portfolio that consists of stock X and stock Y. Compute the portfolio expected return and portfolio risk for each of the following percentages invested in stock X: a. 30% b. 50% c. 70% буху = 5113 d. On the basis of the results of (a) through (c), which port- folio would you recommend? Explain. 5.16 You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following information about the annual return (per $1,000) of each of these investments under different economic conditions is available, along with the probability that each of these economic conditions will occur: Economic Corporate Common Probability Condition Bond Fund Stock Fund 0.10 Recession 70 300 0.15 Stagnation 30 100 0.35 Slow growth 80 100 0.30 Moderate growth 100 150 0.10 High growth 120 350 Compute the a. expected return for the corporate bond fund and for the common stock fund. Q Search PDF PDF PDF PDF PDF ProbDistribution X Sampling Distribution.pdf E-Sign --- Create L J PCF PDF PDF Find text or tools B 0 Q 170 CHAPTER 5 Discrete Probability Distributions b. standard deviation for the corporate bond fund and for the common stock fund. c. covariance of the corporate bond fund and the common stock fund. d. Would you invest in the corporate bond fund or the com- mon stock fund? Explain 5.17 Suppose that in Problem 5.16 you wanted to create a portfolio that consists of the corporate bond fund and the common stock fund. Compute the portfolio expected return and portfolio risk for each of the following situations: a. $300 in the corporate bond fund and $700 in the common stock fund b. $500 in each fund. Oxf = 4161 c. $700 in the corporate bond fund and $300 in the common stock fund d. On the basis of the results of (a) through (c), which port- folio would you recommend? Explain. 5.3 Binomial Distribution The next three sections use mathematical models to solve business problems. MATHEMATICAL MODEL A mathemadcal model is a mathematical expression that represents a variable of interest. When a mathematical expression is available, you can compute the exact probability of occurrence of any particular outcome of the variable. The binomial distribution is one of the most useful mathematical models. You use the binomial distribution when the discrete random variable is the number of events of interest in a sample of n observations. The binomial distribution has four basic properties: ⚫ The sample consists of a fixed number of observations, n exhaustive categories. ⚫ Each observation is classified into one of two mutually exclusive and collectively ⚫ The probability of an observation being classified as the event of interest, , i constant from observation to observation. Thus, the probability of an observation being classified as not being the event of interest, 1-, is constant over all observations. ⚫ The outcome of any observation is independent of the outcome of any other observation. To ensure independence, the observations can be randomly selected either from an infinite population with or without replacement or from a finite popidation with replacement. Returning to the Saxon Home Improvement scenario presented on page 161 concerning the accounting information system, suppose the event of interest is defined as a tagged order form. You are interested in the number of tagged order forms in a given sample of orders. What results can occur? If the sample contains four orders, there could be none, one, two, three, or four tagged order forms. No other value can occur because the number of tagged the range of the binomial random variable is from 0 to n. order forms cannot be more than the sample size, n, and cannot be less than zero. Therefore, Suppose that you observe the following result in a sample of four orders: 50°F Cloudy First Order Second Order Tagged Tagged Third Order Not tagged Fourth Order Tagged What is the probability of having three tagged order forms in a sample of four orders in ability that each order occurs in the sequence is this particular sequence? Because the historical probability of a tagged order is 0.10, the prob- First Order T = 0.10 Second Order 0.10 Third Order Fourth Order = 0.90 TT = 0.10 Q Search