...Risk and return will be very central terms in our analysis and it is essential that the reader clearly understands the meaning of each term and how assets with different payout structures can be compared. General utility theory suggests that the average investor is risk averse. Given the same expected return of two assets with different risks, he would prefer the one with less risk. (This assumption may not be perfectly true for all individuals in all situations, but for the investor community as a whole it is probably true). For an asset with uncertain cash flows and payoffs, which are normally distributed, the mean of the distribution will be the expected return while the standard deviation forms some kind of “risk”. Choosing the “less risky” asset therefore comes down to choosing the asset with the lowest standard deviation in its payout distribution. An investor could also approach the problem from the other direction, choosing among assets with the same risk and then choose the asset with the highest expected return. Risk is usually defined as the volatility of returns, measured by standard deviation. The variance of a portfolio depends not only on the individual variances of the as- sets, but also on the co-variances between the components of the portfolio. As an extreme example, a portfolio consisting of two securities – a long position in a stock and with an appropriately chosen position in a put option on the same stock – will have lower...
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...Period Return HPR=(Ending price-Beginning price+Dividend during period one)/(Beginning price)=(P_1-P_0+D_1)/P_0 Dividend Yield: % return from dividends Expected Return and Standard Deviation E(r)=∑_s▒〖p_s r_s 〗 σ=√(∑_s▒〖p_s (r_s-E(r))〗^2 ) Expected end-of-year value of the investment =Dividend+Ending Price Arithmetic and Geometric Averages Arithmetic Mean (AM) =(∑▒HPR)/N Better predictor of future performance Geometric Mean (GM) = π(1+HPR) )^(1/N)-1 Better measure of past performance GM < AM Sharpe Ratio Sharpe Ratio for Portfolios =(Excess Return)/(SD of Excess Return)=(R_i-R_f)/(σ(R_i-R_f)) Measure the attraction of an investment portfolio by comparing its reward (risk premium) and risk (SD) Excess return per unit of risk Reward-to-variability (volatility) ratio Historical Returns on Risky Portfolios Asset classes that provide higher return are more risky Return: Small Stocks > Large Stocks > Bonds > Bills Risk: Small Stocks > Large Stocks > Bonds > Bills Risk Premium Extra reward (returns) for bearing the risk of investing in equities, rather than in low risk investments, such as bills or bonds Risk Premium=E(r)-r_f Asset Allocation: Four Step Process Step 1: Assessing Risk Tolerance Step 2: Measuring Portfolio Risk and Return Step 3: Modeling Investment Options Step 4: Optimal Asset Allocation Step 1: Assessing Risk Tolerance Dominated Assets Easy to remove from consideration Always choose higher risk premium...
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...Exercises E8-1. Total annual return Answer: ($0 $12,000 $10,000) $10,000 $2,000 $10,000 20% Logistics, Inc. doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. E8-2. Expected return Answer: Analyst 1 2 3 4 Total Probability 0.35 0.05 0.20 0.40 1.00 Return 5% 5% 10% 3% Expected return Weighted Value 1.75% 0.25% 2.0% 1.2% 4.70% E8-3. Comparing the risk of two investments Answer: CV1 0.10 0.15 0.6667 CV2 0.05 0.12 0.4167 Based solely on standard deviations, Investment 2 has lower risk than Investment 1. Based on coefficients of variation, Investment 2 is still less risky than Investment 1. Since the two investments have different expected returns, using the coefficient of variation to assess risk is better than simply comparing standard deviations because the coefficient of variation considers the relative size of the expected returns of each investment. E8-4. Computing the expected return of a portfolio Answer: rp (0.45 0.038) (0.4 0.123) (0.15 0.174) (0.0171) (0.0492) (0.0261 0.0924 9.24% The portfolio is expected to have a return of approximately 9.2%. E8-5. Calculating a portfolio beta Answer: Beta (0.20 1.15) (0.10 0.85) (0.15 1.60) (0.20 1.35) (0.35 1.85) 0.2300 0.0850 0.2400 0.2700 0.6475 1.4725 E8-6. Calculating the required rate of return Answer: a. Required return 0.05 1.8 (0.10 0.05) 0.05 0.09 0.14 b. Required return 0.05 1.8 (0.13 0.05) 0.05 0.144 0.194 c. Although the risk-free rate does not change...
