Submitted by Anonymous on

This forum thread is a continuation of a question that was posted in the FAQ section: http://www.annuitydigest.com/faq#n20

The question basically asked whether there are useful rules of thumb when choosing between bonds and annuities.

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tom replied on Permalink

## Annuities (Longevity) Versus a Zero Coupon Bond

Full Disclosure: Much of the conceptual basis and logic for the material below is contained in a paper that was written by Dr. Jason Scott who is the Managing Director of the Retiree Research Center at Financial Engines.

1) As a highly simplified example, consider a driver with no access to auto insurance. The driver must “self-insure” and therefore must set aside his own funds in the amount of the replacement value of the car. He cannot spend the money he sets aside to self insure. Assume replacement cost is $20,000.

2) Access to auto insurance changes the situation as the person only has to set aside the cost of insurance.

3) Assume (super simplified) all claims are the full value of the car ($20K).

4) Assume the driver has a reasonable driving record and only a 5% chance of a claim.

5) Assume insurance is sold at cost. As a result, care insurance is $1,000 ($20K * 5%).

6) In this highly simplified example, purchasing insurance frees-up the person’s balance sheet and allows the driver $19,000 in additional spending relative to self insurance ($1 results in $19 of additional spending).

7) “Spending improvement per premium dollar” (or, in a sense, leverage per premium dollar using the insurer’s balance sheet), is a good way to select among competing insurance contracts—simply select the insurance product with the highest spending improvement per premium dollar:

a) “S” = spending improvement per premium dollar

b) “P” = probability of insurance payout

c) S = self insurance costs – (P * self insurance costs) / insurance costs

d) This simplifies to 1 – P / P e) In other words, a low likelihood of payout correlates directly with efficient insurance/high leverage (high S), and an insurance contract with a high likelihood of claim payout from an insurer is incredibly wasteful.

Self Insuring Longevity Risk:1) Assume a 65 year old person wants to fund spending (to have a guaranteed payout) for a single year 20 years in the future at age 85.

2) A reasonable choice would be a zero coupon bond (although, in reality, it would be a ridiculously complex and unlikely exercise for most people).

3) The price today for a bond that pays $1 in 20 years depends on prevailing interest rates.

4)Assume interest rates (real) are 2.5% at all maturities.

5) Price of the bond today is $0.61 (1 / (1.025)^20)

6) Thus, each $1 the person wants to spend at age 85 can be secured today for 61 cents.

7) The zero coupon bond is analogous to self insurance in the example above—the money is set aside whether or not the insurance event (the person living to 85) occurs.

Insurance to Fund Longevity Risk:1) To guarantee or secure future spending, an annuity contract is an alternative to the zero coupon bonds above.

2) Assume an annuity similar to the zero coupon bond that pays out $1 in 20 years (such annuities exist—it is referred to as a “longevity annuity” which is an annuity with fixed payouts that begin at a future date).

3) Assume 20 year survival probability for a 65 year old male is 52%.

4) As in the car insurance example, the price of the insurance depends on the cost of self insurance ($0.61 or the cost of the zero coupon bond) * payout or claim probability (52%).

5) Thus, price of the annuity is $0.3172 or @ 50% discount to the zero coupon/self insurance option.

6) “S” (spending improvement) in this example is @ .93 per premium dollar, so future spending that costs $1.93 in the bond market costs $1 in the annuity market.

7) Every annuity dollar allocated to guarantee future spending at age 85 frees up 93 cents for additional, current spending.

8) In addition, the annuity allocation (which would be a relatively small portion of one’s overall portfolio) would potentially allow for more aggressive and beneficial allocation of the remaining, non-annuitized assets.

9) Annuities like the longevity annuity above can be very powerful.

10) Unlike a bond, they are not investments but rather are insurance products. Annuities convert a pool of assets into a fixed stream of payments and can provide protection against outliving one’s assets by guaranteeing payments in perpetuity or any other selected future date.

11) An efficient insurance product frees up spending by providing access to an insurer’s balance sheet for low probability events.

12) Depending on the context (e.g. the age and financial profile of the purchaser), some insurance products and annuities are highly inefficient.

13) Take, for example, an immediate fixed annuity that would provide fixed payments for the 65 year old person starting at age 66:

a) The person likely has a 98.5% chance of living until 66 (extremely high probability claim payout).

b) As a result, the spending improvement per premium dollar is very low (@ 1.5%).

c) Cost relative to a zero coupon bond is also almost a wash (.985 * .61 = @ .61) and likely would be less efficient when insurance product frictions/costs/fees are included.

d) Reality is that most people buying an immediate fixed annuity would have a 10 year or other term so mortality rates would be blended over the 10 years and product would become somewhat more efficient.

tom replied on Permalink

## Annuity Yield

Another (and simpler) way to think about this involves the annuity yield offered through a single premium immediate annuity (SPIA).

With a SPIA, a lump sum premium buys a lifetime of monthly annuity payments. Pretty simple.

The annuity yield is simply the annual income provided by the SPIA divided by the initial premium.

For example, assume a person buys a $100,000 SPIA that provides monthly payments of $700 ($8,400 per year). The annuity yield is 8.4% ($8,400 / $100,000).

The annuity yield will typically be higher than the yield on a government bond because the annuity consists of: 1) interest payments on the $100K; 2) a return of a portion of the $100K, and; 3) a return of a portion of other people's money (the mortality yield or mortality credit).