Life-cycle finance

From Bogleheads

Life-cycle finance begins with the premise that households prefer relatively smooth consumption from year-to-year and have a strong dislike for abrupt shifts in consumption, particularly on the downside. In economics, this premise is known as consumption smoothing (described below). Therefore; in economic life-cycle saving & investing, personal finance is mainly about moving consumption through time and across contingencies. This requires also shifting financial and insurance assets through time and across contingencies.[1]

In this paradigm, consumers are quite serious about setting financial goals and meeting those goals by saving, borrowing, and insuring. How the savings are invested depends on many things, including whether they are on track to meeting a goal.[1]


People seek to smooth spending over their lifetimes in order to obtain the greatest satisfaction from their limited resources, and the problem to be solved is how high this standard of living can be. Because salary, household composition, taxes, mortgage payments, and so forth, vary so dramatically over a household's lifecycle, trying to target basic rules of thumb related to replacement rates, wealth accumulation targets, savings rates, or withdrawal rates, can end up causing more harm than good.[2][note 1]

For example, savings rates generally do not need to be fixed at some level, as it is the spending level which should be fixed. Savings (or dissavings) is what remains after accounting for all income and expenses in any given year. This creates a real disconnect as most of the discussion regarding retirement deals with rules of thumb which are anathema to practitioners of lifecycle finance.[2]

Here are some examples:[1]

Example #1: A young couple buys a house by taking out a mortgage

They are pulling financial assets from the future into the present to afford a nice house that they could not purchase simply from their current income and financial wealth. But they are also each contributing to a 401k plan and pushing current assets far into their retired future when they will have no labor income to support their consumption.

They purchase health insurance to move purchasing power across contingencies – from periods of good health to periods of bad health. They each purchase enough term life insurance so that in the contingency that one dies, the survivor is able to keep the same level of per capita consumption.

They set aside liquid funds for the contingency that one of them could become involuntarily unemployed, and thereby shift assets from good employment times to bad employment times.

Example #2: Saving for retirement

A middle aged couple saves and invests heavily for retirement and also pushes assets from the present into their retired future. Conversely, a retired couple pulls financial assets from the past into the present by drawing down financial assets or dissaving.

The retired couple has a safe floor of retirement income from SS and life annuity income to support a minimum acceptable level of consumption in retirement. Risky assets are used both prior and during retirement to move from the safe floor income goal to the higher aspirational retirement income goal.

Consumption smoothing

If you are below your consumption needs, you are borrowing funds to make up the difference. This is what usually happens when you get out of school - borrowing to pay off loans and carry a mortgage. In mid-life, you are above the line and saving funds - paying off loans and the mortgage. In retirement, you are drawing from your retirement funds.

The mid-life dip below the consumption line is an unexpected event, such as the loss of a job. In this situation, you may be borrowing from an emergency fund to maintain your lifestyle until a new job is found.

Consumption smoothing[3]
Consumption Smoothing.png

Dissaving is negative saving. If spending is greater than income, dissaving is taking place. This spending is financed by already accumulated savings, such as money in a savings account, or it can be borrowed.[4]

Risk management

Risk is managed in life-cycle finance using hedging, insuring, and diversifying. Important minimum goals are met by hedging and insuring using matching strategies. Higher aspirational goals are met by diversifying.[1]

Risk strategies that rely on hedging and insuring are called matching strategies because they match assets to liabilities. Risk strategies based on diversifying are simply called diversification strategies.

Differences between life-cycle and mean/variance approaches

Life-cycle finance is about moving assets across time and contingencies to keep consumption on a relatively smooth trajectory over a household’s entire life-cycle. It is not about leveling or flattening consumption over the household’s life-cycle. That would require an extreme amount of borrowing when people are young, which is neither desirable nor feasible in most cases. Economists jargon for this is that households are “borrowing constrained”.[1]

Life-cycle finance posits that a household saves, borrows, and ensures to keep consumption relatively smooth over its lifetime by moving assets through time and across contingencies. This is different than conventional financial planning that argues that households should save a lot every year, invest those savings at the highest expected return possible given their risk tolerance, and use that high expected wealth to address retirement, children’s education, and life contingencies that crop up.[1]

