**Ever since brokers started swapping shares** under that buttonwood tree in lower Manhattan, parallels have been drawn between Wall Street and the casino. Wall Street itself recognizes the similarities. Many proprietary trading firms, in fact, encourage prospective book runners to hit the green felt tables in order to learn real-life probability theory before they're entrusted with capital.

It's not hard to understand why. After all, casinos — like markets — offer games of chance, not certainties. There's a certain degree of randomness in both contexts.

This randomness is especially vexing when planning for long investment horizons such as those encountered in retirement planning. Variances in mortality, rates of return and inflation can confound attempts to make retirement money last. Just as in the casino, retirement planning must accommodate the unexpected. Provision for the randomness gamblers call “luck” is built into the best gaming strategies. For retirees, luck is manifested as short-term returns.

The similarities between gambling and retirement planning are compelling. Likewise, there are resemblances in risk management techniques used by casino denizens and retirement planners. Effective gamblers control risk through bankroll management. By carefully doling out wagers, good practitioners attempt to forestall the effects of natural variances (read: luck) that can lead to ruin. A player's success rate, average winnings and standard deviation can be mathematically manipulated to estimate a bankroll that provides a near certainty of avoiding ruin.

### Oh, Untimely Death

Managing money in retirement is really no different. There are three basic risk factors that must be reckoned with in any retirement plan: market risk, inflation and mortality.

Short-term market returns are as erratic as card draws. Since most of us can't amass enough pre-retirement wealth to simply go to cash and live upon risk-free drawdowns, we're exposed to investment risk even after we receive our gold watches.

Diversification obviously goes a long way towards reducing portfolio volatility, but it doesn't eliminate market risk. Retiring at a market top, for example, creates a greater probability of ruin than retiring at the beginning of a bull market, but isn't a risk factor that can be diversified away.

Inflation can be the most corrosive element in a retirement projection. Most of us understand inflation as the trend toward higher prices as measured by the Consumer Price Index (CPI). Reliance upon CPI, however, underestimates the deleterious effects of inflation on retirement. Because the consumption patterns of retirees are different from those of the wage-earning population at large, the U.S. Bureau of Labor Statistics maintains an experimental database known as CPI-E (for elderly) alongside the commonly published CPI-W (for workers) figures.

Over the past three decades, CPI-E has risen at an average annual rate of 3.3 percent compared to the 3 percent inflation rate in the CPI-W. It's not difficult to understand why this is so. The elderly devote a substantially larger share of their total budgets to medical care and shelter, segments that have been inflating at a faster pace than the CPI-W market basket.

Of course, retirement money has to literally last a lifetime. Trouble is: What's a lifetime? The actuarial life expectancy spelled out in the tables is a nice guide, but, at best they can only offer you a ballpark figure; in the end, it's just that. We rarely die on schedule. Dying “too soon” means inheritance; dying after the money runs out means ruin.

With these risks in mind, a retirement fund needs to be large enough to accommodate withdrawals and withstand inflation over a lifetime. Many advisors employ the “4 percent rule” when estimating the size of retirement fund take-outs. Under this rule of thumb, a retiree's annual spending is limited to no more than 4 percent of the fund's starting capital. A retiree with a $750,000 portfolio should therefore count on withdrawing no more than $30,000 per year, or $2,500 a month. (See related story on page 51 for more.) Realistically, that's $30,000 of the purchasing power at the point of retirement. Withdrawals should allow for a 4 percent “real” rate of return after inflation — at the higher CPI-E rate.

### Monte Carlo Simulation

Designing a portfolio that delivers $30,000 of inflation-adjusted purchasing power over an indeterminate horizon is tricky. Doable — but tricky. The math isn't pretty for non-calculus types, though. Luckily, retirement modeling can be done through computerized Monte Carlo simulations (MCS).

An MCS model — by taking into account return variance, mortality and projected inflation — allows you to predict the portfolio required, within a certain probability, that avoids ruin. Say for example, a 65-year-old client wants to allocate his $750,000 nest egg to a stock-and-bond mix that has historically produced a 5 percent annualized return with a 10 percent standard deviation. He also wants to withdraw $30,000 annually in inflation- and tax-adjusted purchasing power.

