📈 Investing Concepts

What you’ll learn

1. A Claim on Somebody Else's FutureEstablish that every instrument is a claim on future cash, and that bonds and shares differ by position in the capital-structure queue.The oldest surviving share certificate, issued by the Dutch East India Company in 1606, conveyed no object — only a claim on future earnings, which is still what any security is. A bond is a contractual claim to specific payments with capped upside; a share is a residual claim to whatever remains after everyone else is paid, with unlimited upside and no promise. Position in the queue explains nearly everything else about how each behaves.
2. The Bond: a Loan With a TimetableDefine a bond by its three parameters and show that its cash flows are certain while its counterparty is not.A bond is face value, coupon and maturity: a £1,000 5% five-year bond pays £50 a year and £1,050 in the final year, and that is the complete instrument. The payment schedule carries no ambiguity — the risk lies entirely in whether the issuer survives to honour it. Credit ratings are therefore judgements about survival, not calculations about cash.
3. Why Bond Prices Move BackwardsExplain the inverse price–yield relationship mechanically, and introduce duration as the reason maturity is itself a risk.A bond's coupon is fixed at issue, so when market rates rise the price is the only variable that can adjust — it falls until the bond as a whole offers a competitive yield. Price above face is a premium, below is a discount, and the pivot is where market yield equals the coupon. Longer maturities swing harder for the same rate move because more years of off-market coupons need compensating for: this sensitivity is duration.
4. The Stock: Whatever's LeftDefine a share as a residual claim valued on future cash, explain retained earnings, and show that P/E encodes expectations rather than value.A share's value is the discounted stream of all cash the company will ever return to owners — theoretically correct and practically requiring knowledge of the future, so every ratio is a shortcut for a calculation nobody can perform. A company retaining all earnings isn't withholding value: reinvested well, it raises the worth of the business you own. A low P/E is not a bargain the market missed but an expectation of decline already priced in.
5. The Market Is a Disagreement MachineShow that a price is a resolved disagreement set at the margin, and present the efficient market hypothesis with its real boundaries and its live dispute.Every trade requires two people who disagree, so a price is where the most optimistic remaining buyer met the most pessimistic remaining seller — 'the market thinks' means the marginal participant thinks. The efficient market hypothesis claims prices reflect available information because spotting unpriced information is profitable, not because anyone is wise; Grossman and Stiglitz showed perfect efficiency is self-defeating. Fama and Shiller, who disagree sharply about whether prices are correct, shared the 2013 Nobel Prize.
6. Risk Is Not the Same as FearDistinguish the technical definition of risk as volatility from permanent loss of capital, and name the genuine disagreement about the word.Finance usually defines risk as volatility — standard deviation of returns — which counts upside surprises as risk and is a modelling choice made for tractability. Volatility is price movement that may reverse; permanent loss is money that never returns, and volatility only becomes loss if you are forced to sell. The mainstream defends volatility as a workable proxy; Graham and Buffett argue a lower price on an unchanged business makes it safer, not riskier, and the disagreement is about which thing deserves the word.
7. Diversification: the One Free ThingDerive diversification's benefit from imperfect correlation, show it falls as 1/√n and plateaus, and separate specific from systematic risk.Markowitz's 1952 paper showed a portfolio's risk is less than the average risk of its holdings — for n uncorrelated equal-risk assets, standard deviation falls by a factor of √n, with expected return unchanged — the sense in which it is called the only free lunch. The gains are concentrated in the first handful of holdings and flatten quickly onto a floor. That floor is systematic risk, which diversification cannot touch; specific risk, being removable for free, earns no premium.
8. When Correlation Breaks Its PromiseShow that correlations rise in crises, so diversification thins exactly when needed — the same failure as correlated insurance risk.Diversification runs on imperfect correlation, and correlation rises under systemic stress: forced sellers sell what can be sold, so unrelated assets fall together because the same frightened people own them. Diversification didn't fail in 2008 — it did less than models calibrated on calm-period correlations expected, which was the central error rather than a subtle one. The structural echo with a flood insurer's pool is exact: independence assumed, then withdrawn.
9. What a Fund Actually IsDefine a fund as a container rather than an investment, explain mutual fund vs ETF plumbing, and show that 'index' names a method not a price.A fund pools money to buy a portfolio and sells proportional slices priced at net asset value — the container has no risk level; the contents do. Mutual funds transact with the fund once daily at NAV while ETFs trade on an exchange, kept honest by creation/redemption arbitrage rather than by trust. Bogle's 1976 index fund followed a published rule, and cheapness was a consequence — but ICI data shows index equity mutual funds averaging 0.05% asset-weighted while the 90th percentile charges 1.49%.
10. Fees: the Only Certain Return Is NegativeShow that fees are the only certain term, that they compound, and that the average fund and the average dollar pay very different amounts.A fee is known in advance and charged whether you win or lose, and because it applies to the whole balance every year it removes the compounding that money would have produced: £10,000 at 7% for 30 years reaches £76,123, but £57,435 at 6% after a 1% fee. ICI reports U.S. equity mutual fund costs falling from 1.04% asset-weighted in 1996 to 0.40% in 2025 — a genuine consumer win driven by money moving. But the median fund still charges 0.99% and the simple average is 1.08%: the average dollar gets a good deal, the average fund does not.
11. Active vs Passive: the Argument We Won't SettlePresent Sharpe's arithmetic, the SPIVA evidence, and the sponsored methodological critique of it — and explicitly decline to adjudicate.Sharpe's 1991 arithmetic shows the average active dollar must trail the average passive dollar after costs by construction, though it says nothing about whether individual skill exists or is identifiable in advance. SPIVA's mid-2025 U.S. scorecard found 91.03% of active large-cap funds underperformed the S&P 500 over twenty years, with only 34.70% of funds surviving the period. Cremers, Fulkerson and Riley, sponsored by an active-management body, argue different treatment of exits, asset weighting and investable benchmarks cuts underperformance from 92% to 55% of assets — both sets of choices encode different, legitimate questions.
12. The Same Asset Is a Different Animal in Different HandsEstablish that risk is a relationship between an asset and a holder's obligations, and state plainly the limits of what this course can advise.The same 30-year government bond reduces a pension fund's risk by matching a 30-year liability and increases a two-year saver's risk by forcing an early sale into whatever rates have done — so 'is this safe?' is a malformed question. Risk is a relationship between the asset and the holder's horizon, liabilities and forced-selling constraints, not a property of the asset. That is why no general answer about what to hold exists, and why decisions about real money require a professional who knows the specific situation.

