This post is a follow-up to my previous post in which I stated that just because many retirees do not buy annuities it doesn't necessarily follow that they are not making rational decisions. In response to that post I heard from another actuary, Andrew, who agreed and hypothesized that the non-annuity purchasers might have higher personal discount rates than the rates used by the insurance companies to price annuities, where personal discount rates are the annual theoretical or observed rates at which people value future payments vs. cash in hand. Andrew noted that many (mostly younger individuals who want to consume) frequently run up credit card debt on which they pay interest of 15% per annum or more, thus exhibiting relatively high personal discount rates for purchases of some items. Presumably personal discount rates decrease somewhat as we age (and we worry more about maintaining our lifestyles rather than buying a lot of new stuff). But how high does one's personal discount rate have to be today in order to make not buying an immediate annuity appear to be a rational decision? In this post, I use the spreadsheets in this website to make an estimate.
Based on immediate annuity quotes from Immediateannuities.com, a 65-year old male can purchase a monthly life annuity of $545 ($6,540 per annum) today for $100,000. Using the Excluding Social Security spreadsheet found in the Articles and Spreadsheet section of this website and entering $100,000 of accumulated savings, a 22-year payout period (a little bit less than the life expectancy for a 65-year old male using 2012 Individual Annuity Society of Actuaries tables with 1% per year mortality improvement), a 3.8% interest rate and 0% increases in future benefits, you get annual payments of $6,540, the same amount provided under the immediate annuity quote for $100,000. But if you self-insure your retirement, you will not be eligible to share in the mortality pooling (longevity premium) that will occur if you purchase the annuity contract. Granted, you (your heirs) will receive benefits if you self-insure and die prior to reaching your life expectancy, but no money will be available to you after you reach your life expectancy as it would under the insurance contract. Therefore in order to make a reasonable comparison we should adjust this 3.8% interest rate to reflect the mortality premium provided by the annuity.
If we follow the probabilities of survival in the SoA tables for a 65-year old male (45% survival for 25 years, 24% for 30 years and extrapolate (using my estimates) down to 1% survival at 42 years, plug each scenario into the Excluding Social Security spreadsheet (using 3.8% interest) and probability weight the outcomes (assuming 100% survival prior to 22 years), you get a resulting weighted annual payment of $5,636. This amount is approximately the same as the result you would get by inputting $100,000 of accumulated savings, a 28-year payment period and a 3.8% investment return. As a final step, we solve for the interest rate that would give us payments of $6,540 for $100,000 in savings and a 28 year payment period to find the discount rate inherent in the insurance contract including an estimate for the longevity premium. This interest rate is about 5.25%.
Given that individuals may be concerned about insurance company default, inflation risk, liquidity risk, risk of dying too soon, insurance company profits, risk of buying an annuity at historically low interest rates, etc. , they may be expected to increase their personal discount rate for buying an immediate annuity. Based on the rough estimates above, it appears that a 65 year old male who elects not to purchase an immediate annuity today has a personal discount rate with respect to this purchase greater than roughly 5.25%. Thanks, Andrew, for raising the issue of personal discount rates.