eco105 A risk-averse invertor with W, to invest has two sets available. One is risk fr and pays a return p, while the other is risky and pays & random return of r. Assume that the investor chooses a, the proportion of W, to invest in the risky asset, so as to maximize the expected utility of W=(a-r+ (1-a) p)-.

2. Suppose that could be either r, orr,, each with probability one half and assume that r, >,. Write out the first-order condition for maximization of expected utility. Is the second-order condition satisfied? Explain. Are restrictions required concerning the values ofr, r, and p for a to be bounded?

Suppose that for some parameterization, the optimal value of a is zero. Show that the optimal value of a becomes positive if r, is increased.

Give the Arrow-Pratt measure of relative risk aversion.

UK Corporate Governance Code reporting last year, FRC stated that: "Effectively applying the Corporate Governance Code Principles is much more important than a 'tick box' approach". Our assessments of reports this year now give us an evidence base to drive forward better-quality reporting. This is essential if investors and other stakeholders are to evaluate the quality of governance effectively.

Question 1:

talking about the extent to which UK listed companies are lookinshareholders' role in governance is to appoint the directors and the auditors and to satisfy themselves that an appropriate governance structure is in place.' This remains 2 true today, but the environment in which companies, their shareholders and wider stakeholders operate continues........... Nevertheless, the debate about the nature and extent of the framework has intensified as a result of financial crises and high-profile examples of inadequate governance and misconduct, which have led to poor outcomes for a wide range of stakeholders. At the heart of this Code is an updated set of Principles that emphasise to develop rapidly.' UK Corporate Governance Code (2018) However, an alternative description is that ".... too often companies who are not compliant with the Code, do not declare non-compliance but offer vague explanations, and continue this pattern year on year."

Callie and Trinity Jackson are married and interested in planning for their retirement. Callie is 47 years old, while Trinity is three years younger. They would like to plan on retiring when Callie is age 65, which is when their mortgage on their home will be paid off. Their mortgage payment is $2,000 per month. Callie earns $75,000 and Trinity earns $105,000. They have current savings of $250,000 and would like to plan on a wage replacement ratio (WRR) of 80 percent, including Social Security. They currently save $15,000 each in their respective 401(k) plans. Neither of their plans offer an employer match. They have been reading that 70 percent to 80 percent for wage replacement is optimal. They both reach full retirement age under Social Security at age 67. Callie and Trinity's Social Security retirement benefit at full retirement age is projected to be $2,500 and $3,000 per month, respectively. They want to plan on living until Trinity is age 95. Assume that inflation is two percent and they can earn seven percent on their investments.

1. Calculate their needs at age 65 and their annual savings requirement.

2. Comment on the wage replacement ratio assumption.

3. Recalculate their needs at age 65 based on adjusting the WRR (include assumptions for the new WRR).

4. After spending time discussing retirement scenarios and what they want in their future, the Jacksons ask if they could afford to buy a beach house if they worked until age 70. Assume that the beach house they really want is expected to cost $1.5 million when they retire.

5. The Jacksons like the idea of a $1.5 million beach house, however, they do not like the idea of working until Callie is 70 years old. You suggest that they consider retiring at age 65 with a 65 percent WRR and sell their current house at retirement and buy a beach house they can live in full time. They like the idea and ask how much they could afford for a beach house. Assume that their current house is worth $570,000 and is expected to increase at four percent per year. Ignore real estate closing costs for the calculation. [8:32 PM, 11/15/2021] Flo: Question: Dave, aged 44, and Adele, aged 41, are new clients. Dave works in sales for a large pharmaceutical company. His base salary is $170,000 a year and his annual commissions are around $50,000 a year. Adele, is a real estate agent. She works from home and typically earns $140,000 a year (approximately $100,000 after she pays realtor expenses). Both Dave and Adele are happy with their careers and believe they could find employment easily, if something should happen. Dave has stated that he would like to move into a senior management role at his company or a competitor.

Dave and Adele are married and they have two children: Harvey, aged 17, and Carol, aged 16. Adele's mother, Debbie, lives with them. Debbie is 72 years old and widowed. Debbie mo... [8:34 PM, 11/15/2021] Flo: Question: Dave, aged 44, and Adele, aged 41, are new clients. Dave works in sales for a large pharmaceutical company. His base salary is $170,000 a year and his annual commissions are around $50,000 a year. Adele, is a real estate agent. She works from home and typically earns $140,000 a year (approximately $100,000 after she pays realtor expenses). Both Dave and Adele are happy with their careers and believe they could find employment easily, if something should happen. Dave has stated that he would like to move into a senior management role at his company or a competitor.

Dave and Adele are married and they have two children: Harvey, aged 17, and Carol, aged 16. Adele's mother, Debbie, lives with them. Debbie is 72 years old and widowed. Debbie moved in with Dave and Adele to help with their children, however her health has started to deteriorate. Adele thinks her mother will live until she is 80 years-old.