Questions this course answers

Grounded in trusted sources

• Harry Markowitz, 'Portfolio Selection', Journal of Finance 7 (1952)
• William F. Sharpe, 'The Arithmetic of Active Management', Financial Analysts Journal 47, no. 1 (1991)
• William F. Sharpe, 'Capital Asset Prices', Journal of Finance 19 (1964)
• Eugene F. Fama, 'Efficient Capital Markets: A Review of Theory and Empirical Work', Journal of Finance 25 (1970)
• Sanford J. Grossman & Joseph E. Stiglitz, 'On the Impossibility of Informationally Efficient Markets', American Economic Review 70 (1980)
• Robert J. Shiller, 'Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?', American Economic Review 71 (1981)
• S&P Dow Jones Indices, 'SPIVA U.S. Scorecard Mid-Year 2025' (September 2025) — Reports 1a and 2 (https://www.spglobal.com/spdji/en/spiva/article/spiva-us/)
• K. J. Martijn Cremers, Jon A. Fulkerson & Timothy B. Riley, 'How the SPIVA U.S. Scorecard Understates the Performance of Actively Managed Mutual Funds' — supported by the Investment Adviser Association's Active Managers Council (SSRN 6710358)

Every Wunder lesson is built from real, reputable sources — never invented.

Related Math courses