The above conventional point of view is seen as both unrealistic and undesirable. It leads to big swings in spending (consumption disruption) and high expected returns do not necessarily result in high actual returns. This means that investing in risky assets should be mainly reserved to aspirational goals and safer investing and insuring should be used to meet minimum acceptable goals.[1]

For at least the last 35 years financial economists have approached personal investing from the life-cycle finance point of view. Most financial advisors and investment enthusiasts approach personal investing loosely from the mean/variance approach to investing that was developed by financial economists in the 1950s and 1960s. Many decades ago in financial economics that approach was superseded by the life-cycle approach, which treats the earlier mean/variance approach as a relatively unrealistic special case of the life-cycle approach to personal investing.[5]

While there is a lot of overlap, there are also some significant differences between the two investment approaches. Life-cycle finance is much more goal focused than the older method.[5]

Take retirement planning goals. In the conventional approach the goal is to maximize expected financial wealth in your targeted retirement year, given how much you are willing to save, and how much investment risk you can tolerate. From the life-cycle point of view, the overall goal of retirement planning is to have roughly the same standard of living in retirement as before retirement. Therefore the retirement financial goal is to have reliable retirement income that sustains your standard of living.[5]

The way the income goal is usually framed is by pricing real annuities that supply the retirement income target and not by applying arbitrary rules like 4% of financial assets at retirement converted to income every year.[note 2]

A stress is put on having two income goals. One is the aspirational income goal and the other is a lower floor income goal that is constructed entirely from relatively safe assets such as SS, DB pensions, life annuities, and TIPS and I-bonds.[5]

Another key difference is how risk is managed, which is implicitly alluded to in the above aspirational and safe income goals.

In the older conventional framework investment risk is almost entirely managed thru diversification. In the life-cycle approach all three risk transfer methods (hedging, insuring, and diversifying) are used without particular stress on diversifying. In other words the life-cycle approach relies explicitly on both matching strategies and the conventional diversification strategy in managing investment risk.

Additionally, in the conventional framework risk is hardly ever approached thru a state price approach, but the state price approach to risk is often used in life-cycle finance.[5][note 3]

Quantitative analysis also has a different emphasis. Go to a conventional financial advisor and he will often talk about Monte Carlo simulations of the portfolio. Go to an advisor steeped in the life-cycle approach and she will analyze the problem, at least informally, through the lens of dynamic programming.[5][note 4]

Why the life-cycle finance approach gives a higher probability of reaching the retirement goal

There are many variations on Life-Cycle Finance but all share the following two features. There is a conservative or floor income goal and a higher desired or aspirational income goal.[6]

Several years before retirement you get on track to reach the floor goal by a combination of current size of safe assets, plus expected return on safe assets, plus future expected savings dedicated to safe assets.

The higher desired goal in general is achieved thru a combination of risky and low risk assets that in some manner is more aggressively rebalanced than the traditional rebalancing to a constant mix strategy. In addition, the rebalancing is asymmetric.

Now compare the two methods – Mean / Variance and Life-Cycle Finance. The Mean / Variance method starts a year at 60/40. After a very good year for stocks, like 2013, the portfolio is rebalanced back to the constant mix of 60/40. If stocks have a bad year, the constant mix strategy again rebalances back to 60/40, but this time moving assets from bonds to stocks.

Now look at 2013 using the Life-Cycle Finance approach, where again the year started at 60/40. Stocks have that great year in 2013. If we were on target to hit the aspirational level of retirement income with acceptable probability at the beginning of 2013, then it must be the case that we are now ahead of schedule. So instead of rebalancing to 60/40 the rebalancing might be to 57/43, so that we are now on track to meet the goal with higher probability. The higher probability of meeting the goal is due both to the bigger than expected portfolio size this year, and lower portfolio risk going forward. In the MV approach using constant mix rebalancing, we have increased the probability of exceeding the goal, but increased the probability of meeting the goal only slightly. In the Life-Cycle Finance approach we haven’t increased the probability of exceeding the goal, but we have increased the probability of at least meeting the goal more than in the Mean / Variance approach.

When stocks do poorly the rebalancing done by Mean / Variance would again be back to 60/40, but in the case of Life-Cycle Finance it might be more like 62/38 or 63/37. Since the portfolio is smaller than expected, we are now behind schedule for meeting our income goal, and we compensate by raising both risk and expected return. If we fall further behind and the probability of reaching our income goals drops too low, because of both small portfolio size and increased portfolio risk, we will reach the boundary on increasing portfolio risk as the probability of reaching the floor income goal drops below the acceptable range. At that point we will need to increase savings or postpone retirement to reach our income goals. A third alternative would be to plan to increase annuitization at retirement. In any case this multifaceted strategy has higher probability of reaching the goal than simple constant mix rebalancing.

