We show that the probability of risk parity beating any other portfolio is more than 50 percent. We also prove that if … portfolio performance is measured by Sharpe ratio, risk parity is the only maximin portfolio when (1) all assets' future Sharpe … assets' future Sharpe ratios is greater than some constant. If portfolio performance is measured by expected return, risk …

Most textbook finance literature assumes risk to be the standard deviation of returns (volatility), which is not only … is consistent with investors’ actual perception of risk. Our method is presenting investors return distributions with … different risk characteristics for which they have to state their perceived risk and make investment decisions. Our results hint …

We describe a simple robust technique for incorporating any type of views on expected returns into the Risk parity … remain at risk parity. Second, agnostic (cautious) views always result in a more diversified allocation. We further extend … this framework to arbitrary initial risk budgets, and suggest an alternative to the Black-Litterman methodology …

Volatility is the most widely-used measure of risk but its relevance is questionable in many settings. For long …. Hence, their higher volatility essentially is higher upside risk; that is, uncertainty about how much better, not how much …

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion … may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA … their risk aversion parameter invest less in risky assets than wealthy investors with identical risk aversion uncertainty. …

risk measures for portfolios with infrequently traded securities have not been explored in the literature. We propose a … methodology to calculate market risk measures based on the Kalman filter which can be used on incomplete datasets. We implement … applied to other markets with thinly traded securities. Our methodology provides reliable market risk measures in portfolios …

risk measures for portfolios with infrequently traded securities have not been explored in the literature. We propose a … methodology to calculate market risk measures based on the Kalman filter which can be used on incomplete datasets. We implement … applied to other markets with thinly traded securities. Our methodology provides reliable market risk measures in portfolios …

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest …-additive risk measures, for which the eligible asset is a risk-free bond, on the grounds that the general case can be reduced to the … provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures …

, as a measure of risk, of volatility, Value at Risk and Conditional Value at Risk. This with the aim to take account of … with other robust and non robust models, and with respect to the risk-free portfolio and therefore can have interesting …

/09 another way to deal with diversification came up, that is equally-weighted risk contribution portfolio. This kind of procedure … leads not to equalize the portfolio weights but the risk weights. The only thing to understand is how we can measure risk …. While many authors focus on volatility, in this paper we shall present an alternative and coherent risk measure, that is …