Unbiased Estimate
Also written Unbiased estimator · Unbiased estimate of true value · Price is an unbiased estimate of value
The technical definition of an efficient market price: the market price is an unbiased estimate of a security's true value, so deviations are random rather than one-sided.
In plain language
The popular way to describe an efficient market is to say that price equals fair value. That claim is too strong, and the workbook says so.
In technical terms, an efficient market is one where the market price is an unbiased estimate of the true value of the security.
Read the word unbiased carefully. It does not mean the price is right. It means the price is not wrong in any one direction.
So in an efficient market, price need not equal true value. What matters is that the gaps are random. A share may be dear today and cheap tomorrow. At any moment there is an equal chance that it is under-valued, over-valued or fairly valued.
One more thing follows. Those gaps are not linked to anything you can observe in the market. If they were, somebody could watch that thing and trade on it. Because they are not, no investor should be able to keep finding cheap or dear shares and earn an abnormal return from doing so.
How it works
Three conditions are packed into the one sentence, and each does work.
1. Deviations are random. The price can be greater than or less than the true value. Randomness means there is an equal chance that a security is under-valued, over-valued or fairly valued at any point in time. That is the arithmetic meaning of an unbiased estimate: the errors average out to nothing rather than leaning one way.
2. Deviations are uncorrelated with any observable market variable. This is the stronger half. A bias you can see is a bias you can trade. If mispricing were linked to, say, market capitalisation or the day of the week, an investor could sort on that variable and profit.
3. No strategy earns an abnormal return consistently. The workbook states this as the direct consequence: no investor should be able to consistently find under-valued or over-valued securities using any investment strategy with the objective of generating abnormal return.
What it is contrasted with. Market price is the price at which a security is currently available for trading. Its fair intrinsic value, sometimes called fundamental value, is the value investors would place on the asset if they had a complete understanding of its investment characteristics. Informational efficiency is about the relationship between those two. It is a different idea from operational efficiency, which is about the cost of transacting — impact cost and transaction cost — and improves as trading gets cheaper.
The workbook attaches no figure to this definition. There is no percentage, tolerance band or confidence level in the passage. It is a statement about the shape of the error, not about its size, and an answer that supplies a number is inventing one.
A worked example
Suppose the true value of Ganga Cements Ltd is Rs 500 a share, and the market is informationally efficient. Over ten quarters the closing price on the first trading day looks like this.
| Quarter | Price (Rs) | Deviation from Rs 500 |
|---|---|---|
| 1 | 512 | +12 |
| 2 | 486 | −14 |
| 3 | 500 | 0 |
| 4 | 523 | +23 |
| 5 | 478 | −22 |
| 6 | 495 | −5 |
| 7 | 508 | +8 |
| 8 | 491 | −9 |
| 9 | 519 | +19 |
| 10 | 488 | −12 |
The deviations sum to 0. The average error is nil, so the price is an unbiased estimate of Rs 500. Note what is not being claimed: the price was Rs 500 exactly once in ten quarters.
Now suppose an analyst notices the price is high in every quarter that follows a bonus issue and low in every quarter that follows a rights issue. That pattern is a deviation correlated with an observable variable. A trader could sell after bonus issues and buy after rights issues and earn an abnormal return. The estimate is no longer unbiased, and by the workbook's test the market is not efficient in that respect.
Finally, contrast operational efficiency. Impact cost on Ganga Cements falls from 0.35% to 0.12% as more brokers quote it. That makes the market operationally more efficient and says nothing at all about whether Rs 500 is the right price.
Why NISM asks about it
Chapter 3 (Concept of Informational Efficiency), section 3.1, gives this as the technical definition immediately before section 3.1.1 on market price versus value. The chapter's own sample questions test it twice: one asks which statement would be inconsistent with an efficient market (the answer is that price adjustments are biased), and another asks which statement is false, offering the line that in an efficient market price changes are independent and unbiased.
Expect the examiner to give you the loose definition — price equals fair value — and ask you to pick the technical one. Learn the phrase: the market price is an unbiased estimate of the true value, with random deviations that are uncorrelated with any observable market variable.
Common exam traps
- Unbiased does not mean accurate. In an efficient market price need not equal true value. The errors merely have no direction.
- Random and independent, not small. A large deviation is perfectly consistent with an unbiased estimate as long as the next one is as likely to go the other way.
- Informational efficiency is not operational efficiency. Operational efficiency is about transaction and impact costs. Falling costs do not make prices better estimates of value.
- The bias test is about observable variables. A mispricing nobody can detect does not break efficiency; one that tracks something on a screen does.