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...Investment and Portfolio Management: Risk and Return Marvin Brown is a savvy investor who is always looking for a sound company to include in his portfolio of stocks and bonds. Being somewhat risk-averse, his main objective is to buy stock in firms that are mature and well-established in their respective industries. Wal-Mart is one of the stocks Marv is currently considering for inclusion in his portfolio. Wal-Mart has four major areas of business: traditional Wal-Mart discount stores, Supercenters, Sam's Clubs, and international operations. Although Wal-Mart was established over 50 years ago, it continues to achieve growth through expansion. The Supercenter concept, which combines groceries and general merchandise, is extreme success as 75 new Supercenters were opened last year alone. Another 95 will be opening over the next two years. Sam's clubs have also seen success as 99 Pace stores (Pace is one of Sam's former Competitors) were converted to Sam's stores in 1995. In addition to taking over competitor stores, Sam's also opened 22 new stores of its own. Internationally, the picture is equally as rosy. In Canada, 122 former Woolco stores were converted to Wal-Mart discount stores. Expansion has reached Mexico and Hong Kong as well, as 24 Clubs and Supercenters and 3 "Value Clubs" were established, respectively. Wal-Mart plans to continue its reign as the world's largest retailer through expansion by developing the previously discussed 95 Wal-Mart discount stores, 12 new Supercenters...
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...__________ risk of the portfolio decreases until 10 to 20 securities are included. The portion of the risk eliminated is __________ risk, while that remaining is __________ risk * o diversifiable; nondiversifiable; total o relevant; irrelevant; total o total; diversifiable; nondiversifiable o total; nondiversifiable; diversifiable The higher an asset's beta, * o the more responsive it is to changing market returns o the higher the expected return will be in a down market o the lower the expected return will be in an up market o the less responsive it is to changing market returns __________ probability distribution shows all possible outcomes and associated probabilities for a given event * o A continuous o An expected value o A discrete o A bar chart A beta coefficient of 0 represents an asset that * o is less responsive than the market portfolio o has the same response as the market portfolio o is more responsive than the market portfolio o is unaffected by market movement The financial manager's goal for the firm is to create a portfolio that maximizes return in order to maximize the value of the firm * o False o True The security market line (SML) reflects the required return in the marketplace for each level of nondiversifiable risk (beta) * 212 Gitman • Principles of Finance, Eleventh Edition o False o True The portion of an asset's risk that is attributable to firm-specific, random causes is called * o systematic risk o unsystematic...
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...Chapter 11 Return and Risk: The Capital Asset Pricing Model (CAPM) Copyright © 2015 by the McGraw-Hill Education (Asia). All rights reserved. 11.1 Individual Securities The characteristics of individual securities that are of interest are the: Expected Return Variance and Standard Deviation Covariance and Correlation (to another security or index) 11-1 11.2 Expected Return, Variance, and Covariance Consider the following two risky asset world. There is a 1/3 chance of each state of the economy, and the only assets are a stock fund and a bond fund. Scenario Recession Normal Boom Rate of Return Probability Stock Fund Bond Fund 33.3% -7% 17% 33.3% 12% 7% 33.3% 28% -3% 11-2 Expected Return Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock Fund Rate of Squared Return Deviation -7% 0.0324 12% 0.0001 28% 0.0289 11.00% 0.0205 14.3% Bond Rate of Return 17% 7% -3% 7.00% 0.0067 8.2% Fund Squared Deviation 0.0100 0.0000 0.0100 11-3 Expected Return Scenario Recession Normal Boom Expected return Variance Standard Deviation Stock Fund Rate of Squared Return Deviation -7% 0.0324 12% 0.0001 28% 0.0289 11.00% 0.0205 14.3% Bond Fund Rate of Squared Return Deviation 17% 0.0100 7% 0.0000 -3% 0.0100 7.00% 0.0067 8.2% E (rS ) 1 (7%) 1 (12%) 1 (28%) 3 3 3 E (rS ) 11% 11-4 Variance Scenario ...
