Risk Premium

12 Key excerpts on "Risk Premium"

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  eBook - PDF

  Risk Parity Fundamentals

  • Edward E. Qian(Author)
  • 2016(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  36 ◾ Risk Parity Fundamentals their portfolio. This hedging is most useful during a time of financial stress but it seems to come at a cost to the portfolio’s return over the long run. 2.3.1 Risk Premium 101 Risk Premium, or the expected return of an investment in excess of the return on the risk-free asset or cash, is a required return to compensate investors for taking investment risk. Not all risks have rewards or Risk Premiums. First, it is useful to consider why some risks have Risk Premiums from a fundamental perspective. Take equity Risk Premium, for example. One can think of it as compensation to investors for bearing the business risk of companies. Shareholders provide capital to the company to engage business activities, which could be quite risky. If the business is suc-cessful, the shareholders would be rewarded with a higher share price and larger dividends in the future. But if the business is not successful or fails, the shareholder could suffer losses. For the economy as a whole, equity Risk Premium is the aggregated return to inves-tors for bearing economic growth risk. By the same token, interest rate premium is compensation to investors for bearing infla-tion risk that could erode their future purchasing power. If future inflation is lower than expected, bond yields might fall or rise less than what has been priced in. But if future inflation is higher than expected, bond yields might increase more than expected. Interest rate premium depends on the bond’s maturity—the longer the maturity, the higher the premium to compensate for the higher uncertainty of inflation risks. Second, from an empirical perspective, evidence for equity Risk Premium and interest rate premium has been very strong. In Table 2.14, we list the excess returns and annual-ized standard deviations of three-asset classes: 5-year US government bond, 10-year US government bond, and the S&P 500 index, from 1919 to 2013.

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  No longer available |Learn more

  CFA Program Curriculum 2020 Level II, Volumes 1-6 Box Set

  • (Author)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  In this example, the price discount is not too large because the risk between a one- and two-year US government bond is not that crucial. However, more risky assets, such as equity, will have a higher discount. In addition, the higher Risk Premium on equity still follows from the covariance between the cash flow and the investor’s willingness to invest over the time horizon of the investment. Thus, a higher Risk Premium for stocks arises from a larger value for this covariance.

  The Risk Premium can be computed as follows: The expected holding period return on the s period bond through time t + 1, using the results of Example 5 , is given by

  Equation (7) 

  so the Risk Premium = rt,s – lt ,1 = 0.047681 – 0.047671 = 0.00001.

  Alternatively, Equations 7 and 6 can be manipulated so that14

  Equation (8) 

  which is the return premium demanded by investors because of the uncertain Time 1 price of the riskless two-period bond.

  This relationship implies that an asset’s Risk Premium, in Equation 1 , is driven by the covariance of its returns with the inter-temporal rate of substitution for consumption, and can exist even for a default-free bond because of the uncertainty of its price before maturity. Most risky assets have returns that tend to be high during good times, when the marginal value of consumption is low, and low during bad times, when the marginal value of consumption is high, and so bear a positive Risk Premium. Any asset that tended to have relatively high returns when the marginal utility of consumption was high would provide a type of hedge against bad times and bear a negative Risk Premium and have a relatively high price and low required rate of return.

  3.2 . Default-Free Interest Rates and Economic Growth

  From the previous discussion, it is a relatively small conceptual step to understand the relationship between an economy’s GDP growth and real default-free interest rates. If there is a known independent change in the real GDP growth, or a change that can be forecasted perfectly, then an increase in real GDP growth should lead to an increase in the real default-free rate of interest because more goods and services will be available in the future relative to today. The result is that investors’ willingness to substitute across time will fall, resulting in less saving and more borrowing, so that the real default-free interest rate increases, as in Equation 4

