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B2.2 · Compare investment risk and return

Learn to compare investment risk and return through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Personal Finance

A practical guide to weighing possible gains against uncertainty

When people compare investments, they often notice the possible gain first. But an investment’s possible return is only part of the decision. The chance that its value will fall, or that its results will be unpredictable, matters too. This lesson uses straightforward descriptions and data to compare the two. It does not identify one choice as best for everyone: people may value potential growth and certainty differently.

What you will learn

Explain what investment return and investment risk mean.
Compare investment choices using both possible return and uncertainty.
Use simple data to support a comparison without treating past results as a promise about the future.

1. A short bridge: percentages and gains

A percentage is a rate measured out of 100. For example, a return of 4% means a gain equal to 4 for every 100 invested over the stated period, before any fees or other costs. The time period matters: a rate described as annual is for one year.

To compare a simple gain, find the percentage of the amount invested. If CAD 500 earns a 4% return over one year, the gain is CAD 20 because 4% of 500 is 20. The ending amount would be CAD 520 if there were no fees and the stated return occurred.

The word “if” is important. A stated or past return does not guarantee that an investment will earn the same amount in the future. Before comparing figures, check that they refer to the same time period and are presented on the same basis. A return after fees should not be compared as if it were before fees.

\text{percentage gain} = \text{amount invested} \times \text{return rate}

Return describes the gain or loss over a period.
Compare rates only when their time periods and fee basis are clear.
A possible or past return is not a promise.

2. What risk means in an investment comparison

Investment risk is the uncertainty about what an investment will be worth or earn. An investment has greater risk when its results are less predictable or there is a greater possibility of losing some of the money invested. Risk is not the same thing as a guaranteed loss; it describes uncertainty and the possibility of an unfavourable result.

Return can be positive, zero, or negative. A positive return means the investment increased in value over the period. A negative return means it decreased. For example, a choice that gained 8% in one year and lost 6% in another had changing results. Those changes are evidence that its return can vary. By contrast, a choice with a stated, fixed rate may have more predictable returns under the terms described. Always read what conditions apply; a simple comparison cannot establish that every investment of a certain type is safe.

A higher possible return often comes with greater uncertainty, but this is not a rule that predicts the outcome of every investment. A high advertised return alone does not tell you how likely it is to occur, whether losses are possible, or what conditions apply. Compare both the return information and the risk information rather than assuming one figure tells the whole story.

Risk concerns uncertainty and the possibility of loss.
Variable results are less predictable than results that are fixed under stated terms.
A larger possible return does not by itself show that an investment is a better choice.

3. A fair, useful comparison

Start by making the comparison fair. Check that each option is being considered for the same length of time. Look for whether the figures are possible, expected, fixed under stated terms, or based on past results. Also check whether fees are included. If important information is missing, say so rather than guessing.

Next, describe return in plain language: which option has the larger stated or possible gain? If useful, calculate the gain on the same starting amount. Then describe risk: which option has more variable results or a greater possibility of loss, based on the information provided? Do not call an option “low risk” merely because the example shows one positive result.

A small table can keep the two parts visible. It does not turn uncertain results into promises. The table below uses hypothetical information; it is for practicing comparison, not recommending an investment.

A sound conclusion mentions both sides. For instance, one option may have a higher possible return but less predictable results. Another may have a lower stated return but more predictable results under its stated conditions. Which trade-off is preferable depends on a person’s needs and comfort with uncertainty. The evidence supports a comparison, not a universal answer.

Use the same time period and starting amount when comparing gains.
State what the information says about return and what it says about risk.
Explain the trade-off instead of declaring one investment best for everyone.

4. Read the evidence carefully

Past results can help describe how an investment behaved, but they do not settle what it will do next. A short record may not show the full range of possible results. A single unusually good year is not enough to conclude that the same return will continue.

Check the wording of a claim. “Could earn” describes a possibility, not a certainty. “Earned” describes a result in the past. “Fixed rate under these terms” describes a stated condition, but you still need to understand what the terms cover. If you cannot tell what a number represents, you do not yet have enough information for a fair comparison.

When you explain a choice, be precise and balanced. Name the return information, name the risk information, and identify any missing detail that could affect the comparison. This makes your conclusion more useful than relying on a label such as “safe” or “high return” alone.

Separate past results from future possibilities.
Use careful wording that matches the evidence.
Point out missing information instead of filling gaps with assumptions.

Two ways to compare the hypothetical choices

Choice	Return information	Risk information described
P	Possible 2% return; CAD 40 on CAD 2,000 if it occurs	Results described as staying within a narrow range
Q	Possible 10% return; CAD 200 on CAD 2,000 if it occurs	Large ups and downs, including losses

Worked example

Compare a predictable stated return with changing past results

Two hypothetical options are described for a one-year comparison. Option A has a stated annual return of 3% under the terms provided. Option B had returns of 9%, −7%, and 6% in three past one-year periods. Compare their return and risk information. What would each return mean on CAD 1,000 if it occurred?

