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Teacher Guide: 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.

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10 questions on Investing Basics. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Explain the fundamental relationship between risk and reward in investing
  • Calculate and interpret standard deviation as a measure of investment risk
  • Compute risk-reward ratios for investment decisions
  • Compare investments using risk-adjusted returns
  • Apply risk-reward analysis to real-world financial decisions
Prerequisites
  • • Understanding of percentages and percent change
  • • Basic knowledge of mean (average) calculation
  • • Familiarity with square roots
  • • Understanding of basic investment concepts (stocks, bonds, returns)
Discussion Starters
  • 1. If you had 1000 dollars to invest for 20 years, how much risk would you be comfortable with? Why?
  • 2. Why do you think some people invest in very risky assets like cryptocurrency?
  • 3. A lottery ticket has a terrible risk-reward ratio, yet millions of people buy them. Why?
  • 4. How might your risk tolerance change as you get older?
Common Misconceptions

Past high returns guarantee future high returns

Remediation: Use historical examples of investments that performed well then crashed. Emphasize that past performance doesn't guarantee future results - it's a legal requirement on all investment ads!

Risk only means losing money

Remediation: Explain that risk also includes volatility - even if you don't lose money, wild swings can be stressful and force poor decisions. Risk includes the uncertainty itself, not just the worst outcome.

Differentiation Ideas

For Struggling Students:

  • • Focus on the 2x2 concept: low risk/low reward vs high risk/high reward
  • • Use simple risk-reward ratios with whole numbers (3:1, 2:1)
  • • Provide step-by-step scaffolding for standard deviation calculations

For On-Level Students:

  • • Calculate risk-adjusted returns for multiple investments
  • • Analyze real investment options using historical data
  • • Compare different portfolio allocations

For Advanced Students:

  • • Explore the Sharpe ratio (excess return per unit of risk)
  • • Research beta and systematic vs unsystematic risk
  • • Analyze how correlation affects portfolio risk
Standards Alignment
  • HSS.ID.A.2 (CCSS.MATH.CONTENT.HSS.ID.A.2)

    Use statistics appropriate to the shape of the data distribution to compare center and spread

  • HSS.ID.A.3 (CCSS.MATH.CONTENT.HSS.ID.A.3)

    Interpret differences in shape, center, and spread in the context of the data sets

  • MP.4 (CCSS.MATH.PRACTICE.MP4)

    Model with mathematics - apply mathematics to solve problems in everyday life

Lesson Resources
  • visualRisk-Return Graph

    Interactive chart showing different investments plotted by risk and expected return

  • activityPortfolio Simulator

    Students build portfolios and see how different risk levels affect outcomes

  • worksheetRisk-Reward Calculations

    Practice calculating standard deviation and risk-reward ratios

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

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.

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.

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

What is a 'good' risk-reward ratio?

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.

Can I avoid risk entirely in investing?

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.

Why would anyone choose lower returns?

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

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