305pelusa wrote: ↑Mon Mar 04, 2019 6:37 pm
Ben Mathew wrote: ↑Mon Mar 04, 2019 10:19 am
As a benchmark, the ideal strategy that minimizes risk by spreading it out perfectly across all years would be to borrow to invest $X in the stock market early in life and leave it alone without further contributions and withdrawals to the stock market. All subsequent contributions goes towards paying off the debt and then adding to bonds.

To explain why I don't agree, I'll just give you a counterexample:

You borrow 500k, invest it in stocks and leave as-is. The rest of the years, you only pay for the debt and buy bonds. Let's say stocks stay essentially constant. You will then have 500k invested every year in the stock market. We know this isn't optimal because, as you eloquently put it, 500k at 25 years of age is more money than at 65:

Ben Mathew wrote: ↑Mon Mar 04, 2019 2:18 am$500K at age 25 is a lot more money than $500K at age 65.

As you mentioned before, the trick is to discount all your future contributions, add them to current savings, and invest a set percentage in stocks today (Say, 25 years old). You then have the duty to monitor for the rest of your life. If the stock portion grows at the same speed as the discount rate, then you need not add/subtract anything to it. If it grows slower (or worse, declines from a bear market) then you have to add to it in the future. If it grows faster (which would be ideal and generally expected over the long term), you'll sell some of it from time to time.

You'd get an identical result if every year, you re-did your share calculation like the authors recommend. Every subsequent year, less will be in future contributions and more will be in today's savings. So your current total combined wealth will be larger (less money is discounted and more money you actually have today). So if you invest a constant percentage in stocks, that dollar value will naturally grow as years go by at the discount rate. So if it also happened to grow at the discount rate, no need to add/sell. If anything else happened, you might have to buy/sell more stocks.

And yes, I agree the ideal is to take as big of a loan as you need ASAP to hit the correct number today. Doing anything else (like working up to it slowly with 2:1 leverage) is suboptimal technically speaking. Although still better than not leveraging at all when young (or so the argument goes). I just don't agree with the part that you then leave it as-is. I think you need to continue investing/selling as necessary to maintain the number on target.

Good examples, but the discount rate you're using is not the right one for this application. I'll get to why in a bit. But first, there's a simpler and more direct way to understand how lifecycle investing works. Suppose you put $X into the stock market and leave it alone. You make no further contributions or withdrawals. It will grow to $X(1+r1)(1+r2)...(1+rt) in t years. This formula shows that ri and rj are interchangeable. It does not matter what order the returns come in. A 5% return followed by a 10% return gets the same result as a 10% return followed by a 5% return. There is no sequence of return risk. A 20% gain or loss early is no better or worse than a 20% gain or loss coming in later. That means that this portfolio is not overweight or underweight at any point during the t years. The risk is being spread perfectly evenly across all years.

If, however, an extra contribution is made at some point, any returns after that contribution will have an extra kick. A 20% gain or loss after the extra contribution matters more than a 20% gain or loss before the extra contribution. The portfolio is underweight before contributions, and overweight after.

And vice versa for a withdrawal. Returns prior to the withdrawal have more impact than returns after the withdrawal. So the portfolio is overweight before the withdrawal and underweight after.

The only situation where the order of returns won't matter is the one with no extra contributions or withdrawals. That is the only portfolio that is never underweight or overweight at any point. That's the only strategy which takes the same amount of risk every single year for all t years.

Returning to the issue of discount rates, the right discount rate for this particular application (evaluating the risk exposure of the portfolio over time) is the actual ex-post realized growth rate of the portfolio. This means that if no extra contributions or withdrawals are made, the present value of the stock account will remain constant at $X at t=0. The examples you gave involve a difference between the stock growth rate and the discount rate, which can make sense in some situations, but not in this particular application.

The ideal risk-minimizing strategy of borrowing and investing $X in stock early in life, and then spending the rest of your life paying off the debt and purchasing bonds, is unattainable. But you can try to get close to this benchmark by directing all contributions towards 100% stock for the first several years of your working life. At some point, say 15 years in, you leave that stock account alone to do its thing--no further planned stock contributions. The remaining contributions over the rest of your working life goes into 100% bonds. Risk averse people will make the switch earlier--say, after just 7 years of stock contributions. Risk tolerant people will do the switch later--say, after 25 years of stock contributions.

I have played around with this on a spreadsheet, and it leads me to think that you can get a lot of the benefits using this "stocks first" approach, without having to take on leverage. The key is that because the stocks come in first and therefore get a very long horizon, you only need to allocate a few years' contributions towards stocks to achieve a relatively high stock allocation from a lifetime perspective. So you won't be spreading out your stock contributions over a very long period anyway, even without leverage. Your stocks can be pretty concentrated in the early part of your life with just a 100% stock AA.

I hope more people take lifecycle investing seriously and figure out how much they can benefit from it. I think it has a lot of potential for risk reduction compared to the traditional approach of starting with X% stock and gliding down to Y% in a straight line over a lifetime.