Why does a smoother ride end up with more money?
There is a second half to the free lunch that most explanations skip. Lower volatility does not only feel better — under compounding it mechanically produces a higher realised growth rate from the same average return. This is what turns a risk argument into a wealth argument.
Two paths, one average
Two portfolios. Both average exactly 10% a year over two years.
- Portfolio A: +30%, then −10%.
- Portfolio B: +12%, then +8%.
Average annual return: 10% for both. Now compound them, since compounding is what money actually does.
- A: 1.30 × 0.90 = 1.170 — a 17.0% two-year gain, about 8.2% a year.
- B: 1.12 × 1.08 = 1.210 — a 21.0% two-year gain, about 10.0% a year.
Identical averages, different money. The volatile path lost ground to its own bumpiness.
Over a working lifetime
Repeat each pattern for twenty years, starting from $10,000:
- Portfolio A: about $48,100.
- Portfolio B: about $67,000.
Nearly $19,000 of difference — roughly 39% more money — with no difference in average return whatsoever. The entire gap was created by the size of the swings.
The rule of thumb
The relationship has a compact approximation worth carrying:
compound growth ≈ average return − ( volatility² ÷ 2 )
Check it. Portfolio A's volatility is 20%, so the drag is 0.20² ÷ 2 = 2.0 points → 10% − 2% = 8%, against the true 8.2%. Portfolio B's volatility is 2%, so the drag is 0.02 points → essentially 10%, matching. Close enough to be useful, and honest about direction: volatility always subtracts, and it subtracts as a square. Double the swings and you quadruple the drag.
Why this makes diversification worth more than it first appears
Unit 1 showed that combining different holdings lowers volatility while leaving expected return alone. This lesson adds the consequence: lowering volatility raises the compound growth actually delivered. So the free lunch pays twice — once in a calmer ride, and once in a mathematically better outcome from the same underlying average.
It also explains a result that confuses people. A portfolio whose average return is lower than the best single holding's can still finish with more money, if that single holding's path was violent enough. Compounding rewards steadiness on its own arithmetic terms — no behavioural argument required, though the behavioural one (calmer portfolios get abandoned less often) points the same way.
Try it now
- The chart below is a concentrated growth fund across five years that contain one spectacular year and one badly negative one. Read those two years' returns off it, average them, then compound them. Notice the gap between the two answers.
- Now the same two calendar years on a broader basket. Smaller swings, smaller gap between the average and the compounded result — which is the drag term, visible.
- Apply the rule of thumb to a holding with 40% volatility: how many percentage points a year is the drag? (0.40² ÷ 2 = 8 points.)