1.1.7 40–55 minutes · Read, practise, review
What you will learn
- Calculate simple total return and compound growth under explicit assumptions.
- Explain diversification and distinguish volatility from other risks.
- Interpret price, value, fees and a simplified Sharpe ratio without treating them as guarantees.
1.1 · Introduction to Investing
Introduction to Investing
Introduction to Investing · the work you will do
- 1Start with a purpose
- 2Identify the claim
- 3Trace the risks
- 4Explain the choice
Before you begin
A business is growing quickly. Its shares are expensive relative to your estimate of future cash generation. Is “a good business” enough reason to buy?
Take an initial view. Try the choices as you work through the explanations, then revisit your first view.
Video coming soon · about 5 minutes
Risk, return and value
Use the narration below while the recording is being made, then try the decisions in this lesson.
Read the full narration
Welcome to On Judgement. A business is growing quickly. Its shares are expensive relative to your estimate of future cash generation. Is “a good business” enough reason to buy? Take a first view. You can change it when you have considered the evidence.
For a simple unlevered share investment with a dividend received and no other flows, holding-period return is (ending price − starting price + dividend) divided by starting price. Fees, tax, reinvestment and cash-flow timing require additional care. A one-year figure and a five-year cumulative figure are not directly comparable. Expected return is a forward-looking estimate, not a contractual promise. Realised return is what happened. Taking more risk does not guarantee a higher realised return, and not every risk has an adequate expected reward.
With constant assumed annual return r, no withdrawals, no additional contributions and all returns reinvested, future value equals starting value × (1 + r) raised to the number of years. Changing returns require multiplying the period growth factors rather than substituting an arithmetic average. A gain of 20% followed by a loss of 20% leaves 1.2 × 0.8 = 0.96 of the starting amount, a 4% loss. The arithmetic average is zero, but compound growth is not. Inflation compares purchasing power over time: £100 growing to £105 does not buy 5% more goods if relevant prices also rose.
Business and credit risks concern cash generation and obligations. Liquidity risk concerns obtaining cash when needed without unacceptable price impact. Currency movements affect outcomes measured in another currency. Leverage can amplify gains and losses. Concentration makes results more dependent on fewer exposures. Volatility describes return variation. An illiquid asset with infrequent valuations can show apparently smooth reported prices while carrying substantial economic risk. A long horizon can reduce the importance of some short-term movements, but cannot rescue every failed business or eliminate permanent loss.
Diversification depends on underlying exposures and how they interact, not only the number of line items. Owning twenty similar companies may leave substantial sector risk. Fund holdings can overlap. Correlations can change, especially during stress. A benchmark should be relevant to the mandate. Assess performance alongside risk, fees, currency and period. A portfolio resembling an index but charging much more needs a clear explanation of the value offered. Neither active nor passive is automatically suitable for every objective.
A multiple compares a price or value measure with an operating measure such as earnings. A discounted-cash-flow valuation estimates the present value of future cash flows. Both depend on assumptions. A lower price after bad news may come with a lower estimate of value; the old valuation should not be treated as unchanged fact. The Sharpe ratio is a historical risk-adjusted performance tool: excess return divided by volatility, measured consistently. It can be unstable over short periods and may be inadequate for asymmetric or illiquid risks. It supplements, rather than replaces, understanding of the portfolio.
Let's work through Three calculations, three interpretations. Calculate return, compound growth and a simplified Sharpe ratio under the stated assumptions. Pause here and try the calculation or reasoning before continuing.
Share bought for £40, sold for £43, dividend £1: (43 − 40 + 1) ÷ 40 = 10% holding-period return, before fees/tax. £1,000 at a constant assumed 5% for two years: £1,000 × 1.05² = £1,102.50. One-year illustrative portfolio return 8%, reference return 2%, annual volatility 12%: (8% − 2%) ÷ 12% = 0.50.
The first is a realised holding-period calculation; the second is an assumed growth path; the third divides excess return by one measure of risk. None is a prediction or a full suitability assessment.
Now try the choices in this lesson. If your answer changes, identify the reason. Interpret price, value, fees and a simplified Sharpe ratio without treating them as guarantees. Use the case activities to put the idea into your own words, and return to the evidence when more than one conclusion is defensible.
Return has a numerator, denominator and period
For a simple unlevered share investment with a dividend received and no other flows, holding-period return is (ending price − starting price + dividend) divided by starting price. Fees, tax, reinvestment and cash-flow timing require additional care. A one-year figure and a five-year cumulative figure are not directly comparable.
Expected return is a forward-looking estimate, not a contractual promise. Realised return is what happened. Taking more risk does not guarantee a higher realised return, and not every risk has an adequate expected reward.
