Or, in symbols: RP RM – σP-M the symbols have the obvious meaning. Returns,” or , means taking the difference “Differential σP-M in returns between portpolio P and portfolio M for each time period and then calculating the standard deviation of this set of data using RP RM as the mean of the data. – The idea here is to raise the question as to whether the new portfolio, P, should be added to the existing portfolio, M. A special case arises when M is the riskless asset. In that case: RP RM – σP-M becomes: RP Rf – σP where represents the risk free rate return. In this special case where you are adding a portfolio to an Rf existing cash portfolio, the correct choice will always be the one with the highest Sharpe Ratio (assuming that all of the normality assumptions used earlier still apply). Generally, when the comparison portfolio is something than the risk free asset, the Sharpe Ratio is not very important all by itself because the covariance between the new portfolio, P, and the benchmark portfolio, M, plays a very significant role for all of the usual Capital Asset Pricing Model reasons. Another frequently cited statistic is the which is simply the calculated mean return Information Ratio, divided by the standard deviation. This ratio is also of limited applicability since covariance issues are not taken into account. Arbitrage Pricing Theory Steven Ross, in 1978, developed an alternative theory of prices, that encompasses the CAPM as a special case. Ross's theory is not an equilibrium theory. Instead, Ross employs the no-arbitrage principle that we shall see later in our discussion of the Modigliani-Miller and Black-Scholes theories. Ross's theory permits the use of economic variables to explain asset prices (and returns). This approach compares to using solely return covariances (betas) as explanatory variables in CAPM. In Ross’s Pricing “Arbitrage Theory,” the Capital Asset Model emerges as a special case. The Market” Hypothesis “Efficient EMH Once Ruled The Roost
Or, in symbols: RP – RM σP-M the symbols have the obvious meaning. “Differential Returns,” or σP-M , means taking the difference in returns between portpolio P and portfolio M for each time period and then calculating the standard deviation of this set of data using RP – RM as the mean of the data. The idea here is to raise the question as to whether the new portfolio, P, should be added to the existing portfolio, M. A special case arises when M is the riskless asset. In that case: RP – RM σP-M becomes: RP – Rf σP where Rf represents the risk free rate return. In this special case where you are adding a portfolio to an existing cash portfolio, the correct choice will always be the one with the highest Sharpe Ratio (assuming that all of the normality assumptions used earlier still apply). Generally, when the comparison portfolio is something than the risk free asset, the Sharpe Ratio is not very important all by itself because the covariance between the new portfolio, P, and the benchmark portfolio, M, plays a very significant role for all of the usual Capital Asset Pricing Model reasons. Another frequently cited statistic is the Information Ratio, which is simply the calculated mean return divided by the standard deviation. This ratio is also of limited applicability since covariance issues are not taken into account. Arbitrage Pricing Theory Steven Ross, in 1978, developed an alternative theory of prices, that encompasses the CAPM as a special case. Ross's theory is not an equilibrium theory. Instead, Ross employs the no-arbitrage principle that we shall see later in our discussion of the Modigliani-Miller and Black-Scholes theories. Ross's theory permits the use of economic variables to explain asset prices (and returns). This approach compares to using solely return covariances (betas) as explanatory variables in CAPM. In Ross’s “Arbitrage Pricing Theory,” the Capital Asset Model emerges as a special case. The “Efficient Market” Hypothesis EMH Once Ruled The Roost
Modern-Portfolio-Theory.docx