TheInfoList

# Overview

A risk premium is a measure of excess return that is required by an individual to compensate them for being subjected to an increased level of risk. It is used widely in finance and economics with the general definition being the expected risky return less the
risk-free return The risk-free interest rate is the rate of return In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and inv ...
, as demonstrated by the formula below. $Risk \ Premium = E\left(r\right) - r_f$ Where $E\left(r\right)$ is the risky expected rate of return and $r_f$ is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections. Regardless of the application, the market premium can be volatile as both comprising variables can be impacted independent of each other by both cyclical and abrupt changes. This means that the market premium is dynamic in nature and ever-changing. Additionally, a general observation regardless of application is that the risk premium is larger during economic downturns and during periods of increased uncertainty. There are many forms of risk such as
financial risk Financial risk is any of various types of risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown informati ...
, physical risk, and reputation risk. The concept of risk premium can be applied to all these risks and the expected payoff from these risks can be determined if the risk premium can be quantified. In the
equity market A stock market, equity market, or share market is the aggregation of buyers and sellers of stocks (also called shares), which represent ownership claims on businesses; these may include ''securities'' listed on a public stock exchange, as w ...

, the riskiness of a stock can be estimated by the magnitude of the standard deviation from the mean. If for example the price of two different stocks were plotted over a year and an average trend line added for each, the stock whose price varies more dramatically about the mean is considered the riskier stock. Investors also analyse many other factors about a company that may influence it’s risk such as industry volatility,
cash flows A cash flow is a real or virtual movement of money Image:National-Debt-Gillray.jpeg, In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, in ...
,
debt Debt is an obligation that requires one party, the debtor A debtor or debitor is a legal entity (legal person) that owes a debt Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to ...

, and other market threats.

# Risk Premium application in Finance

The risk premium is used extensively in finance in areas such as asset pricing, portfolio allocation and risk management. Two fundamental aspects of finance, being equity and debt instruments, require the use and interpretation of associated risk premiums with the inputs for each explained below:

## Equity Instruments

In the
stock market A stock market, equity market, or share market is the aggregation of buyers and sellers of stock In finance, stock (also capital stock) consists of all of the shares In financial markets A financial market is a market in whic ...

the risk premium is the expected return of a company stock, a group of company stocks, or a portfolio of all stock market company stocks, minus the risk-free rate. The return from equity is the sum of the
dividend yield The dividend yield or dividend–price ratio of a share is the dividend A dividend is a distribution of profits by a corporation A corporation is an organization—usually a group of people or a company—authorized by the state to act as ...
and
capital gains Capital gain is an economic concept defined as the profit Profit may refer to: Business and law * Profit (accounting) Profit, in accounting Accounting or Accountancy is the measurement, processing, and communication of financial an ...
and the risk free rate can be a treasury bond yield. For example, if an investor has a choice between a risk-free treasury bond with a bond yield of 3% and a risky company equity asset, the investor may require a greater return of 8% from the risky company. This would result in a risk premium of 5%. Individual investors set their own risk premium depending on their level of risk aversion. The formula can be rearranged to find the expected return on an investment given a stated risk premium and risk-free rate. For example, if the investor in the example above required a risk premium of 9% then the expected return on the equity asset would have to be 12%.

## Debt Instruments

The risk premium associated with bonds, known as the
credit spread Image:2005private sector credit.PNG, px, Domestic credit to private sector in 2005 Credit (from Latin ''credit'', "''(he/she/it)'' believes") is the Trust (social sciences), trust which allows one party to provide money or resources to another pa ...
, is the difference between a risky bond and the risk free treasury bond with greater risk demanding a greater risk premium as compensation.

## Risk Premium application in Banking

Risk premiums are essential to the banking sector and can provide a large amount of information to investors and customers alike. For instance, the risk premium for a savings account is determined by the bank through the interest that they set on their savings accounts for customers. This less the interest rate set by the central bank provides the risk premium. Stakeholders can interpret a large premium as an indication of increased default risk which has flow on effects such as negatively impacting the public’s confidence in the financial system which can ultimately lead to bank runs which is dangerous for an economy. The risk premium is equally important for a bank’s assets with the risk premium on loans, defined as the loan interest charged to customers less the risk free government bond, needing to be sufficiently large to compensate the institution for the increased default risk associated with providing a loan.

## Using the risk premium to produce valuations

One of the biggest reasons for determining a risk premium is to estimate the value of financial assets. There are a number of models used in finance to determine this with the most widely used being the
Capital Asset Pricing Model In finance Finance is a term for the management, creation, and study of money In a 1786 James Gillray caricature, the plentiful money bags handed to King George III are contrasted with the beggar whose legs and arms were amputated, i ...
or CAPM. CAPM uses investment risk and expected return to estimate a value for the investment. In Finance, CAPM is generally used to estimate the required rate of return for an equity. This required rate of return can then be used to estimate a price for the stock which can be done via a number of methods. The formula for CAPM is: :CAPM = (The Risk Free Rate) + ::(The Beta of the Security) * (The Market Risk Premium) In this model, we use the risk premium of the market and multiply this with the
beta Beta (, ; uppercase , lowercase , or cursive Cursive (also known as script, among other names) is any style of penmanship Penmanship is the technique of writing Writing is a medium of human communication that involves the represen ...
of the security. The beta of a security is the measure of a stocks relative volatility and measures how closely the share price moves compared to the market. If the beta of a stock is 1 then a 10% increase in the market will translate to a 10% increase in stock price. If the Beta of a stock is 1.5 then a 10% increase in the market will translate to a 15% increase in the stock and if the beta of a stock is 0.5 a 10% market increase will translate to a 5% stock increase and likewise with decreases in the market. This beta is generally found via statistical analysis of the share price history of a stock. Therefore CAPM aims to provide a simple model in order to estimate the required return of an investment which uses the theory of risk premiums. This helps to provide investors with a simple means of determining what return an investment should be relative to its risk.

