Today is 1 July 2020. Joan has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Joan purchased all instruments on 1 July 2014 to create this portfolio and this portfolio is composed of 27 units of instrument A and 48 units of instrument B. Instrument A is a zero-coupon bond with a face value of 100. This bond matures at par. The maturity date is 1 January 2030. Instrument B is a Treasury bond with a coupon rate of j2 = 4.71% p.a. and face value of 100. This bond matures at par. The maturity date is 1 January 2023.

(a) Calculate the current price of instrument A per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ =2.14% p.a.

a. 71.1357

b. 81.6915

c. 71.8968

d. 66.8773

(b) Calculate the current price of instrument B per $100 face value. Round your answer to four decimal places. Assume the yield rate is j₂ = 2.14% p.a. and Joan has just received the coupon payment.

a. 108.5788

b. 107.4293

c. 106.2238

d. 119.8766

(c) What is the duration of instrument B? Express your answer in terms of years and round your answer to three decimal places. Assume the yield rate is j₂ = 2.14% p.a.

a. 2.391

b. 2.840

c. 5.679

d. 4.783

(d) Based on the price in part a and part b, and the duration value in part c, calculate the current duration of Joan’s portfolio. Express your answer in terms of years and round your answer to two decimal places.

a. 6.07

b. 6.66

c. 4.51

d. 4.54

1. The owner of a European put option on a share has the right, but not the obligation, to sell one share for a fixed price known as the option’s strike price, on a fixed date known as the option’s expiry date. If the share price equals S on the option’s expiry date then the option’s payoff function is the larger of 0 and K − S, where K is the option’s strike price. This question illustrates what we can learn about the prices of Arrow-Debreu securities if we can observe the prices of a set of put options on the same stock, but with different strike prices. We assume that the option expires at date 1 and that the state of nature at date 1 is the share price at date 1, where the share price can take the values $0, $1,$2, . . . , $99, $100. Suppose that the Arrow-Debreu security paying out in state “$j” has price θ_j, for j = 0, 1, 2, . . . , 100.

1. Fill in the following table, where Portfolio A comprises one short position in a put option with strike price $51 and one long position in a put option with strike price $52; and Portfolio B comprises one short position in a put option with strike price $52 and one long position in a put option with strike price $53. The missing entries are the date 1 payoffs of the indicated assets (and portfolios) if the share price at date 1 equals the value given at the head of each column.

2. Use the current option prices given in the table above to calculate the prices of Arrow-Debreu securities that pay out when the date 1 share price equals $S, for each of S = 48, 49, 50, 51, 52.

"Scarcity implies that some way of rationing goods must be found." Explain how the market price system promotes greater economic activity than alternative systems of deciding who gets the benefits of production. (eg., first come-first served, equal shares or random lottery.) (6 points)

The economy of Euphoria has the following economic data.

1. Production costs are costs of raw materials, wages, capital goods and services.
2. Productivity index relates to all production inputs.

Examine the data relating to the economy of Euphoria above and answer the following questions.

Q1. What phase of the business cycle was the economy in 2018? Briefly give two reasons for your answer.                                                                                              

Q2. What was the likely cause of the change in the unemployment rate in 2018? What type of unemployment is likely to exist in Euphoria in 2018? Explain your answer.         

Q3. Identify and explain the likely cause of inflation / deflation in 2018?

Include in your answer the contribution that export and import prices made to inflation /   deflation in 2018.        

The current price of Gringotts Bank Corporation is $50. The price will increase by 40% or fall by 35% during each of the next two years. The company will pay a $9 dividend at the end of the first year if the stock price has risen, and will pay a $4 dividend if the price has fallen. It will not pay any dividends at the end of second year. The annualized, continuously compounded interest rate is 5%. What is the value of a 2-year European call option with a $45 strike price? What if it’s an American call option?

An investor discovered that there is no oil change service available in the small town that he has recently moved to and decides to open a shop offering this service. The estimated market demand for the oil change service is given by P=400-10Q. The total cost of the oil change service is TC=150Q²+200 and the marginal cost is MC=30Q

a) If the investor engages in perfect price discrimination, how many oil change services will he offer? What would be his producer surplus?

b) What will be will be the profit maximizing price and quantity if the investor is not allowed to price discriminate, and is forced to charge a uniform price to all the customers? What will be the profits, consumer surplus and deadweight loss?

c) Calculate the price point - elasticity of demand when the price is 100. Is the demand elastic, inelastic or unitary elastic? Explain.

PLEASE ANSWER ALL

15) Which of the following is certainly true if demand and supply increase at the same time? a. The equilibrium price will increase. b. The equilibrium price will decrease. C. The equilibrium quantity will increase. d. The equilibrium quantity will decrease. e. The equilibrium quantity may increase, decrease, or stay the same.

16) If a decrease in price from $2 to $1 causes an increase in quantity demanded from 100 to 120, using the midpoint method, price elasticity of demand equals a. 0.17 b. 0.27 C. 0.40 d. 2.5 e. 3.72

17) If a 2% change in the price of a good leads to a 10% change in the quantity demanded of a good, what is the value of price elasticity of demand? a. 0.02 b.0.2 c. 5 d. 10 . 20

An investor has just taken a short position in a one-year forward contract on a dividend paying stock. The stock is expected to pay a dividend of $2 per share in five months and in eleven months. The stock price is currently selling for $100 and the risk-free rate of interest is 8.50% per year with continuous compounding for all maturities.
a.  What are the forward price and the initial value of the forward contract? The forward price is (sample answer: $75.50) and the initial value is (sample answer: $75.50)
b. Six months later, the price of the stock is $105 and the risk-free rate stays the same. What are the forward price and the value of the position in the forward contract? Now the forward price is (sample answer: $75.50) and the initial value is (sample answer: +$5.50; or -$5.50)

An investor has just taken a short position in a one-year forward contract on a dividend paying stock. The stock is expected to pay a dividend of $2 per share in five months and in eleven months. The stock price is currently selling for $100 and the risk-free rate of interest is 8.50% per year with continuous compounding for all maturities.

a. What are the forward price and the initial value of the forward contract? The forward price is (sample answer: $75.50)

and the initial value is (sample answer: $75.50)

b. Six months later, the price of the stock is $105 and the risk-free rate stays the same. What are the forward price and the value of the position in the forward contract? Now the forward price is (sample answer: $75.50)

and the initial value is (sample answer: +$5.50; or -$5.50)

Consider the competitive market for trader joe’s French brioche in Buffalo, The demand is given by Qd=100 – 5P, The supply is Qs=10+4P, a) Draw the supply and demand curve. b) What are the equilibrium point (equilibrium price and quantity)? c) Calculate the price elasticity of demand and price elasticity of supply at the equilibrium point, determine whether its elastic or inelastic? d) Suppose another trader joe store will open in buffalo, increasing the supply of French brioche by 18 at any price, what will happen to the market clearing price and quantity (hint: what will be the new supply curve, what will be the new equilibrium point) e) Suppose the government sets a price ceiling of $7 per unit of French brioche, will there be excess supply or excess demand? How much is it?