Managerial Finance l
Microsoft Word - Document1 Assignment 08 – Risk and Return BU340 – Managerial Finance Directions: Unless otherwise stated, answer in complete sentences, and be sure to use correct English spelling and grammar. Sources must be cited in APA format. Your response should be four (4) pages in length. Respond to the items below. Part A: Moore Company is about to issue a bond with semiannual coupon payments, a coupon rate of 8%, and par value of $1,000. The yield-to-maturity for this bond is 10%. a. What is the price of the bond if the bond matures in 5, 10, 15, or 20 years? b. What do you notice about the price of the bond in relationship to the maturity of the bond? Part B: The Crescent Corporation just paid a dividend of $2 per share and is expected to continue paying the same amount each year for the next four years. If you have a required rate of return of 13%, plan to hold the stock for four years, and are confident that it will sell for $30 at the end of four years, how much should you offer to buy it at today? Part C: Use the information in the following table to answer the questions below: State of Economy Probability of State Return on A in State Return on B in State Return on C in State Boom .35 0.040 0.210 0.300 Normal .50 0.040 0.080 0.200 Recession .15 0.040 -0.010 -0.260 a. What is the expected return of each asset? b. What is the variance of each asset? c. What is the standard deviation of each asset? BU340V Chapter 8.pptx Financial Management: Core Concepts Fourth Edition Chapter 8 Risk and Return Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. If this PowerPoint presentation contains mathematical equations, you may need to check that your computer has the following installed: 1) MathType Plugin 2) Math Player (free versions available) 3) NVDA Reader (free versions available) 1 Learning Objectives (1 of 2) 8.1Calculate profits and returns on an investment and convert holding period returns to annual returns. 8.2Define risk and explain how uncertainty relates to risk. 8.3Appreciate the historical returns of various investment choices. 8.4Calculate standard deviations and variances with historical data. 8.5Calculate expected returns and variances with conditional returns and probabilities. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Learning Objectives (2 of 2) 8.6Interpret the trade-off between risk and return. 8.7Understand when and why diversification works at minimizing risk, and understand the difference between systematic and unsystematic risk. 8.8Explain beta as a measure of risk in a well-diversified portfolio. 8.9Illustrate how the security market line and the capital asset pricing model represent the two-parameter world of risk and return. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 Returns Performance analysis of an investment requires investors to measure returns over time. Return and risk being intricately related, return measurement helps in the understanding of investment risk. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (A) Dollar Profits and Percentage Returns (1 of 4) Dollar profit or loss = Ending value + Distributions − Original cost Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (A) Dollar Profits and Percentage Returns (2 of 4) Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (A) Dollar Profits and Percentage Returns (3 of 4) Example 1: Calculating Dollar and Percentage Returns Joe bought some gold coins for $1000 and sold those 4 months later for $1200. Jane on the other hand bought 100 shares of a stock for $10 and sold those 2 years later for $12 per share after receiving $0.50 per share as dividends for the year. Calculate the dollar profit and percent return earned by each investor over their respective holding periods. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (A) Dollar Profits and Percentage Returns (4 of 4) Example 1: Answer Joe’s Dollar profit= Ending value − Original cost = $1200 − $1000 = $200 Joe’s HPR = Dollar profit ÷ Original cost = $200 ÷ $1000 = 20% Jane’s Dollar profit= Ending value + Distributions − Original cost = $12 × 100 + $0.50 × 100 − $10 × 100 = $1200 + $50 − $1000 = $250 Jane’s HPR= $250 ÷ $1000 = 25% Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (B) Converting Holding Period Returns to Annual Returns (1 of 3) With varying holding periods, holding period returns not good for comparison. Necessary to state an investment’s performance in terms of an annual percentage rate (APR) or an effective annual rate of return (EAR) by using the following conversion formulas: Simple annual return or APR = HPR ÷ n EAR = (1 + HPR)1 ÷ n − 1 Where n is the number of years or proportion of a year that the holding period consists of. