諾貝爾經濟學獎得主的獲利公式：3階段分配法，讓投資風險更低，報酬更高，提早過上財務自由的人生

by Ian Ayres, Barry J. Nalebuff

Libertarian principles seem basic enough-keep government out of boardrooms, bedrooms, and wallets, and let markets work the way they should. But what reasoning justifies those stances, and how can they be elucidated clearly and applied consistently? In Li

Genres: Finance, Nonfiction, Economics, Personal Finance, Business, Money, Self Help

Unknown Binding

First published January 1, 2010

About the author

Ian Ayres is the William K. Townsend Professor at Yale Law School and the Yale School of Management, and is editor of the Journal of Law, Economics and Organization. In addition to his best-selling SuperCrunchers, Ayres has written for the New York Times, the Wall Street Journal, Financial Times, International Herald Tribune, and The New Republic. He lives in New Haven, Connecticut.Barry Nalebuff is Professor of Economics and Management at the Yale School of Management. His books include The Art of Strategy (an update of the best-selling Thinking Strategically) and Co-opetition. He is the author of fifty scholarly articles and has been an associate editor of five academic journals. He lives in New Haven, Connecticut.

Reviews

[Niel Bowerman · Rating 5 out of 5]

This book has influenced my retirement investment strategy more than any other book I've read.

Top 4 take-aways:
1. Most people diversify their investments across asset classes. This book argues persuasively that diversifying investments across time also makes sense.
2. To do this, consider investing your retirement on 2x leverage when young. Only do this for retirement assets that you don't need for 30 years, not funds you might want soon. When you are young you have long enough for the increased volatility to pay off in increased returns.
3. In practise this is tricky to do, but you can use LEAPs, margin trading with platforms like Interactive Brokers which offer it far cheaper than competitors, or buying a house with a large mortgage.
4. Only invest with leverage if you have the stomach for it and won't pull your money out in a downturn. Perhaps try with a small amount of leverage first to see how it feels.

[Daniel Frank · Rating 5 out of 5]

Provocative, revolutionary, innovative, brilliant; this book is a rare 5/5 gem that deserves every superlative I can think of.

While the book is has some issues, the core idea is so frickin important it deserves 100 stars.

I say this about a lot of books, but I truly wish more people were exposed to this idea (and help create infrastructure for this type of investing).

This is not an exaggeration, if you're reading this review, reading this book may make you $100,000's (+++) richer.

[Thomas Margot · Rating 4 out of 5]

It's pretty weird. Everywhere you go, you only read one thing. "Invest in a globally diversified low-cost index fund". And that's it. Nothing more to it. Everyone repeats the same thing. Buy VWCE or IWDA/EMIM and the puzzle is solved, the question is answered. There is nothing more to discuss, the dogma is created and every movement away is heresy. Other actions that will get you exiled from any "sensible" investing community are, not limited to but including: the usage of loans for investing and investing money you might need in five years or less. Should you disobey these tenets, shame on you: reddit activists will strike you down and perhaps ban you too.

This book is a fresh wind of new ideas. The authors propose not only differentiating horizontally with different assets, but also differentiating vertically throughout time. When we are young we are investing with relatively small amounts, but the older we get, the bigger our capital gets and the more risk is involved. This risk is not evenly distributed throughout our life. Thus the author suggest that we should first calculate what the total amount of savings will be that we will accumulate in life, and then think about how much of that amount we want to allocate in stocks (60%, 70%, 80% etc). When that amount is known, we should strive to constantly have that amount invested throughout our lifetime in order to reduce time-risk. This implies that when we are young, we must use leverage to reach that amount (though leverage no higher than 2:1) and when we are older and getting closer to the desired amount we must deleverage. When we are about to retire and thus no longer have future savings to invest, there will no longer be any leverage involved but the end result will be greater than when we never used any leverage at all.

The book is very convincing and heralds this strategy as the future of investing, just like "normal" index investing was also once seen as weird and unusual but has become mainstream since. Using leverage when young is the rational way to invest and the author make a very clear case why this is so.

