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Investment Analysis: Probability and Payoff

Would you take a bet if you had less than a 50% chance of winning? It depends on the payoff, right?

For example, this is a bad bet:

  • 1/5 chance of winning,
  • $5 cost to play, and
  • $10 payout if you win.

And this is a good bet:

  • 1/5 chance of winning,
  • $5 cost to play, and
  • $100 payout if you win.

In the first scenario, for every $25 you spend, you’ll win $10 on average — not good! In the second scenario, for every $25 you spend, you’ll win $100 on average — woohoo!

Conclusion: The probability of winning or losing isn’t that meaningful without information about the consequences of winning or losing.

Active vs. Passive Investing

Most of the talk about active vs. passive investing focuses on how likely it is that an actively managed mutual fund will outperform its benchmark.

But as Rick Ferri (author of the upcoming The Power of Passive Investing) explains in this interview, probability of winning is only half the picture. For example, the fact that actively managed funds have only a 1/3 chance of outperforming the market over a given period doesn’t necessarily make them a bad bet. If, when they outperformed, they outperformed by 10-times the amount by which the losing funds underperformed, it would make sense to try to pick market-beating funds.

But — and you probably guessed this — they don’t. In fact, they don’t even come close. And that is why attempting to pick market-beating funds is a losing bet.

Retirement Investment Strategies

Similarly, much of the writing about retirement investing strategies tends to focus on how likely it is that a given strategy will result in the investor running out of money. For example, you might read that Strategy X has a 10% historical rate of failure over 30-year periods (that is, 10% of the time, somebody following the strategy would have run out of money).

Surely that’s helpful information, but it’s also important to note at what point the investor runs out of money. Did it happen in year 29 or in year 15?

  • If the failure occurred in the final years, it might not have even happened in a real life situation. An actual investor (as opposed to a computer running through hypothetical scenarios) would probably trim his/her spending once it becomes obvious that cash is running low.
  • On the other hand, if the failure occurred in year 14 or 15, that’s a problem. It takes a lot of trimming to stretch a budget for an extra 15 years.

Probability of Success (or Failure) Isn’t Enough

When you’re reading about investing, remember that probability is only half the picture. Before concluding that the X% success rate or Y% failure rate that you see quoted in an article is good or bad, be sure to find out what “success” looks like and what “failure” looks like.

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Comments

  1. Good post Mike. Many investors and I suspect some advisors do not think in terms of potential reward or the potential timing of downside risk events. The latter is key in retirement planning.

  2. Excellent point, Mike! You make a good case for a fixed SPIA in retirement again with this. Assuming the insurance company doesn’t go under, you have 0% chance of running out of money (if you get an inflation rider).

    Your point about active funds is spot on as well. (Sorry to ooze praise here…) Most people don’t realize that even the active funds that do outperform only do so by about 1% or less. The % of funds that do 2% or better is very, very small – often less than 10%! Not worth the risk at all if you ask me.

  3. @Paul Williams
    > You make a good case for a fixed SPIA in retirement again with this.
    > Assuming the insurance company doesn’t go under, you have 0%
    > chance of running out of money (if you get an inflation rider).

    Don’t jump to that conclusion so fast! It’s only true if expenses stay inflation-adjusted and you don’t need access to the capital that is funding the SPIA payouts.

    Real world example: my mother got along fine on $35k/yr income until her health declined to the point where she needs daily care beyond meals and a room… for the past 3 years, her costs have been $50k/yr.

  4. @George: I’m not sure I’d ever advise putting all your money into a fixed SPIA. Access to capital is one of the severe drawbacks to annuities.

  5. “I’m not sure I’d ever advise putting all your money into a fixed SPIA. “

    Agreed. Dylan phrased this concept well in a recent email: “Most retirees do not require a designated emergency fund, but if your income is entirely SS, pensions, and/or annuities, you’d better have one!”

  6. Would you take the chance of one-third probability of retiring in a very rich lifestyle versus two-thirds probability of not being able to comfortably retire until 5 years after your desired retirement date?

  7. That is a great (and often overlooked) point about active funds. The chances of you performing significantly better than a passive fund is so small, that it usually doesn’t warrant the risk that you’ll under-perform.

    Seems like you’re telling us that reading a few headlines isn’t enough “research” to come to a solid conclusion!

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