I.A.1.7 Risk-Adjusted Performance Measures

Question 1

Static Portfolio Selection

Answer 1

• Start with a set of risky assets that can be bought or sold at the same price in any quantity to create portfolios (linear combinations of assets). Asset returns- gains or losses per unit investment over a given time - are described by a joint probability distribution. An investor has some capital to invest; how should he allocate it?
• If applyin the maximum EU principle the optimal investment should generally depend on the investor’s risk attitude.

Question 2

Efficient Portfolios

Answer 2

all risk-averse investors would agree that some portfolios of risk assets are worse than others. So, they choose their preferred portfolio from a family of better portofilos (the efficient portfolios) according to their personal risk attitude

Question 3

Market Portfolio

Answer 3

• Special cases defined as market equilibrium conditions, all investors will agree on the same optimal mix of risky assets
• An investors personal risk attitude will only determine the amount ro be invested in the market portfolio and he amount to be invested in or borrowed against the risk-free asset

Question 4

Risk-Adjusted Performance Measure (RAPM)

Answer 4

• Measures (usually ratios of expected returns to risk) are designed to provide a preference ranking of risky opportunites acceptable to a majority of investors, assuming only that these investors are risk averse in a simple sense
• Do not seem to require a statment of personal risk attitude
• Range of applicability is very limited because they do not require personal risk attitude
• There are a large number of different definitions For RAPMs, each of which can be applied in a variety of different circumstances
• Examples of RAPMs: Sharp ratio, Treynor ratio, Jensen alpha, RAROC, RoVaR, Kappa indices (Sortino)and Omega index