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...Return, Risk and The Security Market Line - An Introduction to Risk and Return Whether it is investing, driving or just walking down the street, everyone exposes themselves to risk. Your personality and lifestyle play a big role in how much risk you are comfortably able to take on. If you invest in stocks and have trouble sleeping at night, you are probably taking on too much risk. (For more insight, see A Guide to Portfolio Construction.) Risk is defined as the chance that an investment's actual return will be different than expected. This includes the possibility of losing some or all of the original investment. Those of us who work hard for every penny we earn have a hard time parting with money. Therefore, people with less disposable income tend to be, by necessity, more risk averse. On the other end of the spectrum, day traders feel that if they aren't making dozens of trades a day, there is a problem. These people are risk lovers. When investing in stocks, bonds or any other investment instrument, there is a lot more risk than you'd think. In this section, we'll take a look at the different kind of risks that often threaten investors' returns, ways of measuring and calculating risk, and methods for managing risk. Expected Return, Variance and Standard Deviation of a Portfolio Expected return is calculated as the weighted average of the likely profits of the assets in the portfolio, weighted by the likely profits of each asset class. Expected return is calculated...
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...CHAPTER 13 RISK, RETURN, AND THE SECURITY MARKET LINE Answers to Concepts Review and Critical Thinking Questions 1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique portion of the total risk can be eliminated at little cost. On the other hand, there are some risks that affect all investments. This portion of the total risk of an asset cannot be costlessly eliminated. In other words, systematic risk can be controlled, but only by a costly reduction in expected returns. 2. If the market expected the growth rate in the coming year to be 2 percent, then there would be no change in security prices if this expectation had been fully anticipated and priced. However, if the market had been expecting a growth rate other than 2 percent and the expectation was incorporated into security prices, then the government’s announcement would most likely cause security prices in general to change; prices would drop if the anticipated growth rate had been more than 2 percent, and prices would rise if the anticipated growth rate had been less than 2 percent. 3. a. systematic b. unsystematic c. both; probably mostly systematic d. unsystematic e. unsystematic f. systematic 4. a. a change in systematic risk has occurred; market prices in general will most likely decline. b. no change in unsystematic risk; company price will most likely stay constant. c. no change in systematic risk; market prices...
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...Chapter 5 Risk and Return 5.1 RATES OF RETURN McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Learning objectives Use data on the past performance of stocks and bonds to characterize the risk and return features of these investments Determine the expected return and risk of portfolios that are constructed by combining risky assets with risk-free investment in Treasury bills Evaluate the performance of a passive strategy McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Holding Period Return The holding period return (HPR)(보유기간수익률) Depends on the increase (or decrease) in the price of the share over the investment period as well as on any dividend income. Rate of return over a given investment period McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Example 5.1 Suppose you are considering investing some of your money, now all invested in a bank account, in a stock market index fund. The price of a share in the fund is currently $100, and your time horizon is one year. You expect the cash dividend during the year to be $4, so your expected dividend yield is 4%. Your HPR will depend on the price one year from now. Suppose your best guess is that it will be $110 per share. The your capital gain will be $10 (110-100), so your capital gains yield is $10/$100=.10 or 10%. The total holding period rate of return is the sum of the dividend...
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...Determining the cost of equity and rate of return is an important financial principle. Company shareholders are able to make intelligent decisions when the information is readily available. This paper will describe three specific theories and models that yield the cost of equity. After providing a clear description of all three, I will focus on one particular model, the Capital Asset Pricing Model (CAPM), which is a simplistic approach to cost of equity. Then lastly, the CAPM will be applied to a few companies and discussed. Three Models There are several tools available to estimate the rate of return. Three of these tools are capital asset pricing model, the dividend growth model, and arbitrage pricing theory. Although similar, each has their distinct differences. The first model is the capital asset pricing model. This particular model “describes the relationship between risk and expected return, and it serves as a model for the pricing of risky securities.” (Investopedia, N.D.) It goes on to say that if the overall risk outweighs the return, investors should disregard as this would be a loss. CAPM is calculated by using the following formula: “Required (or expected) Return = RF Rate + (Market Return - RF Rate)*Beta” (Investopedia, N.D.) As shown, this calculation factors in a beta rate. The rule of thumb is, the larger the beta rate, the more risk. If the market is up (bull), and there is a high beta, the payout will be high. However, if the market is low...
