Risk and return
No investment offers a higher expected return without accepting more uncertainty. Understanding how that uncertainty is measured is the first step.
Return is only half the picture
Saying a stock returned 10% in a year does not say how it got there. It may have risen steadily, or lost 30% mid-year and recovered. Different paths, same final number, very different experience.
That is why risk measures sit next to returns: volatility, maximum drawdown, expected loss on the worst days.
Volatility
Volatility measures how widely returns spread around their average. The higher it is, the more prices swing. It does not say whether prices go up or down, only how wide the swings are.
Drawdown: the maths of losses
Drawdown is the fall from the previous peak. Losses weigh more than equal gains: after a -20% you need +25% to break even; after a -50% you need +100%.
This is why limiting big losses matters more than chasing big gains.
Return per unit of risk
Indicators such as the Sharpe ratio divide excess return by volatility: how much return was earned for each unit of risk. They are computed on the past and depend on the period chosen.
In short
- Return without risk says nothing about the path.
- Volatility = size of the swings, not direction.
- After a -50% you need +100% to recover.
- Risk measures are historical: they describe the past, they do not guarantee it.
Check your understanding
A stock loses 20%. What return is needed to get back to the starting price?
Show the answer: +25%. From 100 it falls to 80; to return to 100 you must gain 20 on 80, which is 25%.
Two funds both returned 8% in a year. The first had twice the volatility of the second. Which was more efficient?
Show the answer: The second: same return with half the swings, so a better return-to-risk ratio.