- The claim is about consistency. One investor beating the market once proves nothing. Efficiency says no strategy does it consistently.
- Do not attach a number. The workbook gives no tolerance, band or confidence level for how far price may stray.
Check yourself
1.Which of the following would be INCONSISTENT with an efficient market?
- a)Information arrives randomly
- b)Information arrives independently
- c)Stock prices adjust rapidly to new information
- d)Price adjustments are biased
Show the answer
Answer: (d) Price adjustments are biased
This is the workbook's own sample question. Efficiency requires that the market price is an unbiased estimate of the true value of the security... deviations of the price from the value is random in nature... Randomness means that there is an equal chance that security is under or over or fairly valued at any point in time. A biased adjustment leans systematically in one direction and can therefore be exploited, which is exactly what efficiency denies: no investor should be able to consistently find under-valued or over-valued securities using any investment strategy. Random and independent arrival of information, and rapid price adjustment, are all conditions consistent with efficiency.
2.Which of the following statements about efficient markets is FALSE?
- a)Prices in efficient capital markets fully reflect all available information and rapidly adjust to new information
- b)An efficient market requires a large number of profit-maximizing investors
- c)If the efficient market hypothesis is true, price changes are independent and unbiased
- d)None of the above is false — all three statements are true
Show the answer
Answer: (d) None of the above is false — all three statements are true
This is the workbook's own sample question, where the answer is "all the above" — meaning none of the three is false. Statement (a) restates the definition: an informationally efficient market is one in which prices always "fully reflect" the most up to date current information, and the semi-strong form asserts that security prices adjust rapidly and accurately to the release of all public information. Statement (b) is the internal contradiction: to make the market efficient, a large number of profit maximizing participants should seek out opportunities of beating the market. Statement (c) combines the random walk — successive one-period returns are independent — with the technical definition, that price is an unbiased estimate of the true value.
3.Which statement correctly describes prices in an efficient market under the technical definition?
- a)Price always equals true value exactly
- b)Price need not equal true value, provided deviations are random, offer an equal chance of under, over or fair valuation, and are uncorrelated with any observable market variable
- c)Price is always below true value, creating an opportunity
- d)Price and value are unrelated concepts
Show the answer
Answer: (b) Price need not equal true value, provided deviations are random, offer an equal chance of under, over or fair valuation, and are uncorrelated with any observable market variable
In technical terms, an efficient market is one where the market price is an unbiased estimate of the true value of the security. It implies that in an efficient market, price of a security need not be equal to its true value, as long as deviations of the price from the value is random in nature. This means that price can be greater than or less than the true value. Randomness means that there is an equal chance that security is under or over or fairly valued at any point in time. Further it implies that these deviations are uncorrelated with any observable market variable. Option (a) is the looser popular definition — a popular definition of efficient market is one where market price equals fair value of the securities.
Where this is taught
Free preparation for NISM Series XIX-CRelated terms
- Efficient Market HypothesisThe proposition that share prices already incorporate and reflect all relevant information — which, if true, leaves nothing for an analyst to find by studying that information.
- Intrinsic valueWhat an asset is actually worth — the present value of the cash it will generate over its remaining life, as against whatever price the market is quoting today.
- Impact costThe percentage by which a market order's actual execution price degrades against the ideal price — the mid-point of the best bid and the best offer — and so the real cost of trading in size.
- Market anomalyA pattern of returns that departs from what an asset's fundamentals and risk — as measured by CAPM or another pricing model — say it should earn, and so contradicts market efficiency.
- Informational EfficiencyHow fully and quickly security prices reflect available information. It is what "market efficiency" usually means, as against operational efficiency, which is about transaction costs.
- Operational EfficiencyHow cheap it is to transact in a market — the cost of carrying out trades — as distinct from informational efficiency, which asks whether prices already reflect all available information.
- Random Walk HypothesisThe early form of the efficient market model: security price changes occur randomly, so successive one-period returns are independent and identically distributed.
- Semi-strong-form EfficiencyThe hypothesis that prices reflect all historical and publicly available information and adjust rapidly to news — so neither technical nor fundamental analysis earns above-average risk-adjusted returns.
- Strong-form EfficiencyThe most extreme form of the efficient market hypothesis: prices reflect all historical, public and insider information, so no group of investors can earn above-average risk-adjusted returns.
- Weak-form EfficiencyThe hypothesis that current prices already reflect all historical market information — past prices, returns and volumes — so technical analysis cannot earn above-average risk-adjusted returns.