The table at left illustrates the client's potential outcome based upon a series of random returns generated by an MCS. Our client's withdrawal scheme would be appropriate only if he were expected to survive to age 77, because he's likely to run out of money in 12 years. If he were banking on living 15 years beyond retirement, the odds are one-in-10 that he'll run out of money before he dies. Worse still, he can reasonably count on only nine years of his desired distributions. The probability of achieving his objective in years 10, 11 and 12 diminish. If you client's life expectancy were 15 years, an MCS run would tell you that a portfolio of about $1.14 million would be required to support his withdrawals.

### A Cheap (Free) Alternative

Monte Carlo simulators (MCS) are software packages that require thousands of iterations to produce meaningful and reliable results. The software necessary to run the simulations can be expensive. But there is an inexpensive — well, free — alternative: If you plug the analytic expression below into an Excel spreadsheet, you can calculate the probable risk of ruin using spending, longevity and portfolio return inputs.

The analysis reproduces results that are quite close (within 5 percent to 10 percent) to those derived from MCS and can be used to quickly “ballpark” the risk of ruin. The formula, in Excel syntax, is:

Risk of Retirement Ruin = GammaDist(S/β,α,1,TRUE)

The expression relies upon four parameters to calculate the risk: The portfolio's expected return (µ), investment volatility (σ), mortality rate (λ) and the annual withdrawal rate expressed as a percent of the initial retirement portfolio (S). If you don't see all those Greek letters in the equation above, that's because they're embedded in the alpha (α) and beta (β) values.

In Excel syntax, alpha (α) can be defined by the expression:

(2*( µ;+2*λ)/( σ^2+ λ)) - 1

The beta (β ) coefficient is determined as:

( σ^2+ λ)/2

To see how all this works, let's go back to our client with the $750,000 portfolio. Let's say the mortality tables give our client a median remaining lifespan (MRL) of 15 years, meaning there's a 50 percent probability that he may live past age 80. That translates to a mortality rate (λ) of ln(2)/15, or 4.62%.

Mortality represents the average annual death rate for a given age cohort. With mortality now defined, and assuming that historical 5 percent annualized return and 10 percent standard deviation, we can calculate our beta and alpha values:

Alpha is found as:

(2*( .05+2*.046)/( .1^2+ .046)) - 1, or 4.07

Beta (β ) then becomes: (.1^2+.046)/2, or 2.81%

Now for S: Following the “4-percent rule”, our client wants to withdraw $30,000 per year, in inflation-adjusted terms, on a $750,000 portfolio. So S is 4%.

Using this value, together with the alpha and beta figures we can now calculate the risk of ruin as :

GammaDist (.04/.0281),4.07,1,TRUE), or 5.14%

Thus the present likelihood of our client running out of money before death is about 5 percent. That likelihood can change, of course, if we modify our inputs. A higher retirement alpha, for example, will result in a lower risk of ruin, while a higher beta-adjusted spending rate (S/β) will increase the risk.

Changes in spending patterns, too, can raise or lower the risk of insolvency, naturally. If our client wished to increase his retirement spending to $3,500 a month, for example, he'd be looking at a risk of ruin north of 13 percent.

With the spreadsheet at hand, advisors should find it easier to test “what if” scenarios, and better prepare their clients for navigating through the Wall Street casino.

### Monte Carlo Simulation of a $750,000 Retirement Portfolio

Year | Probability | Remaining Principal | Monthly Withdrawal |
---|---|---|---|

1 | 100.00% | $800,601 | $3,281 |

2 | 100.00 | 720,203 | 3,445 |

3 | 100.00 | 646,547 | 3,618 |

4 | 100.00 | 520,033 | 3,798 |

5 | 100.00 | 427,226 | 3,988 |

6 | 100.00 | 347,732 | 4,188 |

7 | 100.00 | 339,976 | 4,397 |

8 | 100.00 | 278,490 | 4,617 |

9 | 100.00 | 179,749 | 4,848 |

10 | 99.99 | 143,944 | 5,090 |

11 | 99.90 | 88,414 | 5,345 |

12 | 99.45 | 23,855 | 5,612 |

Assumes: 5% annualized returns, 10% standard deviation, 5% annual inflation, 20% tax rate | |||

Source: The Kitces Report |