Now we could adjust the asset allocation over time in line with changing financial conditions, increase saving, postpone retirement, or plan to increase annuitization using the Mean / Variance approach. But these options are typically not explicitly in the Mean / Variance approach. They are instead added in an ad hoc fashion, once the plan is far off course. Using goal focused Life-Cycle Finance, these options are baked into the plan in order to stay on course to meeting the goal over time as we approach retirement.

By both planning for a floor and aggressively rebalancing the Life-Cycle Finance approach produces a strategy that gives a higher probability of at least reaching the aspirational income goal, but at the cost of conceding the chances of meaningfully exceeding the goal. The Mean / Variance approach produces a strategy that has some probability of exceeding the goal, but a lower probability of at least meeting the goal. The “or more” than the goal has value, and the Life-Cycle Finance approach employs that value to increase the probability of meeting the goal.

Now a financial engineer can accomplish what has been laid out as a Life-Cycle Finance strategy in a manner more economically efficient than the method just described. Nevertheless, you can use the method outlined above in practice, or simply use it as a way of thinking about what is going on in Life-Cycle Finance methods in order to achieve a goal with high probability.


  1. An example of a rule of thumb is the Safe withdrawal rate.
  2. Also known as the Safe withdrawal rate.
  3. State price: In financial economics, a state-price security is a contract that agrees to pay one unit of a currency if a particular state occurs at a particular time in the future and pays nothing in all the other states. The price of this security is the state price of this particular state of the world.

    In short, the risk in risky assets tends to show up at the worst possible times. Thus you don't want to fund your financial future betting on risky assets and nothing going wrong with the economy or your health. Instead you should have a combination of risky financial assets, relatively safe financial assets, and insurance so that regardless of the future financial state you actually live in, you have a reasonable chance for an acceptable financial life. See: Re: Free Stanford Course: Finance of Retirement & Pensions, by bobcat2.

    The practical idea here is that when planning our financial future we want to think of possible likely states of our world and how we will address these contingencies. We might in the next few years be in good health, but we could be in poor health. We might be fully employed with big salary increases, but we might become involuntarily unemployed. How do we intend to address each of those possible states of our financial world? Life-cycle finance incorporates this point-of-view, which was first developed by Kenneth Arrow in the 1950s, that an investor should consider alternative future outcomes and the amount of consumption obtained in each possible situation. See: Re: Wade Pfau: Lifecycle Finance, by bobcat2.
  4. One approach to finding the smoothest consumption path is called dynamic programming which solves complex problems by breaking them down into a series of simpler, but overlapping, "sub-problems." The smallest problem is solved first, and each increasingly more difficult problem is solved in sequence.[1]

    Overlapping sub-problems are present in consumption smoothing because each period's budget constraint of how much to consume and save in each period, given the level of income and assets, depends on the solutions to all of the later periods' budget constraints.[1]

    To this end, the dynamic program for consumption smoothing begins at the last period (the small one period problem) and works backwards period-by-period to the initial period (the most difficult problem which involves all the periods).[1]

    Another definition: Dynamic programming is an approach to optimization that restates a multiperiod or multistep optimization problem in recursive form.[2]

    [1]See: Re: Wade Pfau: Lifecycle Finance, forum discussion by bobcat2, direct link to post.
    [2]See: Recursive optimization on Wikipedia.

See also


  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Supplied via PM to LadyGeek. Submitted for forum review March 14, 2014. See: Re: Wade Pfau: Lifecycle Finance, direct link to post.
  2. 2.0 2.1 Lifecycle finance: Upending the old retirement rules, Wade Pfau, on
  3. Source is available on Google Drive: Life-cycle finance.odp, LibreOffice Impress format. No preview available.
  4. Dissaving, on Wikipedia.
  5. 5.0 5.1 5.2 5.3 5.4 5.5 Re: Wade Pfau: Lifecycle Finance by forum member bobcat2, direct link to post.
  6. Wade Pfau: Lifecycle Finance by bobcat2, direct link to post.