I am convinced, though we must also not forget that the most important organ of the investor is not his brain but his stomach. Using leverage is nice and is probably truly the optional strategy, but with this strategy especially one must "stay the course" even when crashes occur: leverage cuts in both directions and giving up halfway results in disaster.

Nonetheless, I will give it a shot. Not immediately with everything, but it has given me hope that there are alternative strategies with which one can be succesful.

A must-read book for all open-minded individuals with an interest in investing.

[Bouke · Rating 5 out of 5]

This is a neat little book, with a easy to grasp insight:

1. If you're going to be employed in the future, you will have future savings. You know this for sure.
2. You can see your future savings as a a bond that pays a certain amount per month. You can discount this bond by the prevailing interest rate to get its present value.
3. Your risk tolerance doesn't change during your lifetime. The only thing that changes is your future savings.
4. Therefore, if you want to be 50% exposed to stocks, you will need to borrow money to be properly exposed in your younger years. Investing with leverage when young will lead to higher minimum, maximum, and average returns.
5. The key insight is that investing with leverage early on leads to 'temporal diversification'—you should expose yourself to more market risk early in your life so you can have less risk later on in life. This is less risky than not leveraging when young. Think about it this way: imagine you could invest everything at birth, and pay off the loan over time. If the interest rate is low enough, then this would be the way to go. With a broker like Interactive Brokers, you can borrow at 1.5%, so it's a cheap way to allocate your risk that you would take in your 50s to 60s across your 20s-40s. This would lead to a lower risk with higher returns.

Very good insight. The only reason I'm not jumping to borrow money to invest myself, is because it seems daunting and something that can cause quite some damage.

[Steve Granger · Rating 2 out of 5]

The strategies discussed in this book are a bit more involved than I'm looking for and more advanced than I can currently appreciate. Consequently, I'm not the greatest judge of most of the advice offered in this book. However, I did not find the idea of borrowing money with interest to invest very appealing. I'm sure it makes sense in some circles, but seems too high stakes for me.

[Steve · Rating 5 out of 5]

Not really a review - just some points.

Definately an interesting theory, but I'm still a little skeptical on the practical implementation of using margin. Also it seems like rebalancing the leverage too frequently might impact the overall benefits of leverage. In an endnote, the authors note that their simulations assumed portfolios were rebalanced on a monthly or annual basis. This assumption is key: in rapidly crashing markets this strategy could backfire by increased leverage or no longer rebalancing on a monthly basis. If anyone has experience on how IBKR liquidated margin portfolios (especially during the last 2020 whipsaw market) I would be interested in your opinion of this book's strategy. Other leveraged methods may have similar issues. In a crashing market, this may be where the daily leveraged funds perform better, however they would underperform in bull markets.

For Canadians, this is where the Smith Manoeuvre (or similar HELOC borrowing) may have some advantages, but that is another subject altogether.

It seems the authors diverge from a passive approach by saying to adjust the Samuelson share with CAPE (suggesting you can time the market with PE-10). It is unclear if a high PE-10 is really high when factoring in cheap credit in our current environment; perhaps high PE is a better predictor on a bad time to use leverage due to greater downside risk and incurring a margin call. If you ignore this PE-10 timing strategy, you probably would have done quite well since the book was published; the timing strategy wouldn't have helped for the period post-2009 (you would have been less exposed to equities). This timing strategy also somewhat conflicts with the author's view that equities could be supported at higher valuations.

The Figure on p.107 shows the same general 'bond tent' type strategy, increasing stock allocation after the initial years of retirement. It is interesting to see the same conclusion to mitigate sequence of returns risk by using different analysis.

Overall this is a very interesting strategy, and the basic Samuelson-share consideration for time diversification makes a lot of sense, and should probably replace the "age minus" rule of thumb for bonds many people recommend. However, using leverage would require more research, and of course require a certain kind of very systematic and educated investor. I would be very interested to see if the authors leveraged lifecycle funds are created for the masses, as this would make their strategy easier to implement for individual investors.

I like that this book takes a fairly different viewpoint than most, so while I don't agree with everything written, it is very thought provoking and should be further explored by financial planners.

