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Problem 7.9. (5 points) Assume the Capital Asset Pricing Model holds. You are given the following information about stock X, stock Y, and the market: . The required return and volatility for the market portfolio are 0.08 and 0.25, respectively. . The required return and volatility for the stock X are 0.06 and 0.4, respectively. . The correlation between the returns of stock X and the market is -0.25. The volatility of stock Y is 0.3. . The correlation between the returns of stock Y and the market is 0.2. Calculate the required return for stock Y. (a) 0.0489 (b) 0.0542 (c) 0.0691 (d) 0.0734 (e) None of the above.Solaris is the sole supplier of solar panels in Sunnylandia, Solaris has no fixed costs and can supply solar panels at a constant marginal cost MC of $10 per panel. There are two different categories of customers of solar energy, business and residential. The businesses' demand for solar panels is On(P) = 240-3P. The residential demand for solar panels is OR(P) = 80-5P.Residential market (R) f) Calculate the profit maximizing price Po and number of panels Qp that Solaris will choose to sell to residential clients, as well as the firm's profit NR - g) Use a diagram to illustrate the producer surplus PS. that Solaris enjoys, the consumer surplus of the residential clients CS&, and the deadweight loss DWZ. in the residential market. Then, compute CSR and DWLA. h) The government wants to encourage the production of solar panels for the residential market. In order to do so, it is willing to give to the monopoly a subsidy of s per panel, but the government wishes to calibrate this subsidy such that Solaris would supply an efficient quantity (that is, the same quantity as the one produced under perfect competition) in the residential market. Assuming that the government knows the demand and the costs that Solaris has, compute how much the subsidy s should be. i) Suppose the government wishes to finance the total cost of the subsidy given in h) to the residential market by taxing the panels sold in the business market. What is the minimum amount of tax per unit / that the government would have to charge Solaris for the panels sold in the business market in order to cover the total subsidy needed for the residential market?The AM92 table is based on the mortality of assured male lives in the UK. (i) As there is no corresponding mortality table for female lives, in order to calculate survival probabilities for female policyholders, an actuary decides to use the AM92 table, but with an 'age rating' of 4 years applied, ie a female aged x is considered to experience mortality equivalent to a male aged x-4. (a) Explain the rationale underlying this approach. (b) Calculate the probability that a female policyholder aged 62 survives for at least the next 10 years. (ii) A male policyholder aged 65 is known to be in poor health, and it has been determined that his mortality is 200% of AM92 Ultimate, ie he is subject to q, values equal to twice those of the AM92 Ultimate table. Calculate the probability that this policyholder will die before age 67. A select life table is to be constructed with a select period of two years added to the ELT15 (Males) table, which is to be treated as the ultimate table. Select rates are to be derived by applying the same ratios select : ultimate seen in the AM92 table, ie: qixl q, and 91x1+1 = 9[ * 1+1 qx+1 9 x +1 where the dash notation q, refers to AM92 mortality. Calculate the value of /(60] . The table below is part of a mortality table used by a life insurance company to calculate probabilities for a special type of life insurance policy. X 1x/+1 41 x/+2 4x1+3 /x+4 51 1,537 1,517 1,502 1,492 1,483 52 1,532 1,512 1,497 1,487 1,477 53 1,525 1,505 1,490 1,480 1,470 54 1,517 1,499 1,484 1,474 1,462 55 1,512 1,492 1,477 1,467 1,453 (i) Calculate the probability that a policyholder who was accepted for insurance exactly 2 years ago and is now aged exactly 55 will die between age 56 and age 57. (ii) Calculate the corresponding probability for an individual of the same age who has been a policyholder for many years. (mii) Comment on your answers to (i) and (ii)