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (B) Converting Holding Period Returns to Annual Returns (2 of 3) Example 2: Comparing HPRs Given Joe’s HPR of 20% over 4 months and Jane’s HPR of 25% over 2 years, is it correct to conclude that Jane’s investment performance was better than that of Joe? Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (B) Converting Holding Period Returns to Annual Returns (3 of 3) Example 2: Answer Compute each investor’s APR and EAR and then make the comparison. Joe’s holding period (n) = 4 ÷ 12 = 0.333 years Joe’s APR = HPR ÷ n = 20% ÷ 0.333 = 60% Joe’s EAR = (1 + HPR)1 ÷ n − 1 = (1.20)1 ÷ .33 − 1 = 72.89% Jane’s holding period = 2 years Jane’s APR = HPR ÷ n = 25% ÷ 2 = 12.5% Jane’s EAR = (1 + HPR)1 ÷ n − 1 = (1.25)1 ÷ 2 − 1 = 11.8% Clearly, on an annual basis, Joe’s investment far outperformed Jane’s investment. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (C) Extrapolating Holding Period Returns (1 of 2) Extrapolating short-term HPRs into APRs and EARs is mathematically correct, but often unrealistic and infeasible. Implies earning the same periodic rate over and over again in 1 year. A short holding period with fairly high HPR would lead to huge numbers if return is extrapolated. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.1 (C) Extrapolating Holding Period Returns (2 of 2) Example 3: Unrealistic Nature of APR and EAR. Let’s say you buy a share of stock for $2 and sell it a week later for $2.50. Calculate your HPR, APR, and EAR. How realistic are the numbers? N = 1 ÷ 52 or 0.01923 of 1 year. Profit = $2.50 − $2.00 = $0.50 HPR = $0.5 ÷ $2.00 × 100 = 25% APR= 25% ÷ 0.01923 = 1300% or = 25% × 52 weeks = 1300% EAR = (1 + HPR)52 − 1 = (1.25)52 − 1 × 100 = 10,947,544.25% Answer: Highly Improbable! Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.2 Risk (Certainty and Uncertainty) Future performance of most investments is uncertain. Risky → Potential for loss exists Risk can be defined as a measure of the uncertainty in a set of potential outcomes for an event in which there is a chance of some loss. It is important to measure and analyze the risk potential of an investment, so as to make an informed decision. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.3 Historical Returns (1 of 2) Figure 8.1 Histograms of (A) U.S. Treasury bills from 1950 to 1999, (B) long-term government bonds from 1950 to 1999, (C) large company stocks from 1950 to 1999, and (D) small company stocks from 1950 to 1999. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.3 Historical Returns (2 of 2) Small company stocks earned the highest average return (17.10%) over the 5 decades, but also had the greatest variability 29.04%, and widest range. (103.39% − (−40.54%)) = 143.93%), and were most spread out. Three-month treasury bills earned the lowest average return, 5.23%, but their returns had very low variability (2.98%), a very small range (14.95%−0.86% = 15.91%) and were much closely clustered around the mean. Returns and risk are positively related. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.4 Standard Deviation as a Measure of Risk (1 of 4) Variance and standard deviation are measures of dispersion. Helps researchers determine how spread out or clustered together a set of numbers or outcomes is around their mean or average value. The larger the variance, the greater is the variability and hence the riskiness of a set of values. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.4 Standard Deviation as a Measure of Risk (2 of 4) Example 4: Calculating the Variance of Returns for Large-Company Stocks Listed below are the annual returns associated with the large-company stock portfolio from 1990 to 1999. Calculate the variance and standard deviation of the returns. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.4 Standard Deviation as a Measure of Risk (3 of 4) YearReturn(R-Mean)(R-Mean)2 1990−3.20%−22.19%0.0492396 199130.66%11.67%0.0136189 19927.71%−11.28%0.0127238 19939.87%−9.12%0.0083174 19941.29%−17.70%0.031329 199537.71%18.72%0.0350438 199623.07%4.08%0.0016646 199733.17%14.18%0.0201072 199828.58%9.59%0.0091968 199921.04%2.05%0.0004203 Total189.90%Blank.18166156 Average18.99%BlankBlank Variance0.020184618BlankBlank Std. Dev14.207%BlankBlank Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 8.4 Standard Deviation as a Measure of Risk (4 of 4) Example 4: Answer Variance= ∑(R-Mean)2 ÷ N − 1 = 0.18166156 ÷ 10 − 1 = 0.020184618 Std. Dev. = √Variance = √.020184618 = 14.207% Copyright © 2019, 2016, 2013 Pearson Education