Expected Return

6 Key excerpts on "Expected Return"

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  eBook - PDF

  Contributions to Mineralization

  • Ali Ismail Al-Juboury(Author)
  • 2018(Publication Date)
  • IntechOpen

    (Publisher)

  However, the most common understanding of capital profits is interest, which mainly relates to capital in value depiction, that is, money. In this work it is assumed that the return on invested capital consists of the return rate on capital , expected by investors (both owners and creditors) at a given risk level [9]. It is connected with opportunity cost, that is, Expected Return rate by the investors, which they may resign from when choosing a particular variant of action and therefore resigning from other possibilities available at that moment [11]. The significance of risk should be emphasized when defining the Expected Return rate. Investments of the same risk level have the same return rate. Consequently, the return rate expected by investors, in case of investing capital in a particular undertaking, should be at least equal to the highest total return that the investors could expect if they invested in an alternative portfolio of securities with a comparable risk [12]. According to this approach, the more risky the enterprise’s activity is, the higher return rate should be generated (compare with [13 ]). The Expected Return rate defined in this way has its interpretation in the price that the enterprise pays for the possibility of using capital. This price is expressed in a form of interest rate, reflecting the relation of expenses borne by the capital provider in a yearly scale due to putting capital at someone’s disposal and the value of this capital. In this depiction the Expected Return rate is strictly connected with the source of capital’s origin and accompanies capital coming from any source. It may be described as interest, dividends, other benefits, or even opportunity cost for capital providers. In subject literature the division emerged into the Expected Return rate on equity and debt capital. Individual financing sources, being the components of these groups, are characterized by a different return rate for capital providers.

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  eBook - ePub

  Equity Asset Valuation

  • Jerald E. Pinto(Author)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  For example, with a beginning price of €50.00, an ending or selling price of €52.00 six months later, and a dividend equal to €1.00 (all amounts referring to the past), the realized return is €1.00/€50.00 + (€52.00 − €50.00)/€50.00 = 0.02 + 0.04 = 0.06 or 6 percent over 6 months. In forward-looking contexts, holding-period returns are random variables because future selling prices and dividends may both take on a range of values. Nevertheless, an investor can form an expectation concerning the dividend and selling price and thereby have an expected holding-period return, or simply Expected Return, for the stock that consists of the expected dividend yield and the expected price appreciation return. Although professional investors often formulate Expected Returns based on explicit valuation models, a return expectation does not have to be based on a model or on specific valuation knowledge. Any investor can have a personal viewpoint on the future returns on an asset. In fact, because investors formulate expectations in varying ways and on the basis of different information, different investors generally have different Expected Returns for an asset. The comparison point for interpreting the investment implication of the Expected Return for an asset is its required return, the subject of the next section. 2.3. Required Return A required rate of return (for short, required return) is the minimum level of Expected Return that an investor requires in order to invest in the asset over a specified time period, given the asset’s riskiness. It represents the opportunity cost for investing in the asset—the highest level of Expected Return available elsewhere from investments of similar risk. As the opportunity cost for investing in the asset, the required return represents a threshold value for being fairly compensated for the risk of the asset

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  eBook - ePub

  Encyclopedia of Financial Models

  • Frank J. Fabozzi(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  p is sometimes called the holding period return or the ex post return.

  For example, consider the following portfolio consisting of three assets:

  Asset	Market Value at the Beginning of Holding Period	Rate of Return over Holding Period
  1	$6 million	12%
  2	$8 million	10%
  3	$11 million	5%

  The portfolio’s total market value at the beginning of the holding period is $25 million. Therefore,

  w 1  = $6 million/$25 million = 0.24, or 24% and R 1  = 12%

  w 2  = $8 million/$25 million = 0.32, or 32% and R 2  = 10%

  w 3  = $11 million/$25 million = 0.44, or 44% and R 3  = 5%

  Notice that the sum of the weights is equal to 1. Substituting into equation (1 ), we get the holding period portfolio return,

  The Expected Return of a Portfolio of Risky Assets

  Equation (1 ) shows how to calculate the actual return of a portfolio over some specific time period. In portfolio management, the investor also wants to know the expected (or anticipated) return from a portfolio of risky assets. The expected portfolio return is the weighted average of the Expected Return of each asset in the portfolio. The weight assigned to the Expected Return of each asset is the percentage of the market value of the asset to the total market value of the portfolio. That is,

  (3)

  The E () signifies expectations, and E (

  RP

  ) is sometimes called the ex ante return, or the expected portfolio return over some specific time period.

  The Expected Return, E (

  Ri

  ), on a risky asset i is calculated as follows. First, a probability distribution for the possible rates of return that can be realized must be specified. A probability distribution is a function that assigns a probability of occurrence to all possible outcomes for a random variable. Given the probability distribution, the expected value of a random variable is simply the weighted average of the possible outcomes, where the weight is the probability associated with the possible outcome.