Rock (45) and Cathy Rock (45) are a married couple with two children; Cyrus and daughter Dorothy (8). William is self-employed electrical contractor and earns $125,000 after expenses yearly. He has been running his business as a sole proprietor for over 10 years. He has not incorporated his business due to the hassle if additional regulatory requirements and expenses involved. His business has really taken off during the last three years and he sometimes feel the need to hire more employees to assist him. Cathy just completed her 18 years working as a Legal assistant at one of the leading Law firm and earns $68,000. The law firm provides her all benefit including a group life insurance plan for 3 times her salary. She also has a defined contribution plan at work in which the firm matches a dollar for a dollar to maximum contribution of $3,000 per year by the employer. She has been contributing $200 every month ever since she joined, and the employer matches the same amount. Her funds are invested in a Bond Fund and has a current value $85,000. She has an accumulated contribution room of $66,000. They have a house in Mississauga in their joint names that they purchased 10 years earlier for $600,000 and is currently valued at about $900,000. They have been making extra payments to their $250,000 mortgage and hope to pay it off in nine years. Cathy is always worried about the mortgage and would like to be mortgage free as soon as possible. Cathy inherited a cottage from her parents that is currently valued at $275,000 and is mortgage free. They spend about $6,000 annually to carry the cottage in taxes and maintenance etc. They have so far been spending 4-5 weekends every year at the cottage and enjoy their time. Ideally, Cathy would like their son Cyrus to inherit the cottage and have been considering adding him as a joint owner. However, she is not sure if it is a good idea because she wants to be fair to both her children. Their major cash outflows apart from the mortgage payment of $2,800 per month include; property tax $340; home insurance $120; maintenance $300; utilities $250; groceries $900; clothing $400; William's life insurance $160 (Face Value $300,000); Internet and phone $150; entertainment/dining $900; donations, gifts $100; miscellaneous discretionary $800; Vehicles gas and car insurance $660, Car loan payment $940 per month. William currently leases his truck for a monthly payment of $640 and Cathy has a Volkswagen sedan financed by a loan with a current balance of $25,000 at interest rate of 5.5% and she is paying $300 per month. Each year, they spend $7,200 on vacation. William has credit card balance of $23,000 that he incurred when he purchased a new tool set for his business for which he is paying $450 per month. Cathy has a current credit card balance of $12,000. They also have a $40,000 joint unsecured line of credit from their bank with current balance of $8,000. Each February, William purchases $12,000 of mutual funds via a lump sum contribution to his Registered Retirement Savings Plan (RRSP). The mutual funds include the following: $12,261 in broad-based Canadian equities, $10,675 in Canadian energy companies, $21,024 in U.S. large cap stocks, $5,734 in international equities across multiple continents, and $14,016 in Canadian government bonds. His RRSP account has grown to $63,710 and he currently has $84,000 in unused RRSP contribution room. William has never contributed to a Tax-Free Savings Account (TFSA). When he switched banks almost a decade ago, Aaron set up a pre-authorized monthly transfer of $250 from his chequing account to his savings account to cover emergencies that may arise. This account has grown to $34,000. William as a Universal Life Insurance policy with a Face Value of $300,000 that he purchased when he was very young. Current Cash Surrender Value (CSV) of the policy is $28,000. He has an athletic body and is very active and rarely had any medical issue. He never felt the necessity to obtain disability insurance. Cathy has a group Life insurance policy at work for a face value of 3 times her salary. There is however no disability insurance from employment, and she has also never felt the need to obtain Disability insurance. They sometimes wonder if their insurance coverage is adequate and how could they know their needs for insurance. They both would like to retire in at age 65. At that time, they estimate that they will need $6,000 per month to maintain their lifestyle because their house will be mortgage free. They are both in excellent health and expect to live to age 90. They are worried about their retirement and want to know if they would have sufficient funds upon retirement to maintain their lifestyle. William's parents gifted $11,000 each to their children on their 50th wedding anniversary 5 years ago, that was invested in GIC yielding annual interest rate if 2.5% maturing next month. They believe that the cost of post secondary education for each child would be $50,000. They will prefer that their children do not have to resort to student loans. They would like to find ways to have adequate funds for the post-secondary education of their children. They both plan to retire at age 65 and they expect to live to age 90. They have calculated that would need at least $6,000 per month after retirement to maintain their current lifestyle. How much should they have at the time of retirement to ensure $6,000 per month in retirement? Are they contributing enough to fulfill the objective of receiving $6,000 per month in retirement? answer all

