we can watch the game on TV? No, Sharky's is too noisy. Ok, how about we get pizza at the Pie Hub? The Hub is great with me." In that conversation the statement "The Hub is great with me" would be analyzed and mapped as __________.

Answers

This question is incomplete because the options are missing; here are the options:

In that conversation the statement "The Hub is great with me" would be analyzed and mapped as __________.

A. A counterargument

B. The chosen alternative

C. Rejected alternative

D. A reason

E. A recognition of the need to decide

The correct answer is The chosen alternative

Explanation:

Mapping or analyzing an argument involves considering the function of each part of the argument in terms of categories such as reason, the main argument, counterargument, etc. In the case of the argument presented, the main point is where to eat. Moreover, there are two alternatives: Sharky's and Pie Hub. In this case, Sharky's is the first alternative and the rejected alternative because from the options available this is not chosen. Moreover, the second alternative is the chosen alternative; this is expressed in "The Hub is great with me" because this line shows both speakers have agreed on a place to it and this option or possible solution has been chosen.

Fractional reserve banking increases the money supply in an economy by:
A. preventing depositors from leaving a lot of money in banks.
B. requiring the government to print more money in certain
situations.
C. loaning money that would otherwise be held in a bank.
D. accepting currencies from many different countries to pay off
loans.

Answers

Answer:

C. loaning money that would otherwise be held in a bank.

Explanation:

Fractional reserve banking increases the money supply in an economy by "loaning money that would otherwise be held in a bank."

Fractional reserve banking is known as a system of banking whereby the banks hold a fraction of what customers deposit as reserves. Then the banks use the remaining to give loans and thereby creating and increasing the supply of money. Commercial banks practise this type of banking system. This tells of how commercial banks are affecting the money supply. The bank reserves are usually held as cash in the bank. It can also as balances in the bank's account at their central bank.

Answer:

C. loaning money

Explanation:

just did it on a-p-e-x

Which one of the following businesses would you classify as being in the secondary sector of industry?

A) Oil exploration company
B) Family run farm business
C) Taxi operating business
D) Shoe manufacturer

Answers

Answer:

shoe manufacturer

Explanation:

what is the role of doctors in our society?​

Answers

Their role is to serve the society as others do basically contribution but their actual role is to help others through their medical knowledge.

Helppp please
The fact that a country has less strict labor laws and relaxed environmental regulations are strong reasons for a
company to move production facilities to that country.
True
False

Answers

The answer has to be true

Answer:true

Explanation: I just took the test

What financing source involves wealthy individuals giving their money to fund a startup?

Answers

Answer:

Angel Investors

Explanation:

Angel investment is when a person or a group of individuals use their finances to fund a startup. These investors are wealthy and consider it fit to finance entrepreneurs based on business ideas and proposals.

Angel investors usually have excess funds and willing to risk in the early stages of a startup in anticipation of bigger returns when the business succeeds. Angel investors gain percentage ownership in the business in exchange for funding. They also offer mentorship to entrepreneurs.

Which of the following is NOT a deception method of customers
A)Warning label
B)Pigeon Drop
C)Ponzi Scheme
D)Bait and Switch

Answers

So i feel the answer to this is obvious because a warning label is not meant to trick a consumer so the answer would be a since the rest are trying to bait costumers into something. hope this helps and makes sense to you.

Trish bought a new computer that she has been using for a few weeks. She is starting to experience pain in her wrists, back and neck. What measure should Trish take to reduce strain while working on the computer?

A. complete all her work soon on the computer by sitting at a stretch
B. maximize the brightness of the screen to concentrate better
C. ensure back support by using cushions
D. keep hands and wrists stiff while typing

Answers

Answer:

C ensure back support by using cushions

Answer:

C

Explanation:

Her problem is that be back is hurting, and adding cushions will ensure back support and then that will not be a problem for her anymore.

Chose one scenario and write a paragraph on why you chose it. It’s for economics please help meee

Answers

B
I would prefer to start a babysitting service in my neighborhood because I would be the only business providing this service therefore meaning there wouldn't be any competition. This means that I would be able to make more money as there would be quite a few people with children who need taking care of.
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For what value of x is the equation 224 +7 = 2" true?A. 2B. 4C. 11D. 16E. 44Please lmk soon Springer Corp. has 6,000 cumulative preferred shares that pay a dividend of $1.00 per share. It also has 30,000 common shares outstanding. In 2018 and 2019 it did not pay any dividends due to poor earnings. This year in 2020, the Board of Directors decided to pay out $70,000 in dividends. What is the amount of the dividends that would be paid to the common shareholders? Enter only numbers (do not use a $ sign or comma): $ Answer What would be the perimeter of this figure? i should practice pre-reading, during reading, and post reading strategies to help me understand a text. true false New-Project Analysis Madison Manufacturing is considering a new machine that costs $350,000 and would reduce pre-tax manufacturing costs by $110,000 annually. 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