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The t-statistic will equal the Sharpe Ratio times the square root of T (the number of returns used for the calculation). The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below.
The Sharpe ratio is awkward to interpret when it is negative. Further, it is difficult to directly compare the Sharpe ratios of several investments. For example, what does it mean if one investment has a Sharpe ratio of 0.50 and another has a Sharpe ratio of −0.50? How much worse was the second portfolio than the first?
When a risk-free asset is introduced, the half-line shown in the figure is the new efficient frontier. It is tangent to the hyperbola at the pure risky portfolio with the highest Sharpe ratio. Its vertical intercept represents a portfolio with 100% of holdings in the risk-free asset; the tangency with the hyperbola represents a portfolio with ...
The SFRatio has a striking similarity to the Sharpe ratio. Thus for normally distributed returns, Roy's Safety-first criterion—with the minimum acceptable return equal to the risk-free rate—provides the same conclusions about which portfolio to invest in as if we were picking the one with the maximum Sharpe ratio.
The slope of the capital allocation line is equal to the incremental return of the portfolio to the incremental increase of risk. Hence, the slope of the capital allocation line is called the reward-to-variability ratio because the expected return increases continually with the increase of risk as measured by the standard deviation.
Jensen's alpha was first used as a measure in the evaluation of mutual fund managers by Michael Jensen in 1968. [2] The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset.
The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. [1] It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return , while the Sharpe ratio penalizes both upside and downside volatility equally.
Beta is the hedge ratio of an investment with respect to the stock market. For example, to hedge out the market-risk of a stock with a market beta of 2.0, an investor would short $2,000 in the stock market for every $1,000 invested in the stock. Thus insured, movements of the overall stock market no longer influence the combined position on ...