A one-year zero-coupon bond trades at $952.38 and a two-year zero trades at $898.47. You can extract a forward rate, build a binomial tree, and price a derivative, all without knowing a single investor's risk preferences. That is the power of no-arbitrage pricing, and it is the thread connecting every concept in this lesson.
Market efficiency is about what information is already baked into prices. Eugene Fama defined three forms, and each one tells you which strategies can still earn excess returns.
Weak-form efficiency says prices reflect all past trading data (historical prices, volume, order flow). If weak-form holds, technical analysis fails because moving average crossovers, chart patterns, and momentum signals cannot consistently beat the market when the information they use is already priced in.
Semi-strong efficiency says prices reflect all publicly available information. That includes financial statements, earnings releases, news, and analyst reports. If semi-strong holds, fundamental analysis based on public data cannot consistently produce alpha, meaning a return beyond the compensation for the risks the investment bears.
Common mistakes
- Confusing the three forms of market efficiency. Weak-form covers past trading data only. Semi-strong covers all public information. The trap: a question describes a strategy based on financial statement analysis and asks if it can generate alpha under weak-form efficiency. It can, weak-form only rules out technical analysis, not fundamental analysis.
- Computing a simple average instead of the geometric forward rate. With spot rates of 3.0% and 3.5%, the arithmetic midpoint is 3.25%, but that is not the forward rate. The correct forward rate is 4.0%. The difference comes from compounding. The forward rate formula uses multiplication, not averaging.
- Using real-world probabilities in a binomial tree. The question asks you to price a derivative using a binomial tree. Plugging in your own estimate of the probability that the stock rises gives the wrong price. Risk-neutral pricing requires the pseudo-probability p = (R - d) / (u - d), not any subjective forecast.
Bottom line
- Market efficiency is cumulative: weak-form reflects past trading data, semi-strong all public information, strong-form all information including insider. Markets settle at an "efficiently inefficient" equilibrium where the marginal cost of skill-based trading equals its marginal revenue.
- Six drivers of informational efficiency: market value, trading frequency, trading frictions, regulatory constraints, information access, and valuation certainty.
- Discount factor = PV of $1; spot rate = yield on a default-free zero-coupon bond; a coupon bond's yield blends several spot rates; Fisher: nominal rate = real rate + expected inflation.
- Forward rates exist for any interval t to T; forwards lie above (below) spot for upward (downward) curves and exaggerate slope.
Exam shortcut
When a question gives you two spot rates and asks for the forward rate, go straight to the no-arbitrage condition: (1 + s(t))^t × (1 + F(t,T))^(T − t) = (1 + s(T))^T, and solve for F(t,T). Keep each spot rate's maturity as its exponent.
The full lesson (about 14,446 words, 96 min read) adds 2 worked examples, all 9 common mistakes, a self-check, free in the app.
Learning objectives
- defining alts
- blurred lines
- risk return characteristics
- goals
- history us
- history asia
- buy sell side
- service providers
- legal structures
- fund types
- fund features
- fund terms
- drawdown fees
- waterfall calcs
- hedge fund fees
- fees and behavior
- return math
- irr
- irr problems
- modified irr
- other measures
- j curve
- notional principal
- return distributions
- moments
- covariance correlation
- beta autocorrelation
- std dev variance
- normality testing
- market efficiency
- time value
- forward rates
- binomial trees
- single-factor default-free bond models
- reduced-form modeling credit risk
- single-factor equity pricing models
- single factor models
- hypothesis testing
- sampling problems
- forwards vs futures
- forward foundations
- forwards on rates
- carry forwards
- managing long short
- option exposures
- rate options
- option pricing
- risk measures
- var
- benchmarking
- ratio measures
- risk adjusted
- estimating alpha
- pricing data
- appraisals smoothing
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