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The variance risk premium can also be analysed from the perspective of asset allocation. Carr and Wu (2009) examines whether the excess returns of selling or buying variance swaps can be explained using common factor models such as the CAPM model and the Fama-French factors, which include returns of different segments of stocks on the market.
r it is return to stock i in period t r f is the risk free rate (i.e. the interest rate on treasury bills) r mt is the return to the market portfolio in period t is the stock's alpha, or abnormal return is the stock's beta, or responsiveness to the market return
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.. In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.
Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
For Brownian walk, Sharpe ratio / is a dimensional quantity and has units /, because the excess return and the volatility are proportional to / and / correspondingly. Kelly criterion is a dimensionless quantity , and, indeed, Kelly fraction μ / σ 2 {\displaystyle \mu /\sigma ^{2}} is the numerical fraction of wealth suggested for the investment.
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]
In 2015, Fama and French extended the model, adding a further two factors — profitability and investment. Defined analogously to the HML factor, the profitability factor (RMW) is the difference between the returns of firms with robust (high) and weak (low) operating profitability; and the investment factor (CMA) is the difference between the returns of firms that invest conservatively and ...
[] / [] is the "beta", return mentioned — the covariance between the asset's return and the market's return divided by the variance of the market return — i.e. the sensitivity of the asset price to movement in the market portfolio's value (see also Beta (finance) § Adding an asset to the market portfolio).