# Risk Premium Application in Managerial Economics

The risk premium concept is equally applicable in managerial economics. The risk premium is largely correlated with
risk aversion In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies ...

with the larger the risk aversion of an individual or business the larger the risk premium the party will be willing to pay to avoid the risk. Regarding workers, the risk premium increases as the risk of injury increases and manifests in practice with average wages in dangerous jobs being higher for this reason. Another way in which the risk premium can be interpreted from the workers perspective is that risk is valued by the market, in the form of wage discrepancies between risky and less risky jobs, with a worker able to determine what amount they are willing to forgo to engage in a less risky job. In this instance the risk premium provides insight into the strength of correlation between risk and the average job type earnings with a larger premium potentially suggesting that there is a greater risk and/ or a lack of workers willing to take the risk. The level of risk associated with the risk premium concept does not need to be physical risk but it can also incorporate risk surrounding the job, such as job security. Higher risk of unemployment  is compensated with a higher wage with this being a reason as to why fixed-term contracts generally include a higher wage. CEO's in industries with high volatility are subject to increased risk of dismissal. Dismissed CEO's often undergo a period of unemployment after dismissal and frequently settle for jobs in smaller firms with lower remuneration. Due to this, and assuming there is demand competition within the labor market, they often require a higher remuneration than CEO's in non-volatile industries as a risk premium.

# In public goods

## In invasive species management

The option value of whether to invest in
invasive species An invasive species is an introduced organism that becomes overpopulated and negatively alters its new environment. Although their spread can have beneficial aspects, invasive species adversely affect the invaded habitat Ibex in an ...
quarantine and/or management is a risk premium in some models.

# In agriculture

## Of crop pathogens

Farmers cope with crop pathogen risks and losses in various ways, mostly by trading off between management methods and pricing that includes risk premiums. For example in the northern
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...

, Fusarium head blight is a constant problem. Then in 2000 the release of a multiply-resistant cultivar of wheat dramatically reduced the necessary risk premium. The total planted area of MR wheats was dramatically expanded, due to this essentially costless tradeoff to the new cultivar.

## Of investment in genetic research

Estimates of costs of research and development - including
patent A patent is a type of intellectual property Intellectual property (IP) is a category of property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depe ...

costs - of new crop genes and other agricultural biotechnologies must include the risk premium of those which do not ultimately obtain patent approval.

# Example of observed risk premium

Suppose a
game show A game show is a genre Genre () is any form or type of communication in any mode (written, spoken, digital, artistic, etc.) with socially-agreed-upon conventions developed over time. In popular usage, it normally describes a Category of being ...
participant may choose one of two doors, one that hides \$1,000 and one that hides \$0. Further, suppose that the host also allows the contestant to take \$500 instead of choosing a door. The two options (choosing between door 1 and door 2, or taking \$500) have the same expected value of \$500, so no risk premium is being offered for choosing the doors rather than the guaranteed \$500. A contestant unconcerned about risk is indifferent between these choices. A contestant will choose no door and accept the guaranteed \$500, while a
risk-loving In accounting Accounting or Accountancy is the measurement, processing, and communication of financial and non financial information about economic entity, economic entities such as businesses and corporations. Accounting, which has been called ...

contestant will derive utility from the uncertainty and will therefore choose a door. If too many contestants are risk averse, the game show may encourage selection of the riskier choice (gambling on one of the doors) by offering a positive risk premium. If the game show offers \$1,600 behind the good door, increasing to \$800 the expected value of choosing between doors 1 and 2, the risk premium becomes \$300 (i.e. \$800 expected value minus \$500 guaranteed amount). Contestants requiring a minimum risk compensation of less than \$300 will choose a door instead of accepting the guaranteed \$500.

# Empirical estimates of risk premium from securities markets

Schroeder estimated risk premiums ranging from 4.83 to 7.75 percent in securities markets in the United Kingdom and the European Union under multiple models, with most estimates ranging between 6.3 and 7.2 percent..

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Equity risk Equity risk is "the financial risk involved in holding equity Equity may refer to: Finance, accounting and ownership *Equity (finance), ownership of assets that have liabilities attached to them ** Stock, equity based on original contributions o ...
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Interest In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money availa ...

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Risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty Uncertainty refers to Epistemology, epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to ...

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Risk aversion In economics Economics () is a social science Social science is the Branches of science, branch of science devoted to the study of society, societies and the Social relation, relationships among individuals within those societies ...

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Risk neutral In economics Economics () is the social science that studies how people interact with value; in particular, the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods an ...
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Risk-loving In accounting Accounting or Accountancy is the measurement, processing, and communication of financial and non financial information about economic entity, economic entities such as businesses and corporations. Accounting, which has been called ...
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Minimum acceptable rate of returnIn business and for engineering economics in both industrial engineering and civil engineering Civil engineering is a Regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and mai ...
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Expected utility hypothesis The expected utility hypothesis is a popular concept in economics Economics () is a social science Social science is the branch A branch ( or , ) or tree branch (sometimes referred to in botany Botany, also called , p ...
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LIBOR–OIS spread An overnight indexed swap (OIS) is an interest rate swap In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money a ...
* Risk premia parity *
Kelly criterion In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressi ...