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I've frequently heard that the conventional wisdom is to be invested in an 'aggressive' investment strategy when young, and as you approach retirement age, migrate to a more conservative strategy. Given that I've heard it so often, I figure... it must be sound.

But can anyone explain why?

Mathematically it seems like the expected rate of return, whatever that might be, is the same for both. An aggressive strategy is higher risk and higher reward. A conservative strategy is lower risk and lower reward.

Why is the overall expected return better by being aggressive in the beginning? Do they outperform conservative strategies, or does it imply your ability to 'time the market' and get out of the aggressive strategy at a particular time?

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Mathematically it seems like the expected rate of return, whatever that might be, is the same for both. An aggressive strategy is higher risk and higher reward. A conservative strategy is lower risk and lower reward.

That is not true. Roughly, the mathematical analogue of "higher risk and higher reward" is "higher standard deviation and higher mean". In other words, the aggressive strategy does have a higher expected rate of return (higher mean). Its disadvantage is that it has a higher likelihood of incurring intermediate losses (and/or higher magnitude of intermediate losses) on the way.

This is classically illustrated with the following chart -

enter image description here

from Vanguard. You can see that the average return is greater the riskier the portfolio (i.e., the more allocated to stocks relative to bonds), but this higher average return comes at the price of a greater range of possible returns. With an aggressive portfolio, you take a greater risk of losses at any given moment for a greater chance of gains over a long period.

Given this, it should be obvious why the advice is to be aggressive early on. Early in life, you don't care about whether your current position is up or down, because you're not taking the money out. If your portfolio is down, you just leave the money in there until it goes back up again. Later in life, you need to spend the money; you now care about whether your current position is up or down, because you can't afford to wait out a down market and may have to realize a loss by selling.

It's important to note that the expected return is always greater for a higher-risk portfolio, as is the expected risk; the expected rate of return doesn't magically change as you age. What changes is your ability to absorb losses to hold out for later gains.

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    +1 Bren - edited to embed the graphic. If you prefer I didn't do that, pls just roll back edit.
    – JTP - Apologise to Monica ♦
    Sep 21, 2015 at 10:02
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    This is right but for the wrong reason. The total return over a lifetime is the product of each year's return. And multiplication is commutative. You'd get the same distribution of expected returns on a dollar you add to the account today if you invert this picture (going more aggressive later and less aggressive earlier). The reason this minimizes downside risk is because you usually add money over time and you are then applying a lower-risk option (e.g. bonds) on more of the money you've put in. This lowers the overall variance (i.e. risk).
    – JoshG79
    Sep 21, 2015 at 21:16
  • "the expected rate of return doesn't magically change as you age" - Peter Diamandis might disagree with that.
    – Dan Dascalescu
    Sep 22, 2015 at 13:11
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As others have said, this opinion is predicated on an assumption that early in your life you have no need to actually USE the money, so you are able to take advantage of compounding interest (because the money is going to be there for many many years) and you are far more tolerant of loss (because you can simply wait for the markets to recover).

This is absolutely true of a pension pot, which is locked away for a great many years.

But it is absolutely NOT true of general investments. Someone in the mid-20s to mid-30s is very likely to want to spend that money on, say, buying a house. In which case losing 10% of your deposit 3 months before you start looking for a house could potentially be a disaster. Liekwise, in your mid-40s if your child's school/college fund goes up in smoke that's a big deal.

It is a very commonly espoused theory, but I think it is also fundamentally flawed in many scenarios.

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I believe it is because you can withstand a loss in your early life better than you can in your retirement. If you lose 25% in your 20s it is a lot less than 25% in your 60s. You, hopefully earn more in your 60s and you have a lot more already in the bank in your 60s.

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    This is a reason why an aggressive portfolio is not a good idea in later life, but it doesn't answer the question, which is why the expected return is greater for a high-risk portfolio.
    – BrenBarn
    Sep 21, 2015 at 5:32
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    The question assumes that you want to be aggressive early in life because of a higher rate of return. That assumption is not correct. It isn't because the rate of return is greater, it is because the greater risk is more tolerable.
    – Jack Swayze Sr
    Sep 21, 2015 at 6:53
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    @JackSwayzeSr: The higher expected rate of return is exactly why one wants to be aggressive. Just because risk is tolerable, is not a reason to tolerate it, unless there is some payoff.
    – Ben Voigt
    Sep 21, 2015 at 18:54
  • Perhaps this article and the associated videos will explain it better than I can. investopedia.com/video/play/riskreturn-tradeoff
    – Jack Swayze Sr
    Sep 21, 2015 at 19:09
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TL;DR

A kid can lose everything he owns in a crap shoot and live. But a senior citizen might not afford medical treatment if interest rates turn and their bonds underperform.

What is risk and return?

In modern portfolio theory, risk/"aggression" is measured by beta and you get more return by increasing risk. Risk-adjusted return is measured by the Sharpe ratio and the efficient frontier shows how much return you get for each level of risk. For simplicity, we will assume that choosing beta is the only investment choice you make.

Examples of setting beta

  • You are buying a house tomorrow all cash, you should set aside that much in liquid assets today. (Return = who cares, Beta = 0)

  • Your kids go to college in 5 years, so you invest funds now with a 5 year investment horizon to produce, with a reasonable level of certainty, the needed cash then. (Beta = low)

  • You wish to leave money in your estate. Invest for the highest return with a horizon of your lifetime. (Return = maximum, Beta = who cares)

In other words, you set risk based on how important your expenses are now or later. And your portfolio is a weighted average.

Your biggest asset

On paper, let's say you have sold yourself into indentured servitude. In return you have received a paid-up-front annuity which pays dividends and increases annually. For someone in their twenties:

  • $5,000 monthly earnings
  • 5% annual raises
  • 40 years of earnings

This adds up to a present value of $1 million.

Blending

When young, the value of lifetime remaining wages is high. It is also low risk, you will probably find a job eventually in any market condition.

If your portfolio is significantly smaller than $1 million this means that the low risk of future wages pulls down your beta, and therefore:

Youth invest aggressively with available funds because they compensate large, low-risk future earnings to meet their desired risk appetite.

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