Risk and return: no "high and safe"

Volatility is how far returns swing from year to year, and it rises with expected return. In the invented series the share index fund has both the tallest bars — up and down — and the highest average, 6% a year.

That higher average comes packaged with more bad years. Counting the negative years: the share index lost in 5 of 20 (worst −28%), the bond fund in 2 (worst −6%), the cash-like option in just 1 (−1%). The ranking of losing years is the mirror image of the ranking of returns.

This is the core trade-off of investing. You cannot pick the high average and leave the swings behind; they are the same thing seen from two sides. The honest question is not "which returns most?" but "which swings can I live through?".

A loss and a gain of the same size don't cancel out, because after a fall you grow from a smaller base. So the rise needed to recover is always bigger than the fall.

Take year 5's −28%: 100 becomes 72. To get back to 100 the fund must rise 100 / 72 − 1 = 0.3889, that is 38.89%, not 28%. A 50% fall needs a 100% rise; a 20% drop then a 20% gain leaves you at 96, not 100.

This asymmetry is why compound growth is lower than the simple average: the same twenty years that average 6% compound to only about 5.2% (100,000 → 275,589). Every drawdown has to be climbed out of, and the deeper it is, the steeper the climb.

How much volatility a pot of money can carry depends on one thing: how long until you need it. A bad year is only dangerous if it lands just before the money is spent.

• Emergency fund — may be needed any day, so it goes somewhere cash-like (worst invented year −1%); it can't wait for a recovery.
• Two-year goal (the kitchen) — handles mild swings or a bond held to maturity (worst −6%); not a −28% year right before the builders.
• Twenty-year saving — has time to climb out of several bad years, so it can take the share index (worst −28%) and its higher long-run growth.

Match the money to the time, not to the highest return. The longer the horizon, the more swing it can absorb, because there is time for the recovery that always follows.

"High return" and "no risk" cannot sit together, so a promise of both is itself the warning sign — before you check who's behind it. Return is the payment for risk; remove the risk and the return falls to what truly safe things pay.

In the invented series even the most aggressive option averaged 6% a year and still had a −28% year. An offer of 25% a year "guaranteed, no risk" is far above that with none of the downside, which means the risk is hidden (or the whole thing isn't real).

Checking the company, the licence and the paperwork is the next step, not a reason to believe the promise. And a small test payment that arrives proves nothing: schemes routinely pay early, small amounts to win trust before the larger money disappears.

An honest description of an investment gives a range, not a point, names the bad years, and admits the future may differ.

"6% a year" hides the swings and even overstates the growth — compounded, the series gives about 5.2%. "Last year made 5%, so expect 5%" treats one year as a forecast. "Best year +23%, so that's what it can do" cherry-picks the top. The honest version: about 5% a year compounded over twenty years, single years from −28% to +23%, and a different period could be better or worse — ideally after fees and inflation.

Saying it this way does two jobs: it sets expectations you can keep in a bad year, and it inoculates you against anyone who describes an investment as a single, certain number.