[Bryan Price · Rating 5 out of 5]

Outstanding research!

[Steven · Rating 5 out of 5]

I was researching leveraged ETFs and this book came up. The main idea is that young people should use leverage to buy stocks for temporal diversification. This seems promising, as long as you invest like a robot, you likely can improve expected returns without increasing your risk. It has been 15 years since this has been proposed, it would be interesting to see how this strategy has performed. I appreciate how the authors made complicated concepts easy to understand and wrote out reasons why one should not follow their strategy. The book is biased towards a US audience, so for non-Americans we need to do more thinking. It also seems non-trivial to implement this strategy automatically, it seems like we need to think a lot about the future and program some spreadsheets. I suppose for those of us in our twenties a 100% equity allocation for retirement savings is an easily implementable partial step towards the full strategy. Overall, it was a great read to learn more about investing strategies.

[Travis Morton · Rating 4 out of 5]

The main premise is that in the same way investors diversify their assets, they should also be diversifing across time periods. The authors argue that an investor should consider their current AND future savings when retirement planning. If you consider that future savings act as a bond that will pay its coupon throughout your life, then most young investors are highly under-invested in equities compared to their target allocation. To address this they suggest young investors deploy 2:1 leverage on equities until they have enough invested in equities to bring down the dominating bond portion of their portfolios.

Personally, the strategy is interesting, although compared to the one-fund ETFs offered in Canada there is currently no easy method for implementation. The two options are investing with margin, or using options, both of which come with their own cons. The other main concern with deploying leverage is being able to stomach the bear markets 🤢

[Ke · Rating 5 out of 5]

读这本书的初衷是因为论坛看到这两支etf/fund的推荐ntsx 和 psldx，想要更详细地了解“lifecycle”对于risk tolerance的影响。之后的ira contribution应该会给到psldx，希望能离FIRE更进一步吧！

A few quotes from the book:
For example, firms are added to the S&P 500 index not because the S&P thinks they’re a good investment, but because the firm is thought to be representative of the market.

And as late as 1986, Alabama and Montana had constitutional provisions prohibiting trust investment in stock.

Indeed, the SEC has concluded that “as a fiduciary, a broker may only make recommendations that are in the best interests of his customer, even when the recommendations contradict the customer’s wishes.”

You should allocate your investments based on your lifetime wealth, not just your current savings.

[Richard Zhu · Rating 4 out of 5]

I didn't need 230 pages of analysis to convince me to get jacked to the tits on leverage...

But the point still stands. The book is a deep analysis of the insight that Paul Samuelson had in 1969: You should allocate your investments based on your lifetime wealth, not just your current savings.

For the vast majority of young people who expect their stable salaries to continue to the uncertain future, the net present value of their total savings can be much greater than whatever savings they have today. To "diversify across time" and balance out the natural tendency to have way more invested in the market when you're old, it makes sense to buy stocks on leverage.

Of course, don't take this as a wholesale endorsement of risky concentrated and leveraged strategies. And at least for today's era of sky-high valuations, be careful - some eventual contraction in PE ratios from 30-40x to 10-20x, despite 50% growth, can still give your portfolio a haircut of 30%.

[Mohit · Rating 1 out of 5]

Ummm, interesting.

Theoretically, fair. I'm sure the math checks out. Publish or perish - so these professors published. I like the idea - diversify across time. If there were few things I could make happen - i.e. lower standard deviation, non-callable debt - I might try it at a much smaller scale.

The Kelly criterion is a beautiful thing, and this just goes counter to Kelly. Plus, it doesn't account for user error - which easily throws the most vanilla strategies out of whack. There's a reason they let you take a mortgage on a house - no mark to market, and non-callable debt. Good luck getting that.

Would read. Would not recommend.

[Russell · Rating 3 out of 5]

Some interesting ideas about "temporal diversification" instead of just "asset diversification". I'm contraindicated per their guidelines but it's still an interesting thing to think about.

I wonder if the authors have made any headway with offering easy target lifecycle funds yet, since they talked about having started to do so in this, which was published now some time ago.

