You are asked today to manage $20 million for one year and offered 25% of the portfolio's abnormal profit as compensation once the investment is over one year from today. You plan to use the compensation to realize your lifelong dream of owning a Ferrari 458 Spider. You expect that one year from today you will be able to purchase the car for $275,000 using only the compensation. You believe that the demand for ham and potato soup is going to increase sharply in the near future. Therefore, you are planning to invest the $20 million in one-year ham futures and one-year potato futures today. Currently, ham futures are trading for $0.80 per pound and potato futures are trading for $0.16 per pound. If the demand for "ham and potato soup" goes up, then ham will be priced at $0.92 per pound and potato will be priced at $0.232 per pound. If the demand does not change or goes down, then ham will be priced at $0.60 per pound and potato will be priced at $0.128 per pound. You believe that "demand going up is four times as likely as demand remaining same or going down. Covariance of ham futures with the market portfolio is 0.000128 and covariance of potato futures with the market portfolio is 0.001152. Annual risk-free rate is 3%. The market portfolio has an annual expected return of 8% and carries a standard deviation of 1.6%. The capital asset pricing model (CAPM) is the valid asset pricing model. Ignore transaction and margin costs. a. Your spouse, consistent with his/her task of demolishing your lifelong dreams, recommends that your portfolio consists of 20 million pounds of ham and 25 million pounds of potato today. Using quantitative analysis, determine whether your expected compensation from this portfolio is sufficient to purchase the Ferrari one year from today.10 b. Calculate how many pounds of ham and how many pounds of potato your portfolio should consist of today such that your expected compensation is just sufficient to purchase the Ferrari one year from today.11 You are asked today to manage $20 million for one year and offered 25% of the portfolio's abnormal profit as compensation once the investment is over one year from today. You plan to use the compensation to realize your lifelong dream of owning a Ferrari 458 Spider. You expect that one year from today you will be able to purchase the car for $275,000 using only the compensation. You believe that the demand for ham and potato soup is going to increase sharply in the near future. Therefore, you are planning to invest the $20 million in one-year ham futures and one-year potato futures today. Currently, ham futures are trading for $0.80 per pound and potato futures are trading for $0.16 per pound. If the demand for "ham and potato soup" goes up, then ham will be priced at $0.92 per pound and potato will be priced at $0.232 per pound. If the demand does not change or goes down, then ham will be priced at $0.60 per pound and potato will be priced at $0.128 per pound. You believe that "demand going up is four times as likely as demand remaining same or going down. Covariance of ham futures with the market portfolio is 0.000128 and covariance of potato futures with the market portfolio is 0.001152. Annual risk-free rate is 3%. The market portfolio has an annual expected return of 8% and carries a standard deviation of 1.6%. The capital asset pricing model (CAPM) is the valid asset pricing model. Ignore transaction and margin costs. a. Your spouse, consistent with his/her task of demolishing your lifelong dreams, recommends that your portfolio consists of 20 million pounds of ham and 25 million pounds of potato today. Using quantitative analysis, determine whether your expected compensation from this portfolio is sufficient to purchase the Ferrari one year from today.10 b. Calculate how many pounds of ham and how many pounds of potato your portfolio should consist of today such that your expected compensation is just sufficient to purchase the Ferrari one year from today.11