  In our case, the random variable is the uncertain return of asset i . Having specified a probability distribution for the possible rates of return, the expected value of the rate of return for asset i is the weighted average of the possible outcomes. Finally, rather than use the term “expected value of the return of an asset,” we simply use the term “Expected Return.” Mathematically, the Expected Return of asset i

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  eBook - ePub

  Principles of Equity Valuation

  • Ian Davidson, Mark Tippett(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  2   The relationship between return and risk

  §2-1. In Chapter 1 , we identified some of the pitfalls that can arise from the incorrect calculation and averaging of the returns that accrue on shares, bonds, portfolios and other financial instruments. Historical returns are often used to provide guidance about the likely magnitude of future returns on a given security or financial instrument and of the current prices that ought to be paid for them. Moreover, historical returns are also used to assess the risks that are likely to arise from particular investments. Our purpose in this chapter is to summarize the relationships that exist between the returns that arise on particular investments and the risks that must be taken to achieve them. We also determine what implications these relationships will have for the pricing of risky assets. We begin our analysis in the next section with a consideration of how the risks associated with investments shape the returns that we can expect from them. We then go on to demonstrate how assets are priced so as to be compatible with the risks and returns that arise from them.

  §2-2.   Consider a portfolio comprising j = 1,2,3,4, …, N risky assets. The Expected Return on the portfolio, E(Rp ), will be

  where E(Rj ) is the Expected Return on the jth asset and wj is the proportion of the investor’s wealth that is invested in the jth asset. Sometimes, we will use the symbol μ = E(Rp ) to represent the Expected Return on the portfolio; the two symbols will be used interchangeably. Thus, the Expected Return on an N = 2 or two-asset portfolio will be computed from the following formula:

  We can illustrate the application of this formula by supposing that the Expected Return on the first asset is E(R1 ) = 0.2 or 20 per cent (per annum) and the Expected Return on the second asset is E(R2

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  Equity Markets and Portfolio Analysis

  • R. Stafford Johnson(Author)
  • 2014(Publication Date)
  • Bloomberg Press

    (Publisher)

  CHAPTER 6 Expected Rate of Return and Risk—Stock

  Introduction

  Although knowledge of present or past returns is important for security analysts, an investor is more concerned with what a security will yield in the future; that is, she wants to know the expected rate of return, as well as the chance that her expectations might be wrong. For example, after an in-depth analysis, an investor might think a stock would generate a 20 percent rate of return, but she also knows that under certain scenarios she might lose 10 percent or gain as much as 35 percent. Similarly, a bond investor who sees a bond trading to yield 10 percent also knows there is a chance of default in which he might lose 70 percent and also a chance that rates in the market might decrease, causing the bond to sell at a higher price and thus yielding a higher return than the current yield. Whether it is investments in stocks, bonds, investment fund shares, or commodities, investors must deal in a world of uncertainty. As a result, investors have to consider not only the expected rate of return, but also the risk that such a rate may not be attained.

  In this chapter, we extend our analysis of security valuation and return presented in Chapter 3 to stock risk and Expected Return. We begin by first defining a risk-free security and the difference between nominal and real rates of return. We next briefly examine the nature of risk as it relates to stocks. With this background, we then look at a security's Expected Return and risk statistically by examining return distributions and characteristics—mean, variance, and correlation parameters. Finally, we conclude the chapter by examining the relations between Expected Return and risk for a stock.

  Risk-Free Security, Nominal Rates, and Real Rates

  Investment risk is the possibility that the realized return from holding a security will deviate from the expected. Most securities are subject to risk. However, some securities, like a U.S. T-bill, have a future return that is known in advance. For example, an investor who plans to hold a T-bill to its maturity knows with certainty that at that date she will receive the principal. Thus, the rate of return from the time of the investment to maturity is known. Treasury bonds and notes—the Treasury's coupon issues—are, in turn, considered default free with known coupon and principal payments. However, they technically are not risk-free securities since investors are subject to reinvestment risk when they reinvest their coupon income at unknown rates.

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  CFIN

  • Scott Besley, Eugene Brigham, Scott Besley(Authors)
  • 2021(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  For this reason, most financial assets are held in portfolios. From an average investor’s standpoint, then, the fact that the price of one particular stock goes up or down is not very important. What is important is the return on his or her portfolio and the overall risk of the portfolio. As a result, the risk and return character- istics of an investment should not be evaluated in isola- tion; instead, the risk and return of an individual security should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held. Portfolio Returns. The Expected Return on a portfolio, r / p , is simply the weighted average of the Expected Returns on the individual stocks held in the portfolio, with each stock’s weight being the proportion of the total funds invested in that stock (Equation 8.6): Here r / j represents the Expected Return on Stock j, w j is the weight that represents the proportion of the total funds invested in Stock j, and the portfolio includes N stocks (investments). Note two points: (1) w j is equal to the value of the investment in Stock j divided by the total value of the portfolio and (2) the w j s must sum to 1.0. To illustrate, suppose securities analysts estimate the following Expected Returns on four large companies: If we formed a $100,000 portfolio by investing $25,000 in each of these four stocks, the expected portfolio return of this portfolio would be 11.0 percent: Of course, after the fact and one year later, the actual realized rate of return, r $ , on each stock will almost cer- tainly differ from its expected value, so r $ p will be some- what different from r / p 5 11%. For example, Microsoft’s stock might double in price and provide a return of 1100 percent, whereas Citigroup’s stock price might fall sharply and provide a return of 275 percent.

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