Monday, September 24, 2012

Efficient Frontiers with Stocks and Something Else


Yesterday, I posted about my new research article, "An Efficient Frontier for Retirement Income."

In the comments, Aaron wrote:


Wade
Great article and I love your paper.
Getting the right splits in the product allocation is something we are spending some time considering here.
The dominance of the partial annuity strategies in your chart is consistent with out work here, but I suspect many will find the level of dominance a little surprising.
One question I have is in regard to the nominal/ indexed annuity differences. I understand why the nominal is on the frontier, given pricing and the effective discount rates. However, how far away is the indexed frontier in your model, and indeed the VA frontier. I would be very interested to see your figure with the 4 frontiers of stocks with bonds/ fixed SPIA/ nominal SPIA/ VA as a comparison.
Regards
Aaron



Aaron, thanks, and here's the answer. This figure shows all of the combinations between stocks and one other asset (bonds, VA/GLWBs, inflation-adjusted SPIAs, and fixed SPIAs):


To just provide more intuition about what I'm doing, I will explain why the allocation to 100% Real SPIAs is where it is.  The lifestyle goal and minimum needs are a real 6% of assets. 2% comes from Social Security. The real SPIA payout is 3.88%.  Thus, every year of retirement, the real SPIA supports  (2 + 3.88) / 6 = 98% of retirement spending needs. That is constant every year in every simulation. It is the only point that won't have any variability in the outcome. Since lifestyle goals are not met with this allocation, nothing is ever returned to the investment portfolio, and the remaining financial assets are always 0. Thus, the point is at x=98, y=0.

P.S. I'd like to thank Taylor Larimore for starting a thread about the article at the Bogleheads Forum. More discussions can be found there.

7 comments:

  1. When you say that a mix is, say, 70% stock and 30% Fixed SPIA, are you referring to the mix at retirement? What happens as one moves through retirement? Can you illustrate how the investments would change as time moves forward? I am having trouble visualizing exactly the scenario you are modeling.

    Also, did you look at any scenarios where the allocation is not fixed, but the stockk portion is gradually moved into bonds?

    ReplyDelete
    Replies

    1. Hi, yes, that refers to the mix at retirement.

      30% of assets are used to buy a fixed SPIA. This leaves 70% of the initial financial assets in the financial portfolio. That 70% now becomes 100% again for remaining financial assets and the 70/0 numbers for stocks and bonds imply a 100% stock allocation for those assets.

      For the rest of retirement, no more SPIAs are purchased. Remaining financial assets are kept at 100% stocks.


      About shifting gradually to bonds, I've just looked at a fixed asset allocation here. But evidence I've seen made suggests that actually, in retirement, the optimal glide path is to increase stocks rather than to decrease stocks! For that reason, a fixed allocation would at least work better than a decreasing allocation. I think the reason being that the time to lower stocks is when you are most vulnerable to absolute losses from stocks, and that is at the start of retirement. At least, I don't think a glidepath to lower stocks will improve the efficient frontier.

      Thank you

      Delete
  2. Wade
    Thanks for the update. The chart above provides some very interesting comparisons.
    I showed the chart to one of the sales team here and he said it looks like a shark. The front and back of the shark's fin shows the dominance of the annuity over nominal bonds in a retirement income portfolio.
    I think that refinements and extension to your approach here would be beneficial to consider. I will look forward to seeing more results.
    Regards
    Aaron

    ReplyDelete
    Replies
    1. Thank you Aaron.

      You are right, it does look like a shark fin.

      I'll get back to you via email too. Thank you, Wade

      Delete
  3. Wade,
    Can you explain how the person with 0% stocks and 100% SPIA is left with 30% at end of life?

    ReplyDelete
    Replies
    1. Yes, it's in the article. Since the SPIA rate is higher than the spending needs at the start of retirement, I assume that the excess SPIA income is reinvested into stocks. It's not an error.

      Delete
  4. To follow up on this 0/100 data point, why doesn't the curve turn to the lower left if all income is met at something < 100% SPIA?

    ReplyDelete