20. Assume the Black-Scholes framework. Consider a stock, and a European call option and a European put option on the stock. The current stock price, call price, and put price are 45.00, 4.45, and 1.90, respectively. Investor A purchases two calls and one put. Investor B purchases two calls and writes three puts. The current elasticity of Investor A's portfolio is 5.0. The current delta of Investor B's portfolio is 3.4. Calculate the current put-option elasticity. (A) -0.55 (B) -1.15 (C) -8.64 (D) -13.03 (E). Consider a chooser option (also known as an as-you-like-it option) on a nondividend-paying stock. At time 1, its holder will choose whether it becomes a European call option or a European put option, each of which will expire at time 3 with a strike price of $100. The chooser option price is $20 at time t = 0. The stock price is $95 at time t = 0. Let C(T) denote the price of a European call option at time t = 0 on the stock expiring at time T, T > 0, with a strike price of $100. You are given: (i) The risk-free interest rate is 0. (ii) C(1) = $4. Determine C(3). (A) $ 9 (B) $11 (C) $13 (D) $15 (E) $17

31. You compute the current delta for a 50-60 bull spread with the following information: (i) The continuously compounded risk-free rate is 5%. (ii) The underlying stock pays no dividends. (iii) The current stock price is $50 per share. (iv) The stock's volatility is 20%. (iv) The time to expiration is 3 months. How much does delta change after 1 month, if the stock price does not change? (A) increases by 0.04 (B) increases by 0.02 (C) does not change, within rounding to 0.01 (D) decreases by 0.02 (E) decreases by 0.04

You own one share of a nondividend-paying stock. Because you worry that its price may drop over the next year, you decide to employ a rolling insurance strategy, which entails obtaining one 3-month European put option on the stock every three months, with the first one being bought immediately. You are given: (i) The continuously compounded risk-free interest rate is 8%. (ii) The stock's volatility is 30%. (iii) The current stock price is 45. (iv) The strike price for each option is 90% of the then-current stock price. Your broker will sell you the four options but will charge you for their total cost now. Under the Black-Scholes framework, how much do you now pay your broker? (A) 1.59 (B) 2.24 (C) 2.86 (D) .48 (E) 3.61

Consider an economy with three consumers, three different inputs and three different outputs. Each consumer i is initially endowed only with one unit of input and consumes only output i (i=1,2,3). The consumers live on A circle, facing inward, and each consumer can use its input to produce the output it consumes and/or to produce the output that is consumed by its neighbor to the left (clockwise along the circle). Formally, consumer i (i=1,2,3) can use &; 2,0 units of input i to produce f, units of output i and can use L. 20 units of input i to produce 2L, units of output i+ 1, where f,+Li 1. Here, "output 4" is another name for output 1 and "consumer i = d" is another name for consumer 1. Consumer gets utility z, by consumning z, 20 units of good i.

(a) Specify the set of feasible allocations for this economy, assuming that there is free disposal of all goods. Use the notation above and any other notation you need, defining any notation you introduce.

(b) Suppose that the consumers are not able to trade. They can only produce (using their own initial endowments) and consume. What are their optimal input, output and consumption choices?

(c) Suppose, instead, that any two consumers can freely trade any goods with each other. Each consumer i is still the only consumer able to produce output using input i Assume that trading does not use up any resources (either inputs or outputs). No consumer is forced to trade and no trade by a pair of consumers occurs if it reduces a consumer's utility. What trades might consumer 2 make with consumer 3 that both consumers would agree to, with no involvement of consumer 1? What trades might consumer 2 make with consumer 1 that both consumers would agree to, with no involvement of consumer 3? What conclusion can you draw about the final allocation if the only possible trades are bilateral (between two consumers, without involvement of the third)? Explain.

A risk-averse invertor with W, to invest has two sets available. One is risk fr and pays a return p, while the other is risky and pays & random return of r. Assume that the investor chooses a, the proportion of W, to invest in the risky asset, so as to maximize the expected utility of W=(a-r+ (1-a) p)-.

2. Suppose that could be either r, orr,, each with probability one half and assume that r, >,. Write out the first-order condition for maximization of expected utility. Is the second-order condition satisfied? Explain. Are restrictions required concerning the values ofr, r, and p for a to be bounded?

Suppose that for some parameterization, the optimal value of a is zero. Show that the optimal value of a becomes positive if r, is increased.

Give the Arrow-Pratt measure of relative risk aversion.

A risk-averse invertor with W, to invest has two sets available. One is risk fr and pays a return p, while the other is risky and pays & random return of r. Assume that the investor chooses a, the proportion of W, to invest in the risky asset, so as to maximize the expected utility of W=(a-r+ (1-a) p)-.

2. Suppose that could be either r, orr,, each with probability one half and assume that r, >,. Write out the first-order condition for maximization of expected utility. Is the second-order condition satisfied? Explain. Are restrictions required concerning the values ofr, r, and p for a to be bounded?

Suppose that for some parameterization, the optimal value of a is zero. Show that the optimal value of a becomes positive if r, is increased.

Give the Arrow-Pratt measure of relative risk aversion.