In Uncategorized on November 12, 2009 at 12:53

The article below first appeared in our Washington Post column yesterday. I’m reproducing it in full here because there is an important correction, thanks to a response by Andrew Biggs. I’ve fixed the mistake and added notes in brackets to show what was fixed. Also, I want to append some additional notes about the data and some issues that didn’t fit into the column.


Recent volatility in the stock market (the S&P 500 Index losing almost 50% of its value between September and March) has led some to question the wisdom of relying on 401(k) and other defined-contribution plans, invested largely in the stock market, for our nation’s retirement security. For example, Time recently ran a cover story by Stephen Gandel entitled “Why It’s Time to Retire the 401(k).”


However, the shortcomings of our current retirement “system” predate the recent fall in the markets, will not be solved by another stock market boom. The problems are more basic: we don’t save enough, and we don’t invest very well.


We ran several scenarios of what a typical two-adult household that entered the job market last year at age 22 might expect to receive on retirement at age 65 in 2051. For each scenario, we assumed that our household would earn the median amount for its age group every year. We began with data from the U.S. Census Bureau on 2008 earnings by age group, and assumed that real incomes would grow by 0.7% per year (the average growth rate for the 1967-2008 period). According to analysis by Andrew Biggs, medium earners typically accumulate Social Security benefits equivalent to 52% of their pre-retirement income, which comes to $40,265 per year. (All figures are in 2008 dollars.) For our scenarios, we used different estimates of the household’s savings rate and of the rate of return it would earn on its savings. [Correction: I initially used the online Social Security Social Security benefits calculator, which says it provides estimates in “today’s dollars,” but actually uses wage-indexed dollars. See Biggs’s explanation of the difference.]


For the first scenario, we assumed the average economy-wide savings rate of 2.4% over the last ten years (1999-2008) and a real rate of return of 6.3% — the long-term average real return for the stock market. (In his book Stocks for the Long Run, Jeremy Siegel calculates the annual real rate of return from 1871 to 2006 as 6.7%; updating that figure through 2008, we get 6.3%.) At retirement, this yields accumulated savings of $298,064. Today, a 65-year old couple could convert $298,064 into a joint life annuity of $18,467 (we did an online search for annuity rates), meaning that they would receive that amount each year (not indexed for inflation, however) as long as either person were still alive. (Anything other than buying an annuity is gambling that you won’t outlive your money.) $18,467 is only 24% of the household’s income at age 64. Combined with Social Security, the couple would receive $58,732 per year, or a respectable 76% of its pre-retirement income of $77,432. [Correction: Originally this was 59%; all later figures were also 17 percentage points too low.]


Savings were unusually low over the past decade. The current savings rate (first three quarters of 2009) is 3.6%. Plugging this into our spreadsheet, we get an annuity of $28,092 and retirement income of $68,357, or 88% of pre-retirement income.


But this overlooks the fact that people do not earn the rate of return of the stock market. Even assuming that people are investing in stocks, most do so via stock mutual funds which, on average, do worse than the stock market as a whole. For example, in the 1990s the average diversified stock fund had an annual return 2.4 percentage points lower than the Wilshire 5000 Index (which reflects the performance of the overall market). The main reason for this underperformance is that mutual funds have to pay fees to their managers — who, on average, do not earn those fees through superior stock-picking (to put it mildly).


If we use a 3.9% annual return instead of a 6.3% annual return, now our annuity is only worth $15,347 per year, and combined with Social Security our household is only earning 72% of its pre-retirement income. But wait — it gets worse.


The average investor in mutual funds does not even do as well as the average mutual fund. The reason is that investors tend to chase returns. They take money out of funds that have recently done badly and move it into funds that have recently done well. Because of mean reversion (the tendency for trends away from the average to return back to the average), this means they take money out of funds that are about to go up and put it into funds that are about to go down. Among large blend stock funds (the category that includes S&P 500 index funds), research from Morningstar shows that the gap between mutual fund performance and investor performance ranges from 0.9 to 2.2 percentage points, depending on fund volatility. (It can be much higher — over 10 percentage points — for other types of funds.)


Taking an average gap of 1.6 percentage points, our expected annual returns are now just 2.3%. Now our cumulative savings are only $172,853 and our annuity is only $10,709; combined with Social Security our household is only earning 66% of its pre-retirement income.


Now, you can get close to that 6.3% expected return through a simple strategy: buy a stock index fund and don’t touch it. But this has another problem — you are 100% invested in stocks, the riskiest of the major asset classes. Whatever your expected cumulative savings, there is a 50% chance that your actual savings will be lower, and they could be a lot lower.


