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. Event-driven strategies based on merger announcements would also struggle because the announcement is public.
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%, students often answer 3.25% (the arithmetic midpoint). 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. Students sometimes plug in their estimate of the probability that the stock rises. 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 zero-coupon bond; Fisher: nominal rate = real rate + expected inflation.
Exam shortcut
When a question gives you two spot rates and asks for the forward rate, skip the theory and go straight to the formula: (1 + s1)(1 + f) = (1 + s2)^2, solve for f. The trap answer is always the simple average or simple difference of the two spot rates. Eliminate those immediately. For market efficiency, classify the information the strategy uses. Historical prices = weak-form.
The full lesson (about 6,520 words, 43 min read) adds 2 worked examples, all 9 common mistakes, a self-check, free in the app.
Learning objectives
- defining alts
- blurred lines
- history us
- history asia
- risk return characteristics
- goals
- 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
- arbitrage
- binomial trees
- single factor models
- hypothesis testing
- sampling problems
- forwards vs futures
- forward foundations
- forwards on rates
- carry forwards
- managing long short
- option exposures
- rate options
- rate swaps
- option pricing
- risk measures
- var
- benchmarking
- ratio measures
- risk adjusted
- pricing data
- appraisals smoothing
- alpha beta overview
- estimating alpha
- return attribution
- statistical issues
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