Further reading

Introductory articles

Nationally there are perhaps only two dozen financial planners that follow the life-cycle approach rather than the conventional approach based on the older MPT paradigm. Probably the best known of these planners is Paula Hogan, who is based in Milwaukee. Paula has written several articles on the differences between the conventional MPT approach and the life-cycle approach. Her articles are very accessible to lay readers, which is something that can't be said of many of the papers by economists written on life-cycle household economics.[1]

Here are links to several of Paula's articles that discuss these two approaches to personal finance and highlight the differences.

Article Publication
Life-Cycle Investing Is Rolling Our Way Paula H. Hogan, Journal of Financial Planning, May 2007
Human Capital and the Theory of Life-Cycle Investing Paula H. Hogan, AAII Journal, May 2008
Paula Hogan: Journal Financial Planning: A Look from the Outside In Paula H. Hogan, June 4, 2012. Subscription required to view article.
The Emerging New Model for Wealth Management Paula Hogan, Zvi Bodie, March 2008
The Role of Inflation-Indexed Annuities Paula Hogan, The American Association of Individual Investors (AAII) Journal, March 2011
For Long-Term Investors The Focus Should Be on Risk Paula Hogan, Zvi Bodie, The American Association of Individual Investors (AAII) Journal, June 2005
Houston We've Landed Paula Hogan, introductory remarks at the 2007 NAPFA West Region Conference
Consumer Financial Protection in the Current Economy Paula Hogan, The American Association of Individual Investors (AAII) Journal, May 2012

Here are articles by three prominent economists on the life-cycle approach which are accessible to investment enthusiasts.[1]

The first is from Robert Merton, one of the fathers of life-cycle economics, writing in the Financial Analysts Journal. The second is by Larry Kotlikoff writing in the Journal of Financial Planning. The third is Zvi Bodie's paper from 2002. In addition there is Bodie's short companion piece to this article,

Also, you may want to follow William Sharpe's life-cycle blog - RetirementIncomeScenarios. Oddly enough, Sharpe has a second blog site devoted to life-cycle finance, this one is titled Lifetime Finance.

A recent entry is Sharpe once again discussing the obvious deficiencies of SWR rules.

Books and papers

This list of books and papers on life-cycle economics is generally a little more advanced than the above list, but for the most part fairly accessible to the interested general reader.[1]

Recommended books

  • Bodie, Zvi; Merton, Robert; Cleeton, David. Financial Economics 2nd edition (or its first and cheaper edition). ISBN 978-0131856158.
  • Stevens, Aaron. Personal Life-Cycle Economics. ISBN 978-1475292367.

Easy to understand

  • Milevsky, Moshe A. Are You a Stock or a Bond?: Identify Your Own Human Capital for a Secure Financial Future, Updated and Revised. ISBN 0133115291.
  • Milevsky, Moshe A.; Macqueen, Alexandra C. Pensionize Your Nest Egg: How to Use Product Allocation to Create a Guaranteed Income for Life. ISBN 978-0470680995.
  • Kotlikoff, Laurence J.; Burns, Scott. Spend 'Til the End: Raising Your Living Standard in Today's Economy and When You Retire. ISBN 1416548912.
  • Bodie, Zvi; Taqqu, Rachelle. Risk Less and Prosper: Your Guide to Safer Investing. ISBN 978-1118014301.
  • Bodie, Zvi; Clowes, Michael J. Worry-Free Investing A Safe Approach to Achieving Your Lifetime Financial Goals. ISBN 978-0130499271.

More difficult

  • Bernstein, William. The Ages of the Investor: A Critical Look at Life-cycle Investing (Investing for Adults). ISBN 1478227133., Bogleheads forum discussion here and here
  • Charupat, Narat; Huang, Huaxiong; Milevsky, Moshe A. Strategic Financial Planning over the Lifecycle: A Conceptual Approach to Personal Risk Management. ISBN 978-0521148030.
  • Zwecher, Michael. Retirement Portfolios: Theory, Construction and Management. ISBN 978-0470556818.
  • Zick, Cathleen D. The Economic Organization of the Household. ISBN 978-0521805278.
  • Friedman, Milton. Theory of the Consumption Function (National Bureau of Economic Research). ISBN 978-0691138862.
  • Deaton, Angus. Understanding Consumption (Clarendon Lectures in Economics). ISBN 978-0198288244.