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...RISK –RETURN TRADE -OFF ON THE NIGERIAN STOCK EXCHANGE OLOWE, OLUSEGUN BANKING AND FINANCE DEPARTMENT COVENANT UNIVERSITY OTA. NIGERIA E-mail: oreoba2000@yahoo.com oreoba2000@gmail.com 1 ABSTRACT Expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist for long period. Changes in investment opportunities can alter the risk-return trade-off of bonds, stocks, and cash across investment horizons, thus creating a term structure of the risk-return trade-off. This term structure can be extracted from a parsimonious model of return dynamics, which was illustrated with data from the stock market in Nigeria using the VAR model in the light of the reforms in the financial services sector coupled with the stock market crash and the global financial crisis. Using annual returns over the period of 1981 to 2008, volatility persistence, asymmetric properties and riskreturn relationship are investigated for the Nigerian stock market visà-vis the calendar effects on stock market performances. The degree of volatility persistence and leverage effect supporting the work of Nelson (1991) was visible in the relationship between value index of stocks, market capitalization and the volume of transactions. Key words: Calendar effect, Volatility, Stock market, Financial Reforms, Global Financial crisis, Volatility persistence, VAR, Risk-return tradeoff 2 INTRODUCTION The major flow...
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...vehicle in the next five years. The vehicle I am most interested in purchasing is the Ford Escape and at this time the 2012 Ford Escape is roughly around $21,440.00 for a base model. I would ideally like to buy this vehicle with a very small loan, and pay at least half of the cost of the vehicle as a down payment. While it might be best to pay full price for the vehicle as I have a very low credit scoring and it is hard for me to get approved for a loan without a co-signer, I know that if I would like to build up my credit rating I will need to at least take a loan out on half of the cost of the vehicle and make monthly payments on time for a few years. By using the Savings calculator available on Bankrate.com, and assuming a 0.78% rate of return on my savings for the next 5 years (as provided by the Treasury Department (USDT, 2011)), I would need to save $200.00 a month to reach my savings goal. Based on this data, I would need to save $200.00 x 12 = $2,400.00 per year. If I continued to save this amount then at the end of the five years I will have saved $12,234.90 to put as a down payment on my dream vehicle. Considering the time value of money to be the quantification of the value of a dollar over time, my regard for the money that I am saving says that I am much more interested in my dream vehicle than using that money for other purposes. Moreover, my dream car is worth more to me in the future than that money can be for me today as well as knowing that I was able to purchase...