Check the comparison
Both descriptions use one-year periods. Option A is a stated rate under described terms; Option B’s figures are past results. They are not the same kind of evidence, so keep that distinction in the conclusion.
Find Option A’s gain
Find 3% of CAD 1,000. Convert 3% to 0.03 and multiply by the starting amount. This gives a gain of CAD 30 if the stated rate applies and there are no other costs.
$0.03 \times 1000 = 30$
Interpret Option B’s results
The three past results include both gains and a loss. Their changes show that Option B’s return varied over those periods. They do not tell us what its next return will be.

Answer: Option A has a stated 3% annual return under the described terms, equal to CAD 30 on CAD 1,000 if it applies. Option B had less predictable past results, including a loss, so its record shows more variation. The information does not prove either option’s future result or provide enough detail to rank every aspect of their risk.

Check: The Option A calculation is correct: 3% of CAD 1,000 is CAD 30. Option B’s negative result indicates a loss in that past period.

Worked example

Compare possible returns and risk descriptions

A person is comparing two hypothetical choices for the same one-year period and starting amount of CAD 2,000. Choice P describes a possible 2% return and says results have stayed within a narrow range in the information provided. Choice Q describes a possible return of 10% and says its value has had large ups and downs, including losses. Compare the choices without assuming either possible return will occur.

Compare the possible gains
Calculate each stated possible rate on the same starting amount. Using the same amount makes the dollar figures easier to compare, but they remain possibilities rather than guaranteed gains.
$0.02 \times 2000 = 40, \qquad 0.10 \times 2000 = 200$
Compare the risk descriptions
Choice P is described as having a narrow range of past results. Choice Q is described as having larger changes and losses. Based on these descriptions, Q has more evidence of variable results and possible loss.
State the trade-off
Q has the larger possible gain, while its described results are less predictable. P has the smaller possible gain and a narrower range in the information provided. The description does not make either possible gain certain.

Answer: If the possible rates occurred, P would gain CAD 40 and Q would gain CAD 200 on CAD 2,000. Q offers the higher possible return but has the more variable risk description. P’s described results are narrower, but its possible gain is smaller.

Check: The calculations are correct: 2% of CAD 2,000 is CAD 40, and 10% is CAD 200. The comparison distinguishes possible gains from guaranteed outcomes.

Common mistakes and how to avoid them

Treating a past or possible return as guaranteed.

Correction: Use wording that reflects the evidence. A past result happened before; a possible return may not occur.

Choosing the largest return figure without considering risk.

Correction: Compare the return information and the uncertainty or possibility of loss together.

Comparing rates for different time periods as if they were equivalent.

Correction: Check the stated period first. If periods differ, the comparison is not yet fair.

Calling an investment risk-free because one example shows a gain.

Correction: One result cannot establish that losses are impossible. Describe only what the available information supports.

Lesson summary

Return is the gain or loss over a stated period; risk is uncertainty and the possibility of loss.
A fair comparison uses the same time period and checks whether figures are past, possible, or stated under particular terms.
A larger possible return may come with less predictable results. Compare both features and avoid treating possibilities as promises.

Check your understanding

Question 1

Two choices have possible one-year returns of 3% and 8%. The information says the 8% choice has had much larger changes in value, including losses. Which comparison is supported?

The 8% choice has the higher possible return and more evidence of variable results.
The 8% choice is guaranteed to earn more.
The 3% choice cannot lose money.
The 8% choice is best for every investor.

Show answer and explanation

The 8% choice has the higher possible return and more evidence of variable results.

The information supports a higher possible return and greater variation for the 8% choice. It does not guarantee a gain or establish which choice is best for everyone.

Question 2

An investment gained 5% in a past year. What can you conclude from that fact alone?

It will gain 5% next year.
It gained 5% in the past year, but its next result is not established.
It cannot have a negative return.
It has no investment risk.

Show answer and explanation

It gained 5% in the past year, but its next result is not established.

A past result describes what happened during that period. It does not guarantee a future result or show that losses are impossible.

Question 3

A stated possible return is 4% for one year. What is the possible gain on CAD 500 if that rate occurs and there are no other costs?

CAD 4
CAD 20
CAD 50
CAD 200

Show answer and explanation

CAD 20

Four percent of CAD 500 is CAD 20, because 0.04 times 500 equals 20. The wording “if that rate occurs” keeps the result conditional.

Key terms

Investment: Something a person puts money into with the aim of earning a return, while accepting that results may be uncertain.
Return: The gain or loss from an investment over a stated period, often described as a percentage.
Risk: Uncertainty about an investment’s result, including the possibility that its value or return will be lower than hoped.
Variable: Changing rather than staying the same.
Stated rate: A rate described in the information or terms for an investment; its meaning depends on those terms.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MBF3C), expectation B2.2. It is a study resource, not an official curriculum publication.

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