Impact of Gender on Annuity Payments
Introduction Females have longer life expectancy than males in virtually all countries. Gender related differences in life expectancy make it more likely that females will out-live their retirement resources than will males. Females, because of their longer life expectancy, might choose to purchase a longer-term annuity.
Question: A 75-year old person has $100,000 to spend on an annuity., which makes monthly payments for a fixed period. She or he wants to reduce the probability of outliving the annuity to below 10 percent.
What annuity term would accomplish this goal for a male and for a female?
How does the longer life expectancy of the female affect the size of the monthly annuity payment?
Data Source: This analysis is based on the United States Life Tables, 2008 published on September 24, 2012 by the National Center for Health Statistics of the Centers for Disease Control and Prevention
http://www.cdc.gov/nchs/data/nvsr/nvsr61/nvsr61_03.pdf
Table Two of the report has life statistics for males and Table Three of the report has life statistics for females. Both tables can be downloaded directly into an EXCEL Spreadsheet.The data in the Table below is from the CDC life tables.
| Age | Total number of females alive at age x | Proportion of 75-year-old females who survive to age X | Total number of Males Alive at age X | Proportion of 75-year Males surviving until age X |
| 75 | 73,974 | 61,980 | ||
| 76 | 71,973 | 97.3% | 59,531 | 96.0% |
| 77 | 69,831 | 94.4% | 56,962 | 91.9% |
| 78 | 67,539 | 91.3% | 54,268 | 87.6% |
| 79 | 65,080 | 88.0% | 51,437 | 83.0% |
| 80 | 62,448 | 84.4% | 48,469 | 78.2% |
| 81 | 59,647 | 80.6% | 45,390 | 73.2% |
| 82 | 56,688 | 76.6% | 42,227 | 68.1% |
| 83 | 53,563 | 72.4% | 38,994 | 62.9% |
| 84 | 50,253 | 67.9% | 35,694 | 57.6% |
| 85 | 46,782 | 63.2% | 32,360 | 52.2% |
| 86 | 43,166 | 58.4% | 28,996 | 46.8% |
| 87 | 39,414 | 53.3% | 25,650 | 41.4% |
| 88 | 35,567 | 48.1% | 22,372 | 36.1% |
| 89 | 31,677 | 42.8% | 19,213 | 31.0% |
| 90 | 27,805 | 37.6% | 16,223 | 26.2% |
| 91 | 24,017 | 32.5% | 13,448 | 21.7% |
| 92 | 20,380 | 27.6% | 10,928 | 17.6% |
| 93 | 16,962 | 22.9% | 8,691 | 14.0% |
| 94 | 13,821 | 18.7% | 6,754 | 10.9% |
| 95 | 11,006 | 14.9% | 5,122 | 8.3% |
| 96 | 8,549 | 11.6% | 3,783 | 6.1% |
| 97 | 6,467 | 8.7% | 2,719 | 4.4% |
| 98 | 4,754 | 6.4% | 1,898 | 3.1% |
| 99 | 3,392 | 4.6% | 1,286 | 2.1% |
| 100 | 2,345 | 3.2% | 844 | 1.4% |
Analysis:
Calculation the Annuity Term:
Based on this cohort of 100,000 females, 73,974 females have survived to page 75. Around 90% of these females are still alive until somewhere between age 95 and 96.
In a cohort of 100,000 men 61,980 are still alive at age 75 and the 90% survival mark for these 75-year olds is reached somewhere between age 94 and 95.
Let’s interpolate to get an exact number of months for our annuity formula.
For females we get 96-75 (21) years plus (11.6-10)/(11.6-8.7) x 12 or (7) months. The 75-year old female must buy an annuity of 259 months to reduce the probability that she will outlive the annuity to 10 percent.
For males we get 94-75 (19) years plus (10.9-10)/(10.9-8.3) x 12 or 5 months (I am rounding up to fulfill the contract.) The 75-year old male must buy an annuity of 233 months to reduce the probability that he will outlive the annuity to 10 percent.
Calculating the Impact on Annity Payments:
So now we calculate the annuity payments for the female and the male with the PMT function. The only input that differs is the duration of the contract – 259 months for females and 233 months for males.
The annuity payment calculations were obtained from the PMT function in Excel.
| Female | Male | |||
| Rate 0% | 0 | 0 | ||
| Rate 3% | 0.03 | 0.03 | ||
| Rate 6% | 0.06 | 0.06 | ||
| NPER | 259 | 233 | ||
| PV | $100,000 | $100,000 | ||
| Type | 1 | 1 | DIFFERENCE | % DIFFERENCE WITH FEMALE AS BASE |
| PMT rate=0 | $386.10 | $429.18 | ($43.08) | -11.2% |
| PMT rate =3% | $524.96 | $566.77 | ($41.81) | -8.0% |
| PMT rate=6% | $689.45 | $727.62 | ($38.17) | -5.5% |
Conclusions: Females must buy a longer-term annuity to obtain the same reduction in longevity risk as a male. This reduces their monthly annuity payment.
This annuity calculator on the web confirms that females receive lower annuity payments and or pay higher prices for a comparable annuity. I am not familiar with the specific formulas used by this calculator or the product that it pertains to. My sole interest here is to provide some insight on how gender determines longevity risk.
http://www.annuityfyi.com/immediate-annuities/