Two investments start at $100 and reach $120 after three periods. Looking only at the final line, they seem equivalent. Yet one fell as low as $60, while the other had only a small interim decline. If a payment were due at the second period's end, would you still describe them as the same experience?
Risk can lie before the endpoint and outside the curve altogether. Follow the two paths first, then investigate what prices cannot establish: why an asset might lose value, whether you can sell it, and whether your financial circumstances allow you to wait.
What you will be able to do
- Calculate drawdown from a previous high and distinguish it from a loss since purchase.
- Compare decline depth, time without recovery, and the gain needed to recover, without treating history as a future ceiling.
- Combine asset quality, concentration, liquidity, and payment timing in one risk record.
Master the reasoning and simple drawdown calculations here. You only need an initial intuition for volatility; G68 develops standard deviation and annualization separately. Avoid letting a list of statistics replace questions about what could go wrong.
Do not skip to the last line
These are independent synthetic sequences in U.S. dollars, with equally long periods and no deposits, withdrawals, dividends, or fees. Assume no additional prices between the supplied observation points. Path A is 100, 110, 105, 120. Path B is 100, 120, 60, 120. Neither is actual fund performance, and neither implies that real investments will recover on schedule.
Both finish 20% above the initial $100. But A falls from 110 to 105, while B falls from 120 to 60. At the second period's end, those are very different account values. The identical ending return describes the change from start to finish, without telling you what the holder experienced in between.
A drawdown is a decline relative to an earlier running high. This chapter reports its magnitude as a positive number: previous high minus current value, divided by that high. Some software reports a negative number instead, so align the sign convention before comparing. Maximum drawdown is the deepest peak-to-trough decline within the observation interval. [1]
For A, 110 is the high reached before the value falls to 105. The $5 decrease divided by 110 is about 4.55%. B falls $60 from its earlier high of 120 to 60, a 50% drawdown. At these four supplied observations, their maximum drawdowns are therefore approximately 4.55% and 50%.
The observation qualification matters. If only the start and finish survived in the record, both investments would appear to have risen without an observed decline. Month-end data can miss a large mid-month fall too. Report the data frequency, dates, and valuation convention with a maximum drawdown. A small number without those details may tell you more about what was omitted than about a smooth experience.
Earlier gains also establish a drawdown reference
At 105, A is still $5 above the original $100 but about 4.55% below its prior high. At 60, B is 40% below the initial investment and 50% below its prior high. Neither calculation contradicts the other. They use different denominators because they answer different questions.
Profit or loss since purchase asks what happened to the amount invested at that starting point. Drawdown asks how far the path retreated from a high it had already reached. “I am still ahead” cannot make the drawdown zero. Conversely, a 50% drawdown does not establish that this holder lost 50% relative to the purchase price.
Recovery changes the denominator again. B must rise from 60 to 120 to regain its high: a 100% gain, not 50%. A must rise from 105 to 110, about 4.76%. A decline and a subsequent gain of equal percentage do not cancel because the gain acts on the reduced base. Writing the values makes the asymmetry visible without memorizing a separate recovery formula.
Depth is only one part of the experience. Two investments can have the same maximum drawdown while one recovers quickly and the other remains below its high for years. Record the peak, trough, and recovery dates when available. If recovery has not occurred by the observation end, say so. Do not assign a completed recovery time by assuming it will happen tomorrow.
Deposits and withdrawals can also distort a balance-based path. A deposit may create a new account high without an investment gain; a withdrawal may reduce the balance without an investment loss. Address external flows using an appropriate return convention before examining the investment-value path. This is the same boundary problem introduced in the return chapter, now applied to risk measurement.
What if the tuition payment is due in period two?
Change one condition. At the end of the second period, the investor must pay $60 and has no other available money. Assume immediate sale at the recorded value and no fees. This is a deliberately stressed mismatch between investment timing and a payment, not an example of an appropriate allocation.
A is worth $105 then. After paying $60, the investor retains $45. B is worth only $60, so funding the payment leaves no investment at all. The original path's later return to 120 does not restore the gains of someone who has already sold the entire holding. A market recovery and your ability to participate in it are separate facts.
It would be misleading to diagnose B's holder as insufficiently patient. A payment date is an external constraint that determination cannot remove. Protecting money for necessary spending helps address forced-sale pressure. Before interpreting an asset's historical risk, also ask whether your cash arrangements let you live through the path you are examining.
The reverse also matters: not needing money soon does not make every declining asset worth holding. If the underlying ability to generate value has been damaged, waiting can prolong the exposure. Check both the asset and your time constraints. Neither a distant spending date nor a convincing company story removes the need for the other investigation.
A smooth line may simply be an old price
Volatility describes variation in returns, commonly including upward and downward movements. Drawdown focuses on the downward path from prior highs. Both can be useful, but neither directly answers how much can be sold at the recorded price. A stable series can therefore conceal an important risk.
Suppose an asset has been recorded at $100 for several weeks. Today, an actual buyer offers only $80, or there may be insufficient bids for the holding. The old transaction price looked steady because trading was infrequent or valuations updated slowly. Little movement in the record did not establish that losses were unlikely or that the holding could be converted into $100.
Liquidity concerns completing a transaction when needed at an acceptable price and size. It is more than a yes-or-no ability to sell. A small amount may trade readily while exiting the entire holding requires a larger concession. Even after execution, further steps may separate sale proceeds from usable payment funds. [2]
Keep three questions separate in the risk record: What price was observed? What size could plausibly transact under which conditions? When would the cash become available? A halt, redemption restriction, or interruption of the trading channel can invalidate a planned exit. A stop price is also not a guaranteed fill price; the order and execution conditions from G07 still apply.