[Donovan · Rating 3 out of 5]

The title is a bit misleading. The promoted strategy is not new or safe, but it is definitely audacious.

Years ago, this book was my first real introduction into the theory of lifecycle investing, so I am grateful to it for that. However, I am not a big fan of the strategy Ayres and Nalebuff propose, nor do I like the optimistic way they paint it.

The strategy is to leverage your stock portfolio when young (the recommendation was 2 times your equity) to get closer to your true optimal investment fraction since many people have an implicit investment in their future income (human capital). However, the potential risk of one's human capital was not thoroughly examined nor considered during the author's simulations. The authors cite a couple of early studies stating the correlation between human capital and stock returns is low. But later studies (such as Benzoni et al., 2007, among others) call this into question (and were available at the time of publication). The book does not mention this at all. Plus, the risk of one's human capital is largely dependent on their job. The opposite recommendation may be more appropriate for someone with a riskier income that is connected to the stock market. The book suggests that young investors in particular should use a lot of leverage, yet these people have highly uncertain human capital.

The strategy is based on Merton and Samuelson's claim that an investor should have a constant fraction of their wealth in stocks. It was not mentioned that this model is based on many crucial assumptions, some relevant ones being that investors have constant relative risk aversion, that they consume a constant fraction of their wealth (this never happens in practice), that they are not habit-forming, and that the risk-free asset does not change over time. When these assumptions are relaxed the optimal lifecycle strategy can change significantly.

Ayres and Nalebuff do not assume that investors consume a constant fraction of their wealth, but they do assume that investors consume a constant fraction of their income. In practice, investors often experience shocks to their consumption, such as when a large unexpected expense pops up.

The recommendation of going from up to 200% equities all the way down to something like 50% is also extreme in terms of degree. Even models that predict higher stock allocation when young often only recommend a slight increase, not a 4 times increase. Overdoing it can make things way worse, even if the underlying idea happens to be correct.

The book is easy to understand and is clearly an introductory text. Despite this, the extremity of the strategy combined with the lack of mentioning its possible flaws make it very dangerous to beginners who don't know better. This puts the book in a weird place, where it is too basic to be intended for experts but too dangerous for beginners.

[Toni Kokkonen · Rating 4 out of 5]

The book did make me think about stock allocations with regards to leverage in more thought. The book largely advocates to investing with 2:1 leverage when young and paring that down quite late to a 85%ish stock allocation at retirement. According to the authors' studies this amount of leverage with a monthly re-calculated allocation would have never gone broke. Will need to look more into this with how it worked during the covid-dip of March 2020. Also the authors did bring forth very interesting views of looking at social security, future income streams from wages and how much like equity one's compensation is linked into the thought processes. This book certainly wouldn't be my first suggestion for personal finance type of literature, but I'd say its more thought out than the average book and a nice addition to read if you're interested in the topic.

[L · Rating 4 out of 5]

Personal finance book that pushes the boundaries on traditional advice.

Core concept is:
- If you want to be 80 / 20 stocks to bonds, you should be 100%+ in stocks because your personal income and social security are basically bonds
- You need to figure out your personal risk tolerance to understand what % stocks you should be (and how exposed your job is to the stock market). They recommend being 2x levered when in your 20s and reducing from there down to 50% bonds in your 60s
- Then you should use options from options xpress or a margin account from interactive brokers to put leverage on your stock investments

Hard to implement in practice for me given interest rates on margin being high now relative to historical stock returns and worries about how indexed I already am to stocks given my job.

[Allen Donne · Rating 2 out of 5]

While this book does offer some valuable information, the most relevant content probably could’ve been published as a research paper or article. That’s important to note considering the price you’re paying for the book.

Also as someone who works in the investment industry, one point of contention I have is the overly simplistic description of LEAPs. While in the money LEAPs do allow for leverage, one major cost that was not covered was how much time value (theta) gets eroded by buying then holding LEAPs. The book glosses over how harmful theta decay could be, which is important in determining when to roll over your option.

