## Wednesday, March 18, 2015

### What Interest Rate is Your Annuity Paying?

If you buy an annuity for \$100,000, and it pays \$6000 per year, that seems like a 6% return. But that’s not actually the interest being paid. Most of each payment is just your own money returned to you. Here I try to work out what interest rate an annuity actually pays.

To do this, I worked out what interest rate the insurance company would have to make to exactly cover all the payments to a large group of people who buy the same annuity. For that I needed actuarial tables that predict how many people will live to each age. I used data from Statistics Canada. Note that this is not the same as just using average life expectancy; I actually assume the insurance company keeps making payments to remaining survivors each year.

There are many types of annuities. Here I focus on the simple case where there is no guarantee period, which means that the payments stop when you die, even if that happens shortly after buying the annuity. I also looked only at single person annuities with level payments (no increases to account for inflation). I repeated the calculations for males and females of ages 60, 65, 70, and 75.

The following chart shows the results. To use this chart, take the annuity payout percentage and find it on the vertical axis. Then see where it meets the appropriate chart line to find the interest rate on the horizontal axis. For example, RBC’s Annuity Calculator tells me that a 70-year old man in Ontario would have to pay \$313,820 to get \$2000 per month (\$24,000 per year) for the rest of his life. This is a payout of 7.65%. The chart says the insurance company needs to earn 1.6% per year on the man’s lump sum to break even.

Of course, this 70-year old man is getting more than just 1.6% interest. He’s also being freed from longevity risk. Well, maybe he’s just being partially freed. After all, the real value of his payments will decline with inflation over the years. Even with the reduced longevity risk, 1.6% interest seems quite dismal. That’s unlikely to keep up with inflation.

I like the idea of reducing longevity risk, but the payouts on annuities just seem way too low. You can see this more clearly if you look at annuities that increase payments every year to account for inflation. The starting payments on these annuities are much lower.

This is just one more example of how you have to sacrifice returns to eliminate risk.

1. These numbers show why annuities have largely fallen out of favour since interest rates crashed and the monthly payments have dropped. Those who bought them when interest rates were 6% and up were able to get much larger monthly payments for much smaller capital investments because the insurers could get bonds with much higher yields.

I wonder how much blue chip stocks (e.g. BCE and the banks etc.) will drop if/when rates rise to somewhere around 5% and the risk-averse can shift back to annuities and bonds and out of the stock market. I know there is a huge slice of "income investing" dollars from seniors in the market right now that wasn't there 20 years ago.

1. @Bet Crooks: You're right that low bond yields are the main reason why people are less interested in annuities. However, this reaction by investors is only partially rational. People should be focusing on real interest rates (factoring in inflation), but they tend to look at the nominal rates. Real interest rates have come down, but nearly as much as nominal rates have come down.

Everything else being equal, higher interest rates would hurt stocks like BCE and the big banks. However, everything else won't be equal. My crystal ball is cloudy.

2. Does this take into account the fees the company takes out before the payment or is that accounted for in the payment to the annuitant? Regardless, you can do as well or better potentially with a straight HISA, with the potential for higher returns ... maybe ... someday ... eventually ...

1. @Anonymous: With annuities, fees are implicit. This is true of many financial products, such as bonds, GICs, and mortgage rates. The fees get baked into the annuity payout, and baked into the interest rate paid that I compute here. If the fees were explicit, we could compute a gross interest rate before fees, but that's not the case here.

You may be able to get better interest rates with a HISA, but you'd be stuck with longevity risk. This means you wouldn't know how long you'd live or how much you could safely spend each month.

3. As I think you've pointed out before, an annuity really only makes sense to me if it's fully indexed to the CPI. Then it addresses longevity risk, market risk and the risk of inflation. I'm a lowly renter and likely to stay that way, so I've often thought about using such an annuity in retirement as a kind of guaranteed income to help pay the rent. Big fan of your blog. Cheers.

1. @Anonymous: If the payouts were better, I could see getting an annuity with a 2% or 3% increase each year to get partial protection from inflation. But I can certainly understand if you choose to avoid annuities altogether. Thanks for the kind words.

4. So many people reject annuities because they all have a story of an aunt or an in-law who purchased an annuity and who then died shortly after, with all that money going to the insurance company. It is my understanding, that in reality, a very large portion of that money simply flows through the insurance company from those who are unfortunate to die young, to those of their age cohort who are fortunate enough to live longer than their life expectancy. These are known as mortality credits and will become by far the largest portion of the payout if one lives long enough. Interest rates become much less important as age goes up.

1. @Garth: In my family, the cautionary stories are the ones where an aunt or grandfather lived to very old age with no payment indexing and ended up with nearly worthless payments. They wish they had known that it wasn't safe to spend all of their early (and more valuable) annuity payments. You're right that fear of dying young shouldn't be a concern unless there is evidence of poor health. When you shed longevity risk, you're giving up both the downside and the upside.

The reason "Interest rates become much less important as age goes up" is because there are fewer years to earn interest. But inflation is still a big concern for anyone who is long-lived.

5. Agreed. Indexing should be a priority. Too bad more Canadian lifecos don't offer true indexing as a choice. It seems that it is commonly available for US citizens.

6. respectfully, the assumptions you've made are so far from what insurance companies use as to make your numerical conclusions worthless.

You're right, lifeco's wouldn't use data from statscan. They're most likely using mortality tables from actual annuitants - not at all the same. That assumption alone likely makes your numbers stray too far from the real numbers.

You also mentioned something about paying the survivors. not sure what that means, but if you're talking about an annuity that pays a spouse a reduced amount upon death of the first person, then your numbers really are out the window. At a minimum you've used mortality tables for one person when it should be probability of the second person surviving. With two people, you're increasing the probability that one of them lives a really long time. That would increase the actual rate of return, possibly substantially.

As for the commentors expessing concern about dying early, that's an easily remedied fix. You can either buy a term certain annuity which guarantees a minimum timeframe for payout (and there's a cost) or you save the cost of that guarantee and guarantee it yourself by purchasing a life insurance policy with the savings (the life policy would return your initial capital upon your death). Or, you can decide not to insure the risk of dying early and take what life hands you. Previous commentors suggested your only choice is to take the risk of dying early - it's not.

I don't do annuities, but last time I looked (quite a few years ago), these options were all available in the Canadian marketplace.

I agree with the conclusion that annuities are a poor performer in low interest rate environments. But this study would make a lot more sense with real numbers from the marketplace.

1. @Glenn: I'd be happy to repeat this calculation with different mortality tables if anyone wished to supply one. However, different tables would only make a modest difference in the computed interest rates, so you're wrong when you say the results are "worthless."

You misunderstand what I mean by paying survivors. The insurance company no longer sends payments to an annuitant who has died. If we imagine 100,000 people buying an annuity at the same time, the mortality tables indicate how many are likely to die each year. So, each year, only the survivors get paid.