Gain 50% one year and lose 50% the next. The average of those two returns is 0%. Your money, though, is down 25%. Which number would you rather be graded on?
Learning objectives. After this week you can (1) compute ROI and CAGR; (2) compute a holding's weight and explain rebalancing; and (3) judge a return against the risk taken to earn it.
Remember this: your mix of stocks, bonds and cash sets most of your risk, and rebalancing keeps the mix you chose.
1) Simple return (ROI)
ROI = Gain ÷ Cost × 100
Return on investment is your gain as a percent of what you put in. $1,000 that grows to $1,200 gained $200, so ROI = 200 ÷ 1,000 × 100 = 20%. Every arena account started with $100,000, so a Total value of $104,000 is an ROI of 4%, the same figure your Account panel shows as Total return.
2) Compound annual growth rate (CAGR)
CAGR = (Ending Value ÷ Beginning Value)1/n − 1
Over several years, ROI hides the yearly pace. CAGR is the steady yearly rate that turns the start into the end. $100 growing to $121 over 2 years: (1.21)1/2 − 1 = 1.10 − 1 = 10% a year. That is the honest version of the opening question: +50% then −50% leaves $75 of every $100, a CAGR of about −13% a year, not 0%.
3) Allocation, weight and rebalancing
Asset allocation is how you split the portfolio among stocks, bonds and cash. It drives most of your risk and expected return: more stocks means more of both, while bonds and cash lower both. An investor with decades ahead can usually ride out more stock risk than one who needs the money soon.
Weight = Position Value ÷ Total Portfolio Value
As winners grow, the mix drifts away from what you chose. Rebalancing means trimming what has grown past its target weight and adding to what has fallen behind, to restore the mix.
| Measure | Inputs | Result |
|---|---|---|
| ROI | $1,000 → $1,200 | 20% |
| CAGR | $100 → $121 over 2 yrs | 10%/yr |
| Weight | $2,000 position in a $10,000 portfolio | 20% |
4) The risk-adjusted view
Two portfolios that both return 10% are not equal if one took far more risk to get there. A risk-adjusted view compares the return with the risk behind it, so a steady 10% beats a wild 10%. It keeps you from crowning a lucky, high-risk bet.
Quick self-check
(a) You invest $4,000 and it becomes $5,000. ROI? (b) A $2,500 position in a $10,000 portfolio. Weight? (c) $1,000 becomes $1,331 in 3 years. CAGR? (Answers: 25%; 25%; 1.3311/3 − 1 = 10% a year.)
Common mistakes
- Averaging yearly returns. Use CAGR for the true multi-year pace.
- Leaving cash out of the mix. Cash is part of your allocation and has its own weight.
- Judging raw return alone. Ask what risk produced it.
This week in the arena
Compute your ROI from your Total value and the $100,000 you started with, and check it against Total return in your Account panel. Then compute the weight of each holding, and of your cash, from the Holdings table. That is the allocation you actually have, which may not be the one you meant to have.