F. Sortino

Performance Measurement in a Downside Risk Framework

is director o f the Pension Research Institute in Sun Francisco, where he has conducted research projects with such Jirms as Royal Dutch Shell and Aegon Insurance in the Netherlands, Manufacturers Liji Insurance Co. o f Toronto, The Cal@rnia State Teachers Retirement System, and the Marin County Employees Retirement System. Dr. Sortino is also professor offnance at Sun Francisco State University. He holds an M . B.A. fiom U. C. Berkeley, and a Ph.D. infinancefrom the University o f Oregon.

Optimization and portfolio selection

This chapter presents a new model, Forsey–Sortino Optimizer, that generates a mean–downside risk efficient frontier. It develops a secondary optimizer that finds the best combination of active managers, to add value, and passive indexes, to lower costs. It intends to provide a starting point from which other researchers around the world can make improvements and in that way make a contribution to the state of the art. The underlying assumption is that the user wants to maximize the geometric average rate of return in a multiperiod framework. Therefore, the three-parameter lognormal distribution suggested by Atchison and Brown should provide a better estimate of the shape of the joint distribution than assuming a bell shape (standard normal distribution). It is recognized that this shape should change when the market is undervalued in that it should be more positively skewed than normal, and that it should be more negatively skewed when the market is overvalued. The user is then allowed to identify which part of the world he or she is operating from. That will determine which currency the indexes will be denominated in and which indexes to use. Next, the user is allowed to select combinations of scenarios from the three buckets of returns. If the user does not wish to make such a decision, the choice should be “unknown,” in which case the returns from all three buckets are used.

Sharing downside risk in defined benefit pension funds

This chapter aims to develop a measurement model that provides information on how risks are allocated across pension fund participants. It calculates the total risk of the portfolio, and determines how risk can be attributed to the individual groups of participants. In order to do this, it uses a simulation model and a set of loss allocation rules. Based on the simulation results, it attributes the risk to individual groups of beneficiaries. Furthermore, it uses downside risk as a measure of risk, and uses the decomposition of downside risk. Thereafter, it decomposes downside risk along the risky assets to see where the risk originates and over the groups of participants in the pension fund. This information is important, as it provides the input for evaluating whether the risks are shared in a responsible way. This presentation format is based on decomposing downside risk over the participants involved in a pension fund. Next to the formal rules, there are informal rules that are dictated by negotiations and the willingness of participants to share losses. The decomposition of downside risk allows the group of participants to evaluate their relative share in the losses. This may facilitate the discussion between sponsor and beneficiaries on strategies in times of underfunding.

Beyond the Sortino Ratio

The investment objective requires the calculation of the return needed to achieve the goal, which is the Desired Target Return ™ (DTR). Thus, the upside potential ratio is a measure of the inherent risk the manager is taking of not achieving the investors DTR relative to the potential of exceeding that desired return. It is not measuring what the manager has done but is an estimate of what he is statistically capable of achieving. It is one thing to have a better concept of measuring performance. It is quite another to obtain reliable estimates of the risk and return measures. Many people are now measuring downside risk as deviations below some number other than the DTR. Also, almost all of them use the managers returns instead of using returns from the managers style blend. At least value at risk (VAR) assumes investors are risk neutral and their utility function is linear below the DTR. Risk-neutral investors believe losing all their money is only twice as painful as losing half of it. Most firms that use Monte Carlo simulation focus on the average return and standard deviation when evaluating managers or determining the asset allocation. Sortino Investment Advisors (SIA) focuses on upside potential and downside risk.