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  eBook - PDF

  Econophysics and Capital Asset Pricing

  Splitting the Atom of Systematic Risk

  • James Ming Chen(Author)
  • 2017(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  139 8.1 THE EQUITY Risk Premium All of finance rests on the premise that investors dislike risk and demand higher returns as compensation for bearing risk. 1 The equity risk pre- mium may be regarded as the additional return that risk-averse investors demand in exchange for enduring volatility and potential downside loss. Although one study has concluded that replacing standard deviation in the conventional capital asset pricing model with a downside risk meas- ure would counsel investors to lower their stock allocations, 2 another study suggests that investors adopt fixed-income positions far beyond the allocation that any strictly rational, utilitarian risk assessment would ever recommend. 3 Actual market data suggests a decisive answer. American equities, at least over a sufficiently long time horizon, have exceeded the return on Treasury bonds by a geometrically compounded average of 4% per year. 4 Given such a “sizeable equity premium,” why should “a substantial frac- tion of investable wealth [be] invested in fixed income instruments”? 5 Downside risk aversion, perhaps the simplest component of systematic risk within this book’s baryonic model of beta, might counsel fixed- income positions as ballast to offset greater downside exposure from value stocks. 6 Still, the extent of the equity premium presents an econometric shock and a persistent theoretical puzzle. In their original 1985 formulation of the “equity premium puzzle,” Rajnish Mehra and Edward Prescott CHAPTER 8 The Equity Premium Puzzle © The Author(s) 2017 J.M. Chen, Econophysics and Capital Asset Pricing, Quantitative Perspectives on Behavioral Economics and Finance, DOI 10.1007/978-3-319-63465-4_8 140 J.M. CHEN found that “the average real annual yield on equity” in hypothetically “competitive pure exchange economies” should be “a maximum of four- tenths of a percent higher than that on short-term debt,” a surrogate for the risk-free rate.

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  eBook - PDF

  Triumph of the Optimists

  101 Years of Global Investment Returns

  • Elroy Dimson, Paul Marsh, Mike Staunton(Authors)
  • 2009(Publication Date)
  • Princeton University Press

    (Publisher)

  In our concluding observations, in section 13.8, we summarize what we can learn from the historical record as an indicator of the future equity Risk Premium around the world. 13.1 Why the Risk Premium matters Investors do not knowingly take on risk unless there is some expected recompense for their risk exposure. For taking on the risks of the equity market, this compensation takes the form of the equity Risk Premium. Why is it that the size of the equity premium has attracted so much attention? Perhaps the most straightforward answer is that the Risk Premium is fun- damental to valuing financial assets, as will be clear with a simple example. Consider the Gordon model, described in section 11.4. We will use this approach to value an investment such as buying the portfolio that comprises the Dow Index. Just before the World Trade Center tragedy, the Dow stood at a level of around 10,000 and its prospective dividend yield was 1.4 percent. So for a $10,000 investment we expected to receive dividends of $140. Since the dividend yield was much lower than the risk free interest rate, investors were presumably expecting Dow dividends to rise over time. The Gordon model values this stream of dividends by assuming that dividends grow at a constant rate g and by discounting them at the expected rate of return r. This simplifies to the well-known constant-growth formula: Value is equal to Dividend divided by r – g. This formula makes a number of strong assumptions, such as that growth will continue indefi- nitely at the same unvarying rate. However, in the interests of pedagogy, we bypass these assumptions, and explore the implications of the Gordon model (Jagannathan, McGrattan and Scherbina ( 2001) present the multiperiod Gordon model). Let us assume real dividends are expected to grow indefinitely at the annual rate of g = 3 per- cent, and that the real required rate of return is r = 4.4 percent.

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  eBook - ePub

  Finance and the Behavioral Prospect

  Risk, Exuberance, and Abnormal Markets

  • James Ming Chen(Author)
  • 2016(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  © The Author(s) 2016 James Ming Chen Finance and the Behavioral Prospect Quantitative Perspectives on Behavioral Economics and Finance https://doi.org/10.1007/978-3-319-32711-2_7

  Begin Abstract

  7. The Equity Risk Premium and the Equity Premium Puzzle

  James Ming Chen 1 

  (1) College of Law, Michigan State University, East Lansing, Michigan, USA

   

  End Abstract

  7.1 The Equity Risk Premium

  All of finance rests on the proposition that investors dislike risk and demand higher returns as compensation for bearing risk. In behavioral terms, the equity Risk Premium may be regarded as the additional rate of return that risk-averse investors, as a class, demand in exchange for the burden of bearing volatility and the attendant risk of downside loss. Although one study has concluded that the replacement of standard deviation in the conventional CAPM by a downside risk measure would advise investors to lower the stock allocations within their portfolios,

  1

  another study suggests that investors’ reliance on fixed-income positions vastly exceeds the allocation that any strictly rational, utilitarian evaluation of risk in equity investing would ever counsel.

