CHAPTER 22 ESTIMATING RISK AND RETURN ON ASSETS RISK is the variability of an asset’s future returns. PROBABILITY AND PROBABILITY DISTRIBUTION Probability is the percentage chance that an event will occur and range between o to 1. If all possible events or outcomes are listed, and the probability is assigned to each event, the listing is called probability distribution. Example : For the election forecast, the following probability distribution could be set up. Outcome Probability Win 0.6 60% Lose 0.4 40% 1.0 100% Expected Value or Expected rate of return on investment is the weighted average of all possible returns from an investment, with the weights being the probability of each return. Objective Probability Distribution based on past outcomes of similar events. Subjective Probability Distribution based on opinions or educated guesses about the likelihood that an event will have a particular future outcome. Discrete Probability Distribution is an arrangement of the probabilities associated with the values of a variable that can assume a limited/finite number of values. Continuous Probability Distribution is an arrangement of probabilities associated with the values of a variable that can assume an infinite number of possible values. Exercise 1: Assume that 2 investment prospects are available to Mr. Martin who has a P100, 000 funds. He is considering the following: a. Investment in ABC Products Inc., a manufacturer and distributor of computer terminals and equipment for a rapidly growing data transmission industry, or b. Investment in PENELCO which supplies an essential service. The rate of return probability distributions for the two companies are as follows:
State of Economy Boom Normal Recession
State of Economy Boom Normal Recession
ABC PRODUCTS, INC. Probability of Rate of Return this State (%) Occurring .30 100 .40 15 .30 (70) Expected Value of Outcome PENELCO Probability of Rate of Return this State (%) Occurring .30 20 .40 15 .30 10 Expected Value of Outcome
Expected Rate of Return (%)
Expected Rate of Return (%)
EXPECTED PORTFOLIO RETURNS (Fp) - Weighted average of the expected returns from the individual assets in the portfolio. n
F p=∑ wi f i i =1
where:
wi = proportion of portfolio invested in asset fi = expected returnof asset n = number of assets in the portfolio
Exercise 2: DEF Properties is evaluating two opportunities, each having the same initial investment. The project’s risk and return characteristics are shown below: Project A Project B Expected Return 0.10 0.20 Proportion invested in each 0.50 0.50 project What is the expected return portfolio combining Project A and project B? STANDARD DEVIATION - A statistical measure of the variability of a probability distribution around its expected value. - It is calculated as follows: 1. Compute the expected value (f) 2. Subtract (f) fromeach possible return to obtain the deviations (ri – f) 3. Square each deviation (ri – f)2 4. Multiply each squared deciation by its probability of occurrence, pi(ri – f)2, and then add. The result is called the variance (σ2), which is the standard deviation squared. 5. Take the square root of the variance to get the standard deviation. where: pi = probability of outcome ri = return of value of outcome n = number of possible outcomes Exercise: Using the data of ABC Products, Inc. and PENELCO above. Compute the standard deviation. QUIZ NO. 2 1. The following projections are available for three alternative investments in equity stocks. Probability of Rate of Return if State Occurs State of State of Stock A StockB Stock C Economy Economy Boom .40 10% 15% 20% Recession .60 8% 4% 0% Required: 1. What would be the expected return on a portfolio with equal amounts invested in each of the three stocks? (Portfolio 1) 2. What would be the expected return if half of the portfolio were in A, with the remainder equally divided between B and C? (Portfolio 2) 3. Compute for the Standard Deviation using expected Portfolio 1 and Portfolio 2.
QUIZ NO. 1 A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information? QUIZ NO. 1 A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information? QUIZ NO. 1 A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information? QUIZ NO. 1 A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information? QUIZ NO. 1 A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information? QUIZ NO. 1 A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information? QUIZ NO. 1
A dealer in luxury yachts may order 0, 1, or 2 yachts for this season’s inventory. The cost of carrying each excess yacht is P50,000, and the gain for each yacht sold is Php 200,000. a. Compute for the expected value of each decision. b. What is the expected value with perfect information? c. What is the expected value of perfect information?