Since we’re talking about survival in old age, ideally our household would not take any risk at all. The closest you can get to this is to invest in inflation-protected Treasury bonds. 20-year TIPS (Treasury Inflation-Protected Securities) currently yield 1.96% on top of inflation. [Note: In the Post column I used 2.4%, the yield at the latest auction; however, that was back in July, and long-term bond yields have come down since then, so this is the current yield according to Bloomberg.] This provides a final annuity of $9,925; combined with Social Security, that’s 65% of pre-retirement income. That’s not very much. And the only way to get higher returns is by taking on risk.


Bear in mind that we’re assuming that Social Security will be around in its current form, as will Medicare (or else seniors will have sharply higher health care costs than they do today). Also, we’ve made a number of optimistic assumptions along the way: that life expectancies do not increase by 2051 (this would reduce the annuity you can get with the same savings); that median-income households save money at the average rate for all households, which is untrue (richer households save at a higher rate, making the average savings rate higher than the median savings rate); and that the savings rate is constant over age (since older people in fact save at a higher rate, the money has less time to build up). In addition, we haven’t started talking about below-median households, who save at a lower rate. [Note: I assumed you can get an annuity yielding 6.2%, from this online site; Biggs, who probably knows better than I, uses 5.4%, which yields lower annuities for the same amount of savings.]


The problems, in short, are that we don’t save enough and we don’t invest very well. One could argue that these are a matter of choice. People could save more, and they could make smarter investing decisions. But given that they don’t, we could very well see tens of millions of seniors without enough money to live decently in retirement. Given that prospect, perhaps we should question leaving retirement security to individual choices and free markets.




Andrew Biggs argues that the numbers show that the retirement system is doing OK. After all, if you assume just a 2.4% savings rate and a 6.3% real return, you get 76% of your pre-retirement income. The system is doing better than I thought it was before Biggs pointed out my error, but that’s almost entirely due to Social Security. Social Security is replacing 52% of pre-retirement income (not 35% as I initially calculated) and private savings are replacing anywhere from 13% to 24%, depending on the scenario. I think the 13% scenario is the most accurate, since is the lowest-risk option; anything else is not retirement saving, it’s retirement gambling.


Biggs also thinks (email to me) that my savings rates are too low, especially with auto-enrollment into 401(k)s on the rise. This is a plausible point; we don’t really know where the savings rate will end up after this recession. If the median worker is auto-enrolled in a 401(k) — and, even better, if he gets an employer match — he may be OK. Then we may be talking about a problem that affects a significant number of lower-income households (who are less covered by 401(k)s and employer matches than higher-income households), though not the median household.


This is the spreadsheet with the scenarios. won’t let me upload an Excel file, so I embedded it in a Word file and uploaded that.


There’s a legitimate question about 2008 vs. 2051 living standards. For example, in our most pessimistic scenario, we still end up with an annuity of $50,190 in 2008 dollars. That might not seem so bad. After all, median income in 2008 was only $53,303, and this is all in real terms, right? However, I don’t think that’s the right approach to take. Living standards will improve on average between now and 2051, and therefore an income of $50,190 2008 dollars will feel very different in 2051 than it felt in 2008. This is why I think the right comparison is to pre-retirement income; that tells you the drop in living standards that people will suffer at retirement. (In practice, most people probably won’t buy annuities, and won’t adjust their living standards down immediately — but that just means they have a higher chance of outliving their money.)


Another possible objection is that we’re leaving out capital gains from housing. Even if the average return that investors get from stock mutual funds is only 2.3%, the fact is that many people invest in their houses and seem to get higher returns. However, I think that we can’t count on these higher returns. First, these returns are largely a product of leverage and subsidized interest rates; real housing prices underperform the stock market. Second, a given house doesn’t really change in real value (the utility it provides to people), even if its price changes; in general, its value goes down, unless you put money into it for maintenance and improvements. If the price of equivalent houses goes up in real terms, that just means that (on average) one generation of home owners is taking money from the next generation of home buyers in the form of higher prices. In other words, it’s a multi-generational Ponzi scheme that can’t go on forever. Third, of course, not everyone owns a house.


In doing the research for this column I came across a paper by Andrea Frazzini and Owen Lamont called “Dumb Money: Mutual Fund Flows and the Cross-Section of Stock Returns.” They find that, at least when looking at historical data, you can make money by doing the opposite of what investors do with their mutual funds. That is, money flowing into mutual funds is a valid predictor that the stocks in those funds will, on average, go down relative to the market. The real beneficiaries are corporate issuers of stock, who are able to issue stock at high prices when demand for it is high. I also like the way they put their findings into context: “These facts pose a challenge to rational theories of fund flows.  Of course, rational theories of mutual fund investor behavior already face many formidable challenges, such as explaining why investors consistently invest in active managers when lower cost, better performing index funds are available.”


Finally, I hate making mistakes. So I wholeheartedly endorse Biggs’s call for the Social Security Administration to fix its misleading calculator.


By James Kwak



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