  2

  Given the presence of a “sizeable equity premium,” why indeed should “a substantial fraction of investable wealth [be] invested in fixed income instruments”?

  3

  But the extent of this premium comes as an econometric shock and presents a persistent, still unresolved puzzle. In their original 1985 formulation of the “equity premium puzzle,” Rajnish Mehra and Edward Prescott found that “the average real annual yield on equity” in hypothetically “competitive pure exchange economies” should be “a maximum of four-tenths of a percent higher than that on short-term debt,” a surrogate for the risk-free rate.

  4

  This result stood “in sharp contrast to the six percent premium observed” in Mehra and Prescott’s actual survey of American economic history.

  5

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  eBook - ePub

  The Conceptual Foundations of Investing

  A Short Book of Need-to-Know Essentials

  • Bradford Cornell, Shaun Cornell, Andrew Cornell(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  2 There is, however, a path forward related to our discussion of stocks, bonds, and bills. Although expected returns are not observable, past returns are. If we can come up with a measure of risk, then it would be possible to examine whether riskier securities have provided greater past average returns. That is the path that research in finance has followed.

  The phrase “risk–return trade-off” seems to imply that if an investor bears risk he or she will be rewarded with greater expected returns, but that is not the case. It is not risk per se that warrants a premium, it is economic risk that cannot be avoided or eliminated by diversification. First, with regard to avoidable risks, most gambling falls into this category. As noted earlier, if my friend and I bet on a football game, we both bear risk but we can't both earn Risk Premiums. So who gets the premium? The answer is neither of us. The risk can be entirely avoided by just not betting on the game. This is not a risk that society must bear as part of ongoing economic activity.

  In this respect, buying Apple stock is different. Apple requires investors to provide it with financing as part of its operation. Therefore, the risk of holding Apple stock is not a risk that can be avoided. Someone must bear the risk if we are to have our iPhones. This makes it sound like the volatility of Apple stock would be the appropriate measure of risk, but that too is wrong. Investors do not have to bear all of that risk, because of diversification.

  To appreciate the impact of diversification, consider the risk of fire damage that homeowners face. For millions of homeowners nationwide this is clearly a risk that cannot be avoided. Typically homeowners are unwilling to bear the risk, so they transfer the risk to insurance companies in the form of a homeowner's policy. From this it seems to follow that the insurance companies should receive a substantial premium for bearing the risk. And while insurance companies do earn a premium, it is much smaller than you would guess based on the risk that individual homeowners face. The reason the premium is small is because insurance companies can drastically reduce the risk by diversifying across hundreds of thousands of policies.

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  eBook - PDF

  2023 CFA Program Curriculum Level III Box Set

  • (Author)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  e idea is to average away cyclical variation in earnings and provide a more reliable base against which to assess the current market price. 5.3 Risk Premium Approaches to Equity Returns e Grinold–Kroner model and similar models are sometimes said to reect the “supply” of equity returns since they outline the sources of return. In contrast, Risk Premiums reect “demand” for returns. 5.3.1 Dening and Forecasting the Equity Premium e term “equity premium” is most frequently used to describe the amount by which the expected return on equities exceeds the riskless rate (“equity versus bills”). However, the same term is sometimes used to refer to the amount by which the expected return on equities exceeds the expected return on default-free bonds (“equity versus bonds”). From the discussion of xed-income building blocks in Sections 3 and 4, we know that the dierence between these two denitions is the term premium built into the expected return on default-free bonds. e equity-versus-bonds premium reects an incremental/building block approach to developing expected equity returns, whereas the equity-versus-bills premium reects a single composite premium for the risk of equity investment. Forecasting Equity Returns 181 Exhibit 5 shows historical averages for both of these equity premium concepts by country for the period 1900–2017. 14 For each country, the bottom portion of the column is the realized term premium (i.e., bonds minus bills) and the top segment is the realized equity-versus-bonds premium. e whole column represents the equity- versus-bills premium. e equity-versus-bills premiums range from 3.0% to 6.3%, the equity-versus-bonds premiums range from 1.8% to 5.2%, and the term premiums range from -0.6% to 2.9%.