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...第四章 风险衡量 第一节 风险的数学表达 对于风险，理论上还没有统一的定义。风险都是源自未来事件的不确定性，从数学角度看，它表明的是各种结果发生的可能性。在公司金融学中，研究风险是为了研究投资的风险补偿，对风险的数学度量，是以投资（资产）的实际收益率与期望收益率的离散程度来表示的。最常见的度量指标是方差（[pic]或[pic]）和标准差（[pic]）。 一、单项证券的期望和方差 将投资收益率视为一个随机变量（[pic]）。期望收益率是指投资前所能预期的所有可能的收益率的期望平均值，用[pic]或[pic]表示。收益率的方差或标准差表示收益率对于期望值的偏离程度，偏离程度越高，未来收益率越波动，风险也越大。 下面以股票投资的例子来说明投资收益率的这些指标是如何计算的。 【例4.1】假设股票A一年后的投资收益率会根据未来不同的经济情况而变化，具体预测情况见表4—1。 表4—1股票A一年后预期收益率情况表 |经济情况 |发生概率（P） |股票A一年后预期收益率（[pic]） | |经济繁荣 |0.5 |20％ | |经济稳定 |0.1 |5％ | |经济衰退 |0.4 |－10％ | 1. 股票A的期望收益率 [pic]＝0.5×20％＋0.1×5％＋0.4×(－10％)＝6.5% 2. 股票A的方差 [pic]＝0.020025 3. 股票A的标准差 [pic]=0.141510=14.15%。 上例中，假设收益率只有三种可能的情况出现，股票A的收益率是离散型分布。如果股票A的收益率连续型分布，有无限的可能结果，就需要根据连续型分布的特征，运用积分计算期望收益率以及方差和标准差。对收益率的一个经常的假设是它符合正态分布。正态分布是对称分布，其特点是只有两个特征变量，即期望值和方差（或标准差）。因此，如果我们已知股票A收益率的期望与方差并且符合正态分布，就可以知道预期收益率的所有变化情况（见图4—1）。 图4—1 股票A收益率服从正态分布 二、证券之间的协方差和相关系数 方差和标准差表示了单个股票收益率的变动程度，如果我们要研究两个证券之间互动关系，就需要了解它们之间的协方差和相关系数。仍以例子说明协方差及相关系数的涵义和计算方法。 【例4.2】 股票A和股票B的相关信息见表4—2，计算股票A、B的协方差和相关系数，分别以[pic]和[pic]表示。 |经济情况 |发生概率（P） |股票A的预期收益率（[pic]） |股票B的预期收益率（[pic]） | |经济繁荣...
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...Risk and Return Essay: Mortgage Crisis of 2008 The American Dream has been a standard set centuries ago with ideas full of prosperity and success that would drive families upward in the social ladder. The American Dream has become the character by which our country is defined; therefore, it has long been a land that is desired by others living in conditions that aren’t geared toward this ideology. It has changed throughout the years as different historical marks have altered the mindset of the United States. The ability to pursue happiness outright, education, owning a business, and leaving a legacy is the pipeline for this dream that is sought not only by people in the United States, but also by those seeking to establish themselves in this land that is overflowing with honey. One of the major factors in the American Dream which hasn’t changed much over the course of time is homeownership. Homeownership is becoming an exclusive members’ club (Jones, 2014). The increase in homeownership after 2001 provided a big boom for our economy; temporarily. In 1999, Congress passed the Gramm-Leach-Bliley Act, which was also known as the Financial Services Modernization Act of 1999. This law repealed some of the Glass-Steagall Act of 1933, allowing banks, securities companies, and insurance companies to act as a combination of an investment back, commercial bank, and an insurance company which created financial supermarkets (Jenkins, 2012). The United States economy was in...
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...Risk and Return Concepts Prepared by: JQY Risk and Return Concepts • Measures of risk and returns • Portfolio risk and returns • CAPM Return – what is earned on an investment: the sum of income and capital gains generated by an investment. Risk – possibility of loss; the uncertainty that the anticipated return will not be achieved. Risk and Return? If you have PHP 1,000,000, will you invest in: 5% 20% Risk and Return General Rule of Thumb: More Risk = More Returns Less Risk = Less Returns It depends on the investor: Risk Seeking – prefers high risk investments Risk Neutral – willing to take on moderate risk Risk Averse – conservative, unwilling to take on high risk investments unless the returns justify and compensates for the high risk taken. Relative Risk & Returns of Asset Classes Source: http://www.weblivepro.com/articles/cpp/cppinfo.aspx Measures of Returns • Historical Returns ▫ Holding Period Return ▫ Alternative Measures Arithmetic Mean Geometric Mean Harmonic Mean • Expected Returns Measuring Historical Returns • Holding Period Return ▫ Total return on an asset or portfolio over the period during which it was held ▫ HPR = MV1 – MV0 + D MV0 MV1 = market value, end MV0 = market value, beginning D = cumulative cash distributions (at the end of period) • Annualized HPR ▫ (1 + HPR) ^ 1/n – 1 Measuring Historical Returns • Example: Mr. A bought an asset in 2005 for P100. He kept it...
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