Suppose my utility function for asset position x is given by u(x) = In(x). **Am I risk-averse, risk-neutral, or risk-seeking? I now have $20,000 and am considering the following two lotteries: L1: With probability 1, I lose $1,000. L2: With probability .9, I gain $0. L2: With probability .1, I lose $10,000. Determine which lottery I prefer and the risk premium of L2.
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- Suppose that you would like to create composite indexes from three stocks: stk1, stk2, stk3. Their stock prices (Pt) and total shares outstanding (Qt) from day 0 to day 1 are shown as follows: stk3 splits two-for-one in day 1. P0 Q0 P1 Q1 stk1 40 250 50 250 stk2 50 100 50 100 stk3 60 150 50 300 Which answer is the closest value to the rate of return on a price-weighted index of the three stocks? A. 20% B. 25% C. 30% D. 35%Suppose that a life insurance company insures 1 million 50-year-old people in a given year. (Assume a death rate of 5 per 1000 people.) The cost of the premium is $200 per year, and the death benefit is $50,000 What is the expected profit or loss for the insurance company?Suppose that spot and futures prices of the underlying asset when hedge is initiated are $3.10 and $2.50 respectively, and when hedge is closed out are $2.90 and $2.80 respectively. 1. What is the meaning of above numbers? 2. What is the basis risk when hedge is initiated? 3. What is the basis risk when hedge is closed out? 4. Is it a perfect hedge? 5. What will be the effective price received (paid) for the hedging asset? (S₂ + F₁-F₂
- A corporate bond that pays 4% per annum semi-annually has a yield of 3% p.a. withcontinuous compounding and a remaining life of 1.5 years (immediate after couponpayment). The yield on a similar risk-free bond is 2% p.a. with continuous compounding. The risk-free rates are 1% p.a. with continuous compounding for all maturities.Assume that the unconditional probability of default per every six months is a constantand that defaults can happen at the end of every six months (immediate before couponpayment). The recovery rate is 40%. Estimate the unconditional probability of defaultusing the “more exact calculation”.The government is attempting to determine whetherimmigrants should be tested for a contagious disease. Let’sassume that the decision will be made on a financial basis.Assume that each immigrant who is allowed into the countryand has the disease costs the United States $100,000, andeach immigrant who enters and does not have the diseasewill contribute $10,000 to the national economy. Assumethat 10% of all potential immigrants have the disease. Thegovernment may admit all immigrants, admit no immigrants,or test immigrants for the disease before determiningwhether they should be admitted. It costs $100 to test aperson for the disease; the test result is either positive ornegative. If the test result is positive, the person definitelyhas the disease. However, 20% of all people who do havethe disease test negative. A person who does not have thedisease always tests negative. The government’s goal is tomaximize (per potential immigrant) expected benefits minusexpected costs. Use a decision…A forward contract exists for a unit of two-year government securities with delivery to take place three years from now. Suppose the price of these securities three years from now is uniformly distributed from a low $800 to a high of $1,400. The one-year expected riskless rate of interest is 5 percent for all periods under consideration. If investors are risk neutral, what should be the current forward price? Suppose now that investors are risk averse and that the forward price is $1,200. What do you know about the relationship between the market value of two-year government securities and overall consumption? Continue to assume (as in (ii)) that the current forward price (at time 0) is $1,200. One year from now (at time 1) the forward price for the same item and same delivery date is $1,000. Determine the time 1 value (to the buyer) of the contract that was agreed upon at time 0.
- Suppose that 2% of the employed lose their job each month. Further suppose that 25% of the unemployed find a job each month. a. What is the average duration of employment in this labor market? b. Do you think this is a reasonable figure given estimates of the natural rate? Why or why not? c. If you wanted to reduce the steady-state level of unemployment, what type of policies might you pursue and why?Suppose that a consumer cannot vary hours of work as he or she chooses. In particular, he or she must choose between working q hours and not working at all, where q > 0. Suppose that dividend income is zero, and that the consumer pays a tax T if he or she works, and receives a benefit b when not working, interpreted as an unemployment insurance payment. a. If the wage rate increases, how does this affect the consumer’s hours of work? What does this have to say about what we would observe about the behavior of actual consumers when wages change? Explained also with the graph b. Suppose that the unemployment insurance benefit increases. How will this affect hours of work? Explain the implications of this for unemployment insurance programs. Explained also with the graphAn online cosmetic seller intends to send parcel on Cash On delivery in an attempt to increase her business. One out of every 10 parcels are returned, and the seller loses Rs. 350 (paid for delivery). But if the parcel is received, she gets a flat profit of Rs. 1000. Should she go for this new strategy? What is her expected net gain on each parcel?
- An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns. What are the (x,y) values? What is the optimal profit?An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns.(x, y)= What is the optimal profit?$Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the load