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  eBook - ePub

  The Risk Premium Factor

  A New Model for Understanding the Volatile Forces that Drive Stock Prices

  • Stephen D. Hassett(Author)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  Part One Exploring the Risk Premium Factor Valuation Model Passage contains an image Chapter 2 The Risk Premium Factor Valuation Model

  The Risk Premium Factor (RPF) Model proposes that the equity Risk Premium (ERP) is a simple function of the risk-free rate. When combined with simplifying assumptions as inputs to the constant growth equation, it explains the observed variation in ERP and changes in price-to-earnings (P/E) ratios and valuations for the Standard & Poor's (S&P) 500 over the past 50 years.

  Conventional theory would hold that if the equity Risk Premium (ERP) were 6.0 percent and 10-year Treasury yield were 4.0 percent, then investors would expect equities to yield 10 percent, but if the 10-year Treasury were 10 percent, then investors would require a 16 percent return—a proportionately smaller premium. I argue that the ERP is not fixed as in the conventional Capital Asset Pricing Model (CAPM) and cannot be determined by looking back or projecting forward, but varies directly with the level of the risk-free rate in accordance with a Risk Premium factor (RPF). While this proportional RPF is fairly stable, it can and does change over longer periods of time.

  To illustrate the concept, with an RPF of 1.48, equities are expected to yield 9.9 percent when Treasury yields are at 4.0 percent and 24.8 percent (10 + 1.48 × 10 = 24.8) when they are at 10 percent to provide investors with the same proportional compensation for risk. In this example, the increase in interest rates (and inflation) caused the Risk Premium to jump from about 6 percent to 15 percent. Notice that with this approach, the cost of capital is lower than with a fixed premium when interest rates are low, but higher than the fixed premium approach when interest rates are high. This implies that interest rates have a greater impact on valuation and market price than generally recognized.

  In order to test this approach, we not only need to determine the RPF, but also determine estimates for other variables. For our long-term growth rate, we simply assume that earnings will grow at the same pace as the economy. This is broken into its components of real growth plus expected inflation. A long-term real growth forecast is provided in the annual federal budget and tends to be stable, even when the economy is not. Inflation is determined by subtracting the underlying real interest rate (the rate without inflation) from the risk-free rate. We apply this to the constant growth equation:

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  eBook - PDF

  CFIN

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

    (Publisher)

  As a result, investors penalize the firm by selling their stock, which causes the value of the firm’s stock to decline. In this chapter, we build on the general concept that was introduced in Chapter 5 by showing how the Risk Premium associated with any investment should be determined (at least in theory). The basis of our discus- sion is Equation 5.2, which we develop further in this chapter as follows: r j 5 Risk-free rate 1 Risk Premium 5 r RF 1 (r M 2 r RF )b j 5 CAPM According to the CAPM, investors should not expect to be rewarded for all of the risk associated with an individual investment—that is, its total, or stand- alone, risk—because some risk can be eliminated through diversification. The relevant risk, and thus the risk for which investors should be compensated, is that Olivier Le Moal/Shutterstock.com 187 CHAPTER 8: Risk and Rates of Return Copyright 2022 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. portion of the total risk that cannot be diversified away. Thus, in this chapter we showed the following: Systematic risk is represented by an investment’s beta coefficient, b, in Equation 8.10. The specific types and sources of risk to which a firm or an investor is exposed are numerous, and vary considerably depending on the situation. A detailed discussion of all the different types of risks and the techniques used to evalu- ate risks is beyond the scope of this book.

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  eBook - ePub

  Empirical Evidence on the Efficiency of Forward and Futures Foreign Exchange Markets

  • Robert J. Hodrick(Author)
  • 2023(Publication Date)
  • CRC Press

    (Publisher)

  5. ECONOMETRIC MODELS OF Risk PremiumS

  DOI: 10.1201/9781003420385-5

  The previous section explored alternative interpretations of the rejection of the unbiasedness hypothesis. While market inefficiency is not a totally implausible hypothesis, a time-varying Risk Premium is perhaps a more likely explanation given the abundant evidence that average holding period returns on assets have varied greatly. Ibbotson and Sinquefield [114 ,115 ] document the existence of large differences in the average holding period returns on a variety of assets. Most financial economists view these differences as a reflection of Risk Premiums that are potentially traceable to risk aversion of individual investors. If agents are risk averse, the asset market theory of exchange rate determination combined with the intertemporal asset pricing theory discussed in Section 2 suggests that Risk Premiums ought to characterize the forward market for foreign exchange.

