How are income annuities priced? It is not as hard as one might think, as the basic recipe requires just three ingredients:
1. Mortality rates (which vary by age and gender) impact how long payments will be made. Younger people will have longer projected payout periods, which means that payout rates must be lower.
2. Interest rates impact the returns the annuity provider can earn on the underlying annuitized assets. Higher interest rates imply higher payout rates because the insurance company will be able to earn more interest on the premiums in their general account supporting the annuity payments.
3. Overhead costs relate to extra charges an annuity provider seeks to cover business expenses and to manage risks related to the accuracy of their future mortality and interest rate predictions.
Pricing for a Life-Only Income Annuity
Exhibit 4.1 provides a simple example to illustrate the basic pricing dynamics for an actuarially fair income annuity. This is an annuity without any overhead costs, and it assumes the underlying projections for mortality and fixed-income returns are correct. I use the capital market expectations I described in Chapter 3, of which the relevant aspect is that I assume the bond yield curve is flat at a nominal 3 percent interest rate. For this example, we consider a sixty-five-year-old female who is offered $10,000 of spending per year as long as she lives. Since we are using a nominal bond yield curve, this spending is fixed. The income annuity is life-only, so payments stop at death. How much is this protected lifetime income stream objectively worth?
Exhibit 4.1 Calculating the Cost of a $10,000 Income Stream for a Sixty-Five-Year-Old Female (Life Only)
Retirement Researcher
Source: Survival Probabilities are calculated from the Society of Actuaries 2012 Individual Annuitant Mortality Tables with improvements through 2019.
Finding how much the annuity is worth requires inputs for investment returns to be earned on the premium financing these payments, and the survival probabilities to each subsequent age. Our example calculation includes some simplifications. With a typical upward-sloping yield curve, payments coming sooner would earn less interest, and later payments would grow at a faster rate. Additionally, many annuity providers will likely seek higher returns than Treasury bonds offer by including high-quality corporate bonds with higher yields to compensate for slightly higher default risk. Annuity providers may also be using more refined mortality data that is better connected to their customer base.
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I also assume the full year of spending arrives at the start of each year, rather than having income arriving on a more typical monthly basis. But the simplifications here will capture the concept of annuity pricing well enough.
The 3 percent bond yield and return acts as a discount rate to reduce the value needing to be set aside today for the future $10,000 payments. For instance, the exhibit indicates that at age seventy-five, the discount factor is 74.4 percent. The interpretation is if I put $7,441 in the bank today, and it grows at an annual 3 percent compounding interest rate for the next ten years, I can expect these assets to grow in value to $10,000 by my seventy-fifth birthday. If I was building a bond ladder, this is the amount I would need to invest into a ten-year zero-coupon bond to provide that $10,000 payment.
The process is the same for the $10,000 payment provided at each age. The later payments are received, the more time they have to compound and grow, requiring less to be set aside today to fund those payments.
The next columns are what differentiates an income annuity from a retirement income bond ladder. For a bond ladder, the total cost is the sum of the Discounted Value of Income column, which is $238,082 through age 104. Annuity owners obtain a discount on the bond ladder pricing because the survival probabilities to each subsequent age indicate whether these payments will need to be made. Any one individual is either alive or dead. But for a large pool of individuals representing the customer base of the annuity provider, the company can rely on the law of large numbers to evaluate what percentage of customers will remain alive at each subsequent age. This is risk pooling.
The data from the Society of Actuaries suggests that a sixty-five-year-old female has a 91.4 percent chance of living to seventy-five. An annuity provider can expect 91.4 percent of their sixty-five-year-old female customers to be alive and receiving income at seventy-five. The company does not know who specifically from among their customers will be alive and receiving payments, but they can be pretty confident with their planning that 91.4 percent of their customers will be alive.
When we multiply this percentage by the discounted value of the funds needed to provide the $10,000 payment at seventy-five, we see that the annuity company plans $6,801 for the cost of providing this payment at age seventy-five. This is the survival-probability weighted discount factor, and the same process is followed for each age. For another example, a $10,000 payment at age 100 requires $3,554 to be set aside today with a 3 percent interest rate for the purposes of an individual building a bond ladder. Given that there is a 10.8 percent chance for the sixty-five-year-old female to reach age 100, the annuity provider further multiplies this amount by the survival probability so that the expected costs for a $10,000 survival-contingent payment is only $384. A sixty-five-year-old female need only pay $384 today for a guarantee to receive $10,000 at age 100 if she accepts that receiving the payment is contingent upon her surviving to that age.
When we add survival-weighted costs by age, we see that the total expected cost to provide $10,000 of annual spending to a sixty-five-year-old female, at least through age 104, is $172,915. If this dollar amount represents the premium charged, then the payout rate on the annuity is the $10,000 income it provides divided by this cost. The payout rate is 5.78 percent. Note that this is also 27 percent less than the cost of the bond ladder. The bond ladder costs more, with the benefit that the bond ladder supports some legacy if retirement lasts less than the full ladder length. But the bond ladder does not provide any additional longevity protection beyond the end date of the ladder as assets are fully depleted at that time. With the income annuity, that longevity protection can be provided with 27 percent less funds.
This is an excerpt from Wade Pfau’s book, Safety-First Retirement Planning: An Integrated Approach for a Worry-Free Retirement. (The Retirement Researcher’s Guide Series), available now on Amazon
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