Wednesday, April 18, 2012

The Power of Single-Premium Immediate Annuities


Over the past few days I’ve been getting back into the programming spirit. This is all preliminary and subject to further checks and refinements.

This evening I’ve been looking at how partial annuitization impacts retirement outcomes. Borrowing on assumptions developed by Joseph Tomlinson, I assume a 65-year old couple can purchase an inflation-adjusted single-premium immediate annuity with a payout rate of 5.05%. 

Update: I did say this was preliminary and subject to further checks. In the comments, Joe Tomlinson pointed out that I was misremembering about the 5.05% payout rate for a real SPIA. That is for a 65 year old male, not a 65 year old couple. Thus my analysis applies to a single male. For a 65 year old couple, 3.88% is the payout rate. I've changed the figure below to point out that it is for a 65 year old male. And I've also added a new corrected figure for the 65 year old couple. My descriptions below are about the male case. For the couple, the results are much less impressive. However, it is still vital to remember that "failure" does not mean the same thing when annuities are included. With systematic withdrawals, failure means your income falls to zero. With annuities, failure means that your income falls to the annuity amount. With 50% annuitization of assets, that would mean your income falls to
100 x .5 x 3.88 / 4 = 48.5% of your original spending level once your financial portfolio runs dry.  For the couple, the advantages of annuities become less obvious, though I think this still reflects positively on them, especially if leaving a bequest is not an overly important consideration. Ultimately, to evaluate the tradeoffs for this couple, we may need to rely on the approach developed by Joe Tomlinson in his February 2012 JFP article. It accounts both for mortality rates and for how much relative importance the retiree puts on leaving a bequest. I'm also in the process of working on some other metrics to evaluate these decisions, though perhaps I should first do more careful checking before posting new material to avoid this sort of embarrassing backtracking :) 

They want to spend at a constant inflation-adjusted withdrawal amount representing 4% of their retirement date assets (the normal 4% rule assumption).

Also, while I usually base Monte Carlo simulations on historical averages, that especially isn’t fair for annuities. The annuity payout rate is based on the low current bond yields, and so I adjust the returns for stocks and bonds both downward by 1.52% so that real bond returns are calibrated to 1% instead of the historical 2.52%. This maintains the same historical equity premium, and I do not change either the standard deviations or correlations. I explained this issue more completely in Lower Future Returns and Safe Withdrawal Rates.

I’m making a retirement income frontier which shows the traditional failure rates for a 30-year retirement on the x-axis, and the median real wealth remaining after 30 years on the y-axis. I show the results for asset allocations between 0 and 100% stocks for two different strategies.





The blue curve represents traditional drawdowns from a portfolio to obtain the desired spending without annuitization. Because of the lower asset returns, failure rates are higher than my figures usually show. Stock allocations above 40% have the lowest failure rates, and these vary between about 20 and 30%. As for median remaining wealth, higher stock allocations support higher expected bequests.

The cyan curve shows what happens when the couple male annuitizes 50% of their wealth, purchasing an inflation-adjusted SPIA at their retirement date. That 50% is arbitrary and is not a maximum allocation to SPIAs or anything like that, I just wanted to see what happens in a basic scenario. This couple then withdraws the necessary amount from their remaining portfolio to top off the annuity and get their 4% spending power. With the 5.05% payout rate, this couple male is getting 2.5% of the 4% of spending from their annuity, and the remaining 1.5% of their spending comes from their portfolio.

The cyan curve shows that partial annuitization reduces failure rates across the board for all stock allocations. Even more than that, with partial annuitization, failure doesn't mean that income falls to zero. It just means that the portfolio is empty. You still have 62.5% (=2.5/4) of your original income amount from the SPIA even in the case of failure. Rethinking Safe Withdrawal Rates: The Meaning of Failure explains more about this issue.

I connected corresponding stock allocations with red dashed lines. The outcomes for remaining wealth are more mixed. With annuitization, stock allocations above about 50% would support lower bequests than the corresponding stock allocation in the no annuitization case, while stock allocations below 50% would support higher bequests.

But what is also rather important to note is that for a risk averse couple male, partial annuitization lowers the failure rates, which could make them more willing to use a more aggressive stock allocation for their remaining portfolio. Essentially, the SPIA acts like a super-bond, and so even 100% stocks with the remaining portfolio corresponds to something closer to an overall 50/50 asset allocation. Consider a couple willing to hold only 40% stocks if they don’t annuitize. With 40% stocks and partial annuitization, they can obtain both a lower failure rate and a higher expected bequest. And they could continue increasing their stock allocation to any level up to 100% to get higher expected bequests while still keeping their failure rates quite a bit lower than with the no annuitization case.

That, to me, suggests that partial annuitization really does have the potential to help retirees obtain better outcomes. I do have to acknowledge that this isn’t the full story. I assume a rather long 30 year period, and annuities will look more attractive as the period under investigation increases. When I wrote my somewhat negative column on GLWBs last December, I suggested that partial annuitization may be a better approach, and these preliminary results do suggest that a full investigation of this issue is in order.