Tuesday, December 16, 2014

Milevsky Probability of Portfolio Ruin Calculator

Thanks to Dirk Cotton for the shout-out in his December 5 post, Think Like a Bayesian Pig.   Another excellent post from Mr. Cotton, and the comments that follow his post are also very worthwhile reading. 

At the bottom of his post, Dirk provides a link to a 2005 paper by Moshe A. Milevsky and Chris Robinson, and in the comment section, he provides a link to the Milevsky Probabililty of Portfolio Ruin Calculator.  

I must admit that the work done by Milevsky and Robinson was unfamiliar to me.  So, thanks to Dirk for bringing it to my attention.   While the paper is somewhat technical, the Probability of Ruin Calculator associated with the paper is not all that complicated,  and it turns out to be a very powerful tool in my opinion.  I was so impressed with it that I am including it in the "Other Calculators/Tools" section of this website.  I believe that that the Milevsky tool can provide retirees and financial planners with another valid point of reference (in addition to the approach recommended in this website and other approaches) to be used in developing a spending budget, particularly if the retiree has no other fixed dollar sources of retirement income (like fixed dollar pensions/annuities) or significant bequest motives.   The remainder of this post will discuss the Milevsky/Robinson approach and how I think it can best be used for budgeting in retirement under certain circumstances.

Milevsky/Robinson Approach

As opposed to the deterministic approach for investment returns and expected payout periods baked into the simple spreadsheet provided on this website,  Milevsky and Robinson advocate an approach that successfully reflects the fact that both investment rates of return and the time until death are stochastic in nature (have certain probability distributions).   By making certain assumptions about the probability distributions,  they develop probabilities of sustainable real dollar spending rates for various combinations of life expectancy, expected real rates of return and portfolio risk (measured by the standard deviation of the distribution of returns).

When using Milevsky's Probability of Portfolio Ruin Calculator, the user should note that the expected portfolio rate of return (an arithmetic mean over the remaining lifetime) input is a real (after-inflation) percentage.  Thus, the expected rate of return comparable to the real rate recommended in this website is 2% (which is approximately the real rate implied by a 5% per annum nominal investment return and 3% per annum inflation).   Also note that the spreadsheet anticipates inputting a whole number of years remaining in retirement equal to the retiree's remaining life expectancy.   Inputting expected rate of return, portfolio standard deviation, withdrawal rate (a percentage of accumulated savings at the current age with such product increasing by inflation in subsequent years) and remaining life expectancy at the current age, the spreadsheet produces a probability of ruin (running out of money prior to death) and it's complement (not running out of money prior to death). 

Keeping in mind that since there is approximately a 50% probability of outliving one's life expectancy, any probability of ruin less than 50% means that the retiree is more likely than not to die before running out of money (assuming no future changes in spending occur).  A probability of ruin of 25% means that the retiree is about three times more likely (75%/25%) than not to die before running out of money (assuming no future change in spending occur).   Since many retirees are almost as worried about not spending enough as those who are worried about spending too much, it does not bother me to develop a spending budget based on a 25% probability of ruin.   As I have previously indicated in this website,  developing a spending budget for retirement is a "balancing act."   It is also important to note that the term "ruin" here may be a misnomer and may more appropriately be considered as a probability that real dollar spending may need to be reduced in the very later years of life as a result of living well beyond one's life expectancy.   This possibility may not be a disaster, but may actually be more consistent with studies that show declining spending needs at older ages.  

I compared results of the Milevsky's Probability of Portfolio Ruin Calculator (using assumptions described below) with the results of the simple spreadsheet in this website (Excluding Social Security V 2.0) using the recommended assumptions.   If I input a 2% real expected rate of return in Milevsky's spreadsheet, 5% standard deviation, male life expectancy based on the average of the 2010 Social Security and 2012 Individual Annuity Mortality Tables available on the Society of Actuaries  website (a link to which resides in the "Other Calculators/Tools" section of this website) and solve for the withdrawal rate that produces approximately a 25% probability of "ruin", I come very close to the withdrawal rates produced using the Excluding Social Security V 2.0 spreadsheet and the recommended assumptions at most ages.   There is some significant deviation at the very older ages, as I recommend using life expectancy if age plus life expectancy is greater than 95.  When I reach my late 80's I may switch to the Milevsky approach depending on how concerned I become at that point about outliving my savings.  Females, who have longer life expectancy, may also wish to look at the Milevsky approach when they reach their mid-80s.

Those of you out there who play with this spreadsheet may find it of interest that inputting a 4.4% withdrawal rate and 20-year life expectancy and an 8% withdrawal rate and 9 year life expectancy will produce about a 25% probability of ruin for each of the following combinations of expected real investment return/standard deviations:  2%/5%, 3%/11.5%, 4%/15.5%, 5%/19%, 6%/21.7% and 7%/24.5%.   This result shows that achieving higher real rates of return by taking on more risk may not increase your retirement budget.

How to best use the Milevsky Spreadsheet (In My Opinion)

As alluded to above, while the Milevsky spreadsheet is a powerful tool that provides retirees with another data point in planning for retirement, it does have some weaknesses.  It  does not, for example, coordinate the spending budget with fixed immediate or deferred annuities/pensions and it does not reflect bequest motives.

In his post, Dirk Cotton says that the Probability of Ruin Calculator is also an actuarial approach.  I'm going to mildly object to this claim.  I would say that it may be used as part of an actuarial approach, but by itself, it is more like an alternative Safe Withdrawal Rate generator, particularly if it is only used once at the retiree's initial retirement age.   I understand that Dirk is not actually suggesting this, but to be clear, to be considered an actuarial approach, it should involve an annual re-measurement (although not necessarily annual redetermination of the actual budget amount).  This is how I would use the Milevsky approach if I did not have other fixed dollar retirement income sources and bequest motives (and I wanted another data point to consider):  Step 1:  Calculate the withdrawal rate at initial retirement consistent with a 25% probability of ruin, a 2% expected investment return, a 5% standard deviation and a reasonable life expectancy for me (not necessarily based on the mortality of individuals who purchase life annuities).  Step 2:  Multiply the withdrawal rate determined in  Step 1 by my accumulated savings at initial retirement.  This is my spending budget for year 1.  Step 3:  In year two, increase the dollar amount determined in the previous year by the increase in inflation over the previous year.  Revisit the spreadsheet using an updated life expectancy (but generally the same other assumptions and probability of ruin used in the first year) and multiply the resulting withdrawal rate by an update of actual accumulated savings (i.e., current year's assets).  If the  spending budget for the previous year is within 10% of the product of the updated withdrawal percentage and updated assets,  just stay with the spending budget for the previous year increased with inflation.  If not, use the corridor value.  Step 4:  Repeat Step  3 each year.    Note that this basically the same approach (involving the same smoothing algorithm) recommended for the Actuarial Approach in this website.