[Zane · Rating 4 out of 5]

Overall, the message is powerful—using leveraged investing early in your life is a very powerful and extremely overlooked investment tool. With that said, the fact that they don't do a serious comparison of non-leveraged tax-free investment vs leveraged taxable investment was a bizarre oversight. I still think that an FHA mortgage on some owner-occupied real estate will return much higher cash-on-cash.

[Michael Jindra · Rating 5 out of 5]

I didn’t find this book to be entertaining, neither funny nor even well written. Yet it is one of the most important books I have ever read.

Idea of “diversifying risk across time” meaning to invest with leverage while young and decrease it with growing income became central to my investing life. It is so profound yet unappreciated that I had to share it with everybody that I talked to about investments.

Please read this book, it will be the best paid couple of hours in your life.

[Ajay · Rating 4 out of 5]

The idea of diversifying across time is totally fascinating. Even if you don't implement the ideas in this book (and at this point I won't be), they're worth reading and thinking about. I'm planning on revisiting this book in a weeks after I've spent some time thinking about the ideas contained within it.

[Phil M · Rating 3 out of 5]

Interesting ideas, but easier to describe than to implement. A strategy that "works" 100% of the time, barring behavioural screw-ups (a very big caveat).

I won't be implementing the strategy whole-hog, but there are a number of takeaways that will make their way into our saving/investing strategy. This is not a book I would recommend to most people I know.

[Stefan Gugler · Rating 5 out of 5]

I've never read a popular financial book that made a more rigorous argument for something as counterintuitive as high leverage. Absolutely splendid read. Every rebut that came to my mind was brought up and often analyzed with real data or simulated data and compared to different strategies including best and worst case scenarios.

It's a bit niche but if you're there, it's really worthwhile.

[Victor · Rating 5 out of 5]

The idea of diversifying over time as well as assets seems obvious in hindsight. Currently it looks nontrivial to attain optimal leverage in practice, but it is trivial to get much closer to the optimal than traditional strategies. Will be doing more research on this topic, happy to discuss it.

[Naraen Sridharan · Rating 3 out of 5]

The book does a good job of making the case of diversifying your investments across time vs just assets. I'm sold that leverage has a place in your investment strategy if you use it wisely and have the necessary guardrails. 3 stars because a long article would sufficed.

[Alvaro · Rating 5 out of 5]

The book is fascinating, reading it is like when for the first time you discover EMH, MPT and passive investing, and aha moment. The key idea is developed in the first two chapters, after that is a lot of technical (but valuable) implementation details.

[周 大為 · Rating 4 out of 5]

一個簡單的概念，生涯投資是依據你的終生資產來定，而不是現有資產。(想像買房的決策大概就理解了) 所以年輕資產少時，把投資的槓桿開高一點，是相當合理的。

換言之，年輕應該藉由槓桿加大投資金額，然後逐年降低投資比例直至退休。

這應用了「分時投資」的概念，其與「標的分散投資」一樣，可以降低風險的同時確保一定報酬。

不過最高別超過200%，不然槓到自己歪頭就沒救了。

很好的投資建議，非常感謝作者。給4星是因為裡面太多段落是在舉例說明這個簡單的概念，稍微有點繁瑣。

[christian blair · Rating 5 out of 5]

New investing concept with actionable steps

New investing concept (time diversification) which the authors go into depth about. The authors also provide actionable steps to implement time diversification for those that are convinced!

[Scott Strang · Rating 5 out of 5]

Every index investor needs to read this. Even if one doesn't have the personal risk tolerance to follow through with their leverage principles, their thoughts about considering time with regard to portfolio allocations are life changing, as well as their arguments about what constitutes a bond.

[Grant Jensen · Rating 4 out of 5]

Idea that I have been interested in for a while, but figured I should read the source material. Unfortunately, it didn’t provide some answers I was looking for such as the validation of the strategy in high interest rates, and more flushed out analysis on different ways to achieve leverage.

[Kalvin · Rating 2 out of 5]

Eh, pretty typical finance book. Not very well written, but I do believe in what the author's are purporting. Could be 1/4 the length (though I read it in about 2 hours). Will implement a 2:1 leveraged portfolio going forward with some sweet, sweet LEAPs.