  In this section I examine alternative econometric models of the Risk Premium. First, models that are based strictly on the time series properties of spot and forward exchange rates and asset prices are considered. Then, models that employ other market fundamentals are examined.

  5.1. Models with no market fundamentals

  There is a long tradition in financial economics of developing tests of asset pricing models that utilize only the comparatively accurately measured returns on assets. Other data that are fundamental from an economic perspective are ignored. This section discusses several tests of asset pricing models that do not incorporate market fundamentals such as the outstanding stocks of assets. Models that incorporate market fundamentals are discussed in Section 5.2.

  In Section 2 a conditional capital asset pricing model is derived in (2.23). This expression is repeated here for convenience as (5.1) since it forms the basis of the empirical models of this section. The representation of the expected normalized profit on a long position in the forward market is

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  eBook - ePub

  Cost of Capital

  Applications and Examples

  • Shannon P. Pratt, Roger J. Grabowski(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Chapter 8

  Equity Risk Premium1

  1. Introduction
  2. Defining the Equity Risk Premium
     1. Nominal or Real?
     2. Estimating the ERP
     3. ERP Is Measured Relative to a Risk-free Rate
     4. Measuring the Average Period of the Expected Cash Flows
  3. Unconditional ERP
     1. Selecting a Sample Period of ex post Data
     2. Bias in Realized Risk Premium Data
     3. Predicting Future ERP
     4. Has the Relationship between Stock and Bond Risk Changed?
     5. Comparing Investor Expectations to Realized Risk Premiums
     6. Causes of Unexpectedly Large Realized Risk Premiums
     7. Unconditional ERP Estimates
  4. Conditional ERP
     1. Forward-looking (ex ante) Approaches
     2. Predicting Future ERP
     3. Conditional ERP Estimates
  5. Concluding on an ERP
  6. Summary
  7. Additional Reading
  8. Appendix 8A: Deriving ERP Estimates
  9. Appendix 8B: Other Sources of ERP Estimates

  Introduction

  The equity Risk Premium (ERP) (often interchangeably referred to as the market Risk Premium) is defined as the extra return (over the expected yield on risk-free securities) that investors expect to receive from an investment in the market portfolio of common stocks, represented by a broad-based market index (e.g., S&P 500 Index or the NYSE Index).

  As Arnott comments:

  For the capital markets to “work,” stocks should produce higher returns than bonds. Otherwise, stockholders would not be paid for the additional risk they take for being lower down in the capital structure. This relationship should be particularly true when stocks are compared to government bonds that (ostensibly) cannot default.2

  In a recent paper, the authors conclude that “The ERP is almost certainly the most important variable in finance.”3

  The effect of a decision that the appropriate ERP is 4% instead of 8% in the capital asset pricing model (CAPM) will generally have a greater impact on the concluded discount rate than alternative theories of the proper measure of other components, such as beta. One academic study looked at sources of error in estimating expected rates of return over time and concluded:

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  eBook - PDF

  The Cost of Capital

  • E. Porras(Author)
  • 2010(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  There is always some deviation from expectations. This is represented in the table in the column showing standard deviation, which shows that the Risk Premium investors have commanded on average over the 79-year period to compensate for the additional risk incurred by purchasing bonds instead of shorter term debt is 2 per cent. The premium is calculated as the difference between what the government has paid investors in Treasury bills and what it has also paid in the form of returns to those investors purchasing long-term government bonds. The interpretation is that over time, in order to encourage lenders to purchase the more risky security, the government has had to pay them, on average, a 2 per cent higher return than that paid for the shorter term instrument. Long-term debt securities from a government are usually (but not always!) less risky than those of corporations established in the same country. The rea- son for this is that governments control the money supply and they can always print more money to fulfil their financial obligations. Thus, moving from the less risky investments to more volatile options the next row up shows the returns obtained when investing in corporate debt. If capital markets are to clear (that is, if supply is to equal demand), firms must offer returns consistent with investors’ expectations. A firm would find no buy- ers if it offers a security for sale at a return below what investors’ require. In this instance, the security will not find buyers unless the firm increases the return by decreasing the price of the instrument, raising the interest paid, increasing the dividend rate, or other means. The securities will remain mostly unsold, and the firm will not be able to raise capital needed to realize its projects. The cost of capital to the firm is therefore equal to the equilibrium rate of return demanded by investors in the capital markets for securities with a spe- cific degree of risk.

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