Risk vs Reward

Learn how risk and potential return are connected in investing, and how to evaluate whether an investment makes sense for your goals.

Advanced25 minLesson
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Definition

Risk in investing refers to the uncertainty of returns - the possibility that you could lose money or earn less than expected. Reward is the potential gain or return on your investment.
The fundamental principle of investing is:
Higher Risk→Higher Potential Reward\text{Higher Risk} \rightarrow \text{Higher Potential Reward}
Lower Risk→Lower Potential Reward\text{Lower Risk} \rightarrow \text{Lower Potential Reward}
Measuring Risk: Standard Deviation
Risk is often measured using standard deviation (σ\sigma), which tells us how much returns vary from the average:
σ=∑(xi−xˉ)2n\sigma = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n}}
A higher standard deviation means more volatility - the investment's value swings more dramatically.
Risk-Reward Ratio
The risk-reward ratio compares potential gain to potential loss:
Risk-Reward Ratio=Potential GainPotential Loss\text{Risk-Reward Ratio} = \frac{\text{Potential Gain}}{\text{Potential Loss}}
A ratio of 3:13:1 means you could gain 3 dollars for every 1 dollar you risk.

Try it now

If an investment has high potential returns, what can you generally expect about its risk?

Worked Examples

Investment A has an expected return of 12% with a standard deviation of 20%. Investment B has an expected return of 6% with a standard deviation of 8%. Which has a better risk-adjusted return?
1

Calculate the return per unit of risk for Investment A

12%20%=1220=0.60\frac{12\%}{20\%} = \frac{12}{20} = 0.60 → 0.60 return per unit of risk
2

Calculate the return per unit of risk for Investment B

6%8%=68=0.75\frac{6\%}{8\%} = \frac{6}{8} = 0.75 → 0.75 return per unit of risk
3

Compare the ratios

0.75>0.600.75 > 0.60, so Investment B provides more return for each unit of risk taken → B has better risk-adjusted return

Common Mistakes

Thinking high returns guarantee high risk is worth taking

Why it's wrong: Expected returns are not guaranteed. A volatile investment might have great returns on average but could lose significantly in any given year.

Correct: Compare risk-adjusted returns. Ask: 'How much return am I getting per unit of risk?'

Assuming low-risk investments are always the best choice

Why it's wrong: Very safe investments (like savings accounts) may not keep pace with inflation, meaning your money loses purchasing power over time.

Correct: Match your risk level to your time horizon and goals. Long-term investors can often afford more risk.

Confusing volatility with permanent loss

Why it's wrong: A stock dropping 20% isn't a loss until you sell. Volatility is short-term price swings; actual loss only occurs when you realize it.

Correct: Understand that volatility is normal. Long-term investors can often ride out short-term drops.

Interactive Visual

Scatter Plot

A: risk 20%, return 12% · B: risk 8%, return 6%

0510152025051015Risk: standard deviation (%)Expected return (%)AB

Bar Chart

Stock X: yearly returns, average 8%

Year 1(5)
Year 2(15)
Year 3(-10)
Year 4(20)
Year 5(10)

Mean = 8

Interactive Sandbox

Expression Calculator

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Practice Problems

16 problems
Problem 1 of 16
Easy
If an investment has high potential returns, what can you generally expect about its risk?

Why It Matters

Understanding risk vs reward is essential for making smart financial decisions:
  • Choosing investments: Should you buy stocks, bonds, or keep money in savings?
  • Setting expectations: Higher potential returns always come with higher risk
  • Avoiding scams: If something promises high returns with no risk, it's likely too good to be true
  • Long-term planning: Young investors can often afford more risk; those near retirement typically want less
Every financial decision involves weighing what you might gain against what you might lose.

Real World Applications

Choosing Between Savings Account and Index Fund

A savings account might offer 2% return with virtually no risk, while a stock index fund might average 8% but with significant year-to-year variation.

Example:

Over 10 years, 1000 dollars at 2% becomes about 1219 dollars. At 8%, it becomes about 2159 dollars - but with years of gains and losses along the way.

1Try It Yourself

You have 5000 dollars to invest. A savings account pays 2% guaranteed. A stock fund has returned an average of 10% but with a standard deviation of 15%.

What is the risk-adjusted return ratio for the stock fund?

Step 1: Write the mathematical expression

Divide expected return by standard deviation:

Evaluating a Trading Opportunity

Day traders constantly evaluate risk-reward ratios before entering trades. A good trader rarely takes a trade with less than a 2:1 reward-to-risk ratio.

Example:

If a trader risks 100 dollars on a trade, they should aim to gain at least 200 dollars to make the trade worthwhile over time.

2Try It Yourself

You're considering buying a stock at 50 dollars. You set a stop-loss at 45 dollars (5 dollars risk) and a target price of 65 dollars.

What is the risk-reward ratio of this trade?

Step 1: Write the mathematical expression

Potential gain divided by potential loss:

Key Takeaways

  • 1Risk and reward are directly connected: higher potential returns require accepting higher risk
  • 2Standard deviation (σ\sigma) measures how much returns vary from the average (volatility)
  • 3Risk-reward ratio = Potential Gain / Potential Loss; ratios above 2:1 are generally favorable
  • 4Risk-adjusted return compares return per unit of risk, helping compare different investments fairly
  • 5Your appropriate risk level depends on your time horizon, goals, and ability to handle losses

Frequently Asked Questions

Most professional traders aim for at least 2:1 (gaining 2 dollars for every 1 dollar at risk). A 3:1 ratio is even better. Below 1:1 means you're risking more than you could gain.
Most professional traders aim for at least 2:1 (gaining 2 dollars for every 1 dollar at risk). A 3:1 ratio is even better. Below 1:1 means you're risking more than you could gain.
No - even 'safe' investments carry inflation risk (money losing purchasing power) or opportunity cost (missing better returns elsewhere). The goal is managing risk appropriately, not eliminating it.
Lower-risk investments provide more stability. Someone retiring next year can't afford a market crash, so they accept lower returns for safety. Risk tolerance depends on your situation.

Glossary

Risk
The uncertainty of investment returns; the possibility of losing money or earning less than expected
Reward (Return)
The gain or profit from an investment, usually expressed as a percentage
Standard deviation
A statistical measure of how much values spread from the average; higher values indicate more volatility
Volatility
The degree to which an investment's price fluctuates over time
Risk-reward ratio
The potential profit divided by the potential loss; helps evaluate if a trade is worth taking
Risk-adjusted return
Return divided by risk (standard deviation); allows fair comparison of investments with different risk levels
Risk tolerance
An investor's ability and willingness to accept potential losses in exchange for potential gains
Today's challengeOne problem, three tries

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