1. F e at u r e Risk Management Trends for Pension Plans By L. Gregg Jo h n s o n , E A, M AAA, M SPA, CFA , a n d M i c h a e l D i e s c h b ou rg, C I M A D ont put all your eggs in Determining the geometric return that the geometric mean is always equal one basket might be the is a bit complicated; however, there is to or less than the arithmetic mean, oldest rule of investment an easy way to estimate the value. The even if there are no losses, and the risk management. This adage suggests estimate is the arithmetic return minus magnitude is dependent on the volatil- diversifying into multiple asset classes one-half of the variance (which is the ity (standard deviation) of returns. in your portfolio so when one goes standard deviation squared). The esti- Obviously, losses increase the magni- down another might go up. Its still the mates in table 1 illustrate that the esti- tude of the standard deviation signifi- bedrock of most basic risk-management mate is a good approximation. The most cantly, so avoiding losses is paramount. approaches and was first formalized enlightening aspect of the estimate is But if equal arithmetic returns can be in modern portfolio theory, created by Harry Markowitz, which seeks the low- TABLE 1: COMPARISON OF ARITHMETIC AND GEOMETRIC PORTFOLIO est risk for allocations among multiple RETURNS OF A $1,000 INVESTMENT asset classes. A B C D Techniques for managing portfolio Year 1 8% 8% 8% 8% risks have evolved since Markowitz Year 2 8% 2% 8% 24% and continue to evolve today. Post- Year 3 8% 14% 24% 8% modern portfolio theory, which focuses Accumulated Wealth $12,597 $12,558 $12,321 $12,321 on downside risks, grew from modern portfolio theory (MPT). Value-at-Risk Arithmetic Return 8.0% 8.0% 8.0% 8.0% and conditional Value-at-Risk techniques Standard Deviation 0.0% 4.9% 13.1% 13.1% were created. New approaches such as Geometric Return 8.0% 7.9% 7.2% 7.2% liability-driven investing and dynamic Geometric Return (Est.) 8.0% 7.9% 7.1% 7.1% asset allocation methods are being used in pension investing. This article will FIGURE 1: RANGE AND STANDARD DEVIATION OF COMPOUND RETURNS discuss the pros and cons of these tech- niques and others to help advisors deal 25.00% with volatility in pension portfolios. 20.00% The Math of Winning One of the crueler vagaries of invest- 15.00% Compound Annual Return ing is the effect that negative returns or returns below a target level have on try- 10.00% ing to achieve a certain long-range rate of return. Table 1 shows the accumula- 5.00% tion from a $10,000 investment at the end of three years under four scenarios 0.00% 0 2 4 6 8 10 that have the same arithmetic return. -5.00% As table 1 shows, the four scenarios accumulate to three different amounts. -10.00% How can that be? The accumulated value of an investment is based on the Year Worst Case Best Case Std. Dev. geometric return on assets rather than the arithmetic average (mean)the arithmetic return is misleading at best. 12 Investments&Wealth MONITORI&WM NovDec12 v1.indd 12 11/12/12 4:13 PM
2. F e at u r e and practice. In practice there is. The FIGURE 2: RANGE AND STANDARD DEVIATION OF WEALTH elegant and formal mathematics of $2,000 MPT has relied too much on theory Millions rather than the reality of market move- $1,750 ments. Experience has proven that in practice, MPT does not deliver the $1,500 promised results, particularly when $1,250 they are needed the most. Post-modern portfolio theory Assets $1,000 (PMPT) focuses on losses or downside risk to seek portfolios that will pro- $750 vide the most return for any expected $500 level of loss or to generally attempt to accurately measure the potential losses $250 in a portfolio. Tail risk, or extreme loss scenarios, are measured using Value- $0 0 2 4 6 8 10 at-Risk (VaR) to attempt to quantify how much a portfolio might lose in any Year Worst Case Best Case Std. Dev. specified period; or conditiona
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