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A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. [1] It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. [2]
The risk-free rate is also a required input in financial calculations, such as the Black–Scholes formula for pricing stock options and the Sharpe ratio. Note that some finance and economic theories assume that market participants can borrow at the risk-free rate; in practice, very few (if any) borrowers have access to finance at the risk free ...
Modern portfolio theory ( MPT ), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning ...
The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future cash flow by the stochastic factor , and then taking the expectation. [1] This definition is of fundamental importance in asset pricing.
Risk-neutral measure. In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to ...
The unbiasedness hypothesis states that given conditions of rational expectations and risk neutrality, the forward exchange rate is an unbiased predictor of the future spot exchange rate. Without introducing a foreign exchange risk premium (due to the assumption of risk neutrality), the following equation illustrates the unbiasedness hypothesis.
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. [1]
R f is the expected risk-free return in that market (government bond yield); β s is the sensitivity to market risk for the security; R m is the historical return of the stock market; and (R m – R f) is the risk premium of market assets over risk free assets. The risk free rate is the yield on long term bonds in the particular market, such as ...