Papers and articles

In 1985 Franco Modigliani won the Nobel Prize in Economics primarily for his pioneering work on the life-cycle hypothesis. In many ways he is the father of life-cycle economics.[2]

The theory of life-cycle economics in its modern state began with companion papers by Paul Samuelson and his student Robert Merton in 1969.[1] These papers brought rigorous dynamics into Modigliani’s life-cycle hypothesis. Samuelson’s paper dealt with the discrete time case using stochastic dynamic programming. Merton dealt with the more difficult case of continuous time using optimal control methods to deal with continuous stochastic variation.[1] These early papers used advanced math techniques and later research relies on math that is more advanced than these methods. While the math to prove these things is difficult, the underlying ideas are fairly intuitive.[1]

What makes this difficult is the dynamic nature of these problems. The decisions I make this year affect this year’s outcome and next year’s decisions, and next year’s outcome. This continues to play out this way for every year of my life from now until when I die.[1]

Vol. 51, No. 3 (Aug., 1969), pp. 239-246from jstor.og. Enable cookies to view.

There have been many papers since these 1969 papers that have updated and refined the connection between human capital and the life-cycle model. In particular the best known and most influential of those papers, "Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model", by Bodie, Merton, and William Samuelson (Paul's son) written in 1992.

The economic literature on household life-cycle economics over the last 40 years is voluminous, but the above is a good start. Life-Cycle Economics is pretty central to the modern economics of the household and the consumer. Seven Nobel prize winners are on these lists of authors. In every case their work on life-cycle economics was a core portion of their research.

Accessible papers and articles on life-cycle economics of the household [1]
Paper Author Note
The Future of Life-Cycle Saving and Investing (2006 papers) CFA Institute, October 2007, Vol. 2007, No. 3. Enable browser cookies to view
The Future of Life-Cycle Saving and Investing: The Retirement Phase (2008 papers) CFA Institute, October 2009, Vol. 2009, No. 4 Enable browser cookies to view
Life-Cycle Investing: Financial Education and Consumer Protection (The Future of Life-Cycle Saving and Investing Conference - 2011 papers) CFA Institute, November 2012, Vol. 2012, No. 3 Enable browser cookies to view
Investment in Human Capital: A Theoretical Analysis Gary S. Becker, Journal of Political Economy Vol. 70, No. 5, Part 2: Investment in Human Beings (Oct., 1962), pp. 9-49, from Enable browser cookies to view
Interpreting the Evidence on Life Cycle Skill Formation Flavio Cunha, James J. Heckman, Lance Lochner, Dimitriy V. Masterov, NBER Working Paper No. 11331, May 2005
Retirement Financial Planning: A State/Preference Approach William F. Sharpe, February 2006
Life Cycle, Individual Thrift and the Wealth of Nations Franco Modigliani This is his Nobel lecture on the life-cycle hypotheses.
Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data Modigliani and Richard Brumberg, 1954 It is the first paper in Volume 6 Franco Modigliani's Collected Papers.
Franco Modigliani and the Life Cycle Theory of Consumption Angus Deaton A paper on the enduring importance of Modigliani’s life-cycle hypothesis.
The Life-Cycle Model of Consumption and Saving Martin Browning and Thomas F. Crossley, Journal of Economic Perspectives—Volume 15, Number 3—Summer 2001—Pages Enable browser cookies to view.

Further reading notes

  1. Abstract: This paper draws upon the modern science of finance to address several important practical issues in personal finance. Chief among these is how much to save for retirement and how to invest those savings. The paper suggests ways that advances in the theory of finance combined with innovations in financial contracting technology might be used to improve social welfare by designing and producing a new generation of user-friendly life-cycle products for consumers. It contrasts the old Markowitz single-period paradigm of efficient diversification with a new Mertonian paradigm that takes account of multi-period hedging, labor supply flexibility, and habit formation.
  2. Abstract: Finance is a branch of economics that deals with budgeting, saving, investing, borrowing, lending, insuring, diversifying, and matching. In setting standards of financial literacy we ought to make sure they are consistent with the basic principles taught in economics courses.

Further reading references

  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Re: Wade Pfau: Lifecycle Finance by forum member bobcat2, direct link to post.
  2. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded to Professor Franco Modigliani, October 15, 1985.

External links