Is the underlying business still the same?
A price decline might reflect sentiment, interest rates, or changed earnings expectations. It might also reflect damage to the business. Losing a major customer, product failure, debt pressure, or governance problems can alter what the enterprise may eventually provide to investors. The price is an observation requiring investigation, rather than a complete explanation.
Permanent loss emphasizes damage to investment value that may be difficult to recover. A falling chart alone cannot diagnose it. Examine cash, debt, operations, and the rights of the security you hold. Calling every loss “only on paper” does not answer those questions. A business continuing to operate does not ensure the old common shares retain value; bankruptcy reorganization can cancel them. [3]
Equally, do not wait for the final outcome and then pretend you had known a particular decline was irreversible. Research works under uncertainty. Record checkable conditions: whether the customer supporting the thesis remains, whether debt-service resources are adequate, and which disclosure would invalidate the earlier judgment. A documented conditional conclusion is more useful than a retrospective label with no decision rule.
Concentration can amplify damage. Different stock names may all depend on the same commodity price or customer group. A common change can hurt them together. If wages, employer equity, and investments depend on one employer, income interruption and investment losses may coincide. Counting security names does not reveal that joint dependence. [4]
Rare but severe outcomes are often discussed as tail risk. Not seeing one in a short sample does not establish that it is absent. Nor should you invent a precise probability when the information does not support one. Record extreme but plausible joint scenarios, such as collapsing demand alongside tighter financing, to examine what options would remain if they occurred.
Those scenarios are not predictions that disaster will arrive. They investigate whether a tolerable response exists if a common dependency fails. A useful risk record therefore includes the dependency, the resulting cash or asset problem, and evidence needed to assess it. A bare list of asset names can miss all three.
Make the distinction yourself
First explain why A at $105 has both a profit and a drawdown. Then identify the problem in this claim: “The largest drawdown from the last three years of month-end values was 8%, so investing RMB 100,000 can lose at most RMB 8,000.” Write your answers before reading on.
For A, the references differ. Relative to the initial $100, it has a 5% gain. Relative to the prior high of $110, it has about a 4.55% drawdown. Both statements describe the same $105 value, but they cannot share a denominator or be used interchangeably.
The second claim converts a historical observation into a future guarantee. It also overlooks declines between month-end observations. Future losses can exceed 8%, with liquidity or execution worsening too. Preserve the 8% as a result for its specific dates, frequency, and convention, then investigate separate stress scenarios. It is not a ceiling on future loss. The renminbi amounts remain a hypothetical illustration, not a proposed investment.
Change the path and remove an exit price
Another synthetic path is 100, 125, 100, 110, without cash flows and under the other conditions of the main example. Calculate its ending return and maximum drawdown, and say whether it has recovered its high by the observation end. Then suppose the final 110 is only a valuation and there is no executable bid today. Can you write “sell for $110”?
The ending gain is 10%. The drop from 125 to 100 is a 20% maximum drawdown. The ending 110 remains below 125, so the prior high has not been recovered within the given observations. From the trough of 100, reaching 125 would require a 25% gain. An ending profit does not erase the intervening decline.
The sale claim remains unverified. A valuation supplies a measurement, not an executable transaction. Without a bid, quantity, and trading channel, the realizable cash amount is unknown. Put that gap in the record rather than assuming that every asset can be sold at the curve's final point.
Keep a risk record that can change
For one research project, record the intended use of the money, earliest spending date, and alternative available funds. Add data dates, observation frequency, fees, and cash-flow treatment, then mark the historical high, maximum drawdown, and recovery status. You may begin with the synthetic sequences rather than disclose personal finances.
Next, add evidence about three areas: causes that could damage asset value and the materials for checking them; common dependencies and joint stress scenarios; and sale size, execution conditions, and cash-availability timing. Label each item known, assumed, or unverified. Give a change that would trigger review, such as lost income or an invalidated business assumption.
Cover the ending return and read the record again. Does it still explain the hardest point in the experience? If only attractive statistics remain, without spending constraints, exit evidence, or unresolved questions, it is not yet sufficient to support action. Your completed record should expose what needs to be checked, not simply decorate a favorable final number.
Put the number back into the experience
Start by aligning data and cash-flow conventions. Then inspect decline depth, time without recovery, and the gain needed to recover. Historical statistics describe the observed path; frequency and sample dates determine how much you can see. They do not impose a future loss limit.
Then step outside the curve. Investigate damage to the asset, shared dependencies across holdings, and the ability to exit when money is needed. Combining the investment path with a payment calendar makes the figures relevant to a decision. Without exit evidence or essential business information, keep the unresolved part visible instead of supplying certainty the record cannot support.
References
- Goldberg and Mahmoud: Drawdown: From Practice to Theory and Back Again. Maximum-drawdown definition; this chapter does not teach the paper's Conditional Expected Drawdown model.
- Investor.gov: What Is Risk?. Basic risk and liquidity distinctions.
- Investor.gov: Bankruptcy for a Public Company. Reorganization and old common-share risk.
- FINRA: Concentrate on Concentration Risk. Correlated holdings and employer-stock concentration. Sources checked October 30, 2026.
AI assisted with writing and checks. Human financial review and target-reader testing remain pending. All paths, amounts, and execution assumptions are original synthetic inputs.