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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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- A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). (a) Calculate the expected profit if the firm follows this benchmark strategy, i.e., E(L)A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). Now suppose the firm can also buy forward contracts on foreign currency to neutralize the effect of the exchange rate on profits. Assume that these provide complete hedging, but that it involves an additional cost, so that following the…A construction company renovates old homes at Garden East in Karachi. Over the time, the company has found that its rupee volume of renovation work is dependent on the area’s payroll. The figures for the company’s revenues and the amount of money earned by wage earners in the area for the past six years are presented in Table 3. If the payroll for next year is expected to be PKR 600 thousand, then what is the predicted value for the company’s sales (include error of prediction in your answer)? Do this for all prediction models. Local Payroll (PKR 100,000/=) Company’s sales (PKR 100,000/=) 3 6 4 8 6 9 4 5 2 4.5 5 9.5 ii) If in part a (above), if we add another input variable along with Local Payroll, then we will obtain a multiple regression model for predicting Company’s sales. How should the correlation between the…
- Consider the following data: Stock M N Average return 26% 16% Risk (Std. Dev.) 20% 10% If the return on stocks M and N are perfectly negatively correlated, what is the range of risk (std dev) associated with all possible portfolio combinations? A. Range of the risk: between 0= risk s10 % OB. Range of the risk: between 0 < risk 10% OC. Range of the risk: between 5% and 10%. OD. Range of the risk (std. dev): between 15% to 20% OE. None of the aboveThe Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 14.7% (i.e. an average gain of 14.7%) with a standard deviation of 33%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. A) What percentage of years does this portfolio lose money, i.e. have a return less than 0%? B) What is the cutoff for the highest 15% of annual returns with this portfolio?Question 3 (Minimum-variance Hedging) A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient…
- i need the answer quickly3.8 CAPM: The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 14.7% (i.e. an average gain of 14.7%) with a standard deviation of 33%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. (please round answers to within one hundredth of a percent) (a) What percent of years does this portfolio lose money, i.e. have a return less than 0%? % (b) What is the cutoff for the highest 15% of annual returns with this portfolio? %A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
- ,./Data on the 30 largest bond funds provided one-year and five-year percentage returns for theperiod ending March 31, 2000 (The Wall Street Journal, April 10, 2000). Suppose we consider aone-year return in excess of 2% to be high and a five-year return in excess of 44% to be high.One-half of the funds had a one-year return in excess of 2%, 12 of the funds had a five-yearreturn in excess of 44%, and six of the funds had both a one-year return in excess of 2% and afive-year return in excess of 44%.a. Find the probability of a fund having a high one-year return, the probability of a fundhaving a high five-year return, and the probability of a fund having both a high one-yearreturn and a high five-year return.b. What is the probability that a fund had a high one-year return or a high five-year returnor both?c. What is the probability that a fund had neither a high one-year return nor a high fiveyear return?The recent economic downturn resulted in the loss of jobs and an increase in delinquentloans for housing. In projecting where the real estate market was headed in the comingyear, economists studied the relationship between the jobless rate and the percentage ofdelinquent loans. The expectation was that if the jobless rate continued to increase, therewould also be an increase in the percentage of delinquent loans. The following data showthe jobless rate and the delinquent loan percentage for 27 major real estate markets. a. Compute the correlation coefficient. Is there a positive correlation between the joblessrate and the percentage of delinquent housing loans? What is your interpretation?b. Show a scatter diagram of the relationship between the jobless rate and the percentage