Compounding and inflation
With constant assumed annual return r, no withdrawals, no additional contributions and all returns reinvested, future value equals starting value × (1 + r) raised to the number of years. Changing returns require multiplying the period growth factors rather than substituting an arithmetic average.
A gain of 20% followed by a loss of 20% leaves 1.2 × 0.8 = 0.96 of the starting amount, a 4% loss. The arithmetic average is zero, but compound growth is not. Inflation compares purchasing power over time: £100 growing to £105 does not buy 5% more goods if relevant prices also rose.
Different risks, different tools
Business and credit risks concern cash generation and obligations. Liquidity risk concerns obtaining cash when needed without unacceptable price impact. Currency movements affect outcomes measured in another currency. Leverage can amplify gains and losses. Concentration makes results more dependent on fewer exposures.
Volatility describes return variation. An illiquid asset with infrequent valuations can show apparently smooth reported prices while carrying substantial economic risk. A long horizon can reduce the importance of some short-term movements, but cannot rescue every failed business or eliminate permanent loss.
Diversification, benchmarks and fees
Diversification depends on underlying exposures and how they interact, not only the number of line items. Owning twenty similar companies may leave substantial sector risk. Fund holdings can overlap. Correlations can change, especially during stress.
A benchmark should be relevant to the mandate. Assess performance alongside risk, fees, currency and period. A portfolio resembling an index but charging much more needs a clear explanation of the value offered. Neither active nor passive is automatically suitable for every objective.
Price versus estimated value
A multiple compares a price or value measure with an operating measure such as earnings. A discounted-cash-flow valuation estimates the present value of future cash flows. Both depend on assumptions. A lower price after bad news may come with a lower estimate of value; the old valuation should not be treated as unchanged fact.
The Sharpe ratio is a historical risk-adjusted performance tool: excess return divided by volatility, measured consistently. It can be unstable over short periods and may be inadequate for asymmetric or illiquid risks. It supplements, rather than replaces, understanding of the portfolio.
Three calculations, three interpretations
Calculate return, compound growth and a simplified Sharpe ratio under the stated assumptions.
- Share bought for £40, sold for £43, dividend £1: (43 − 40 + 1) ÷ 40 = 10% holding-period return, before fees/tax.
- £1,000 at a constant assumed 5% for two years: £1,000 × 1.05² = £1,102.50.
- One-year illustrative portfolio return 8%, reference return 2%, annual volatility 12%: (8% − 2%) ÷ 12% = 0.50.
The first is a realised holding-period calculation; the second is an assumed growth path; the third divides excess return by one measure of risk. None is a prediction or a full suitability assessment.
Put it into practice
1. What risk changed?
Identify the main issue: a borrower loses its biggest customer; an owner needs cash sooner; a fund holds many companies in one industry; an overseas asset falls in the owner’s reporting currency; prices rise faster than a fixed cash balance.
Apply the idea: discuss your reasoning, or add a short note where the task asks for one.
Compare with a model response
Credit/business risk; liquidity and horizon mismatch; shared sector concentration; currency effect; purchasing-power risk. More than one risk can apply. Explain the mechanism, not just the label.
2. Good company, good investment?
Original fictional case: a share trades at £90 while two reasonable estimates of value are £65 and £70. Bad news later reduces price to £55 and the plausible value range to £45–£60. Explain why buying is not automatic at either price.
Apply the idea: discuss your reasoning, or add a short note where the task asks for one.
Compare with a model response
Initially price exceeds the stated estimates, subject to their reliability. After bad news, the price is within the revised range; uncertainty about forecasts, downside, investor objectives and alternatives matters. Accept buy, wait or avoid if supported by consistent assumptions. Do not retain the pre-warning value without review.
3. A two-year fee comparison
£1,000 earns a constant assumed 6% gross each year. An illustrative fee reduces this to exactly 5% net each year. Compare two-year values; ignore other costs and flows.
Apply the idea: discuss your reasoning, or add a short note where the task asks for one.
Compare with a model response
Gross: £1,000 × 1.06² = £1,123.60. Net under the assumption: £1,000 × 1.05² = £1,102.50. Difference £21.10. This simplified convention is not the fee schedule of an actual product.
Jargon buster
Total return
Price change plus relevant income over a specified period, with costs defined.
Compounding
Returns affecting the base for subsequent returns.
Volatility
Variation in returns over a defined period and measurement basis.
Diversification
Combining exposures to reduce dependence on particular outcomes.
Correlation
A measure of how variables move together; it can change.
Intrinsic value
An estimate based on underlying economic prospects and assumptions.
Sharpe ratio
Excess return relative to a reference rate divided by return volatility on a consistent basis.
Knowledge check
Choose on the page. Read the feedback, reconsider mistakes and use Try again to reset a question.
What to take forward
Define return consistently, distinguish risk measures, compound correctly and compare price with an uncertain estimate of value. Diversification and time help with some risks, not all.