Market Efficiency and Arbitrage

TIP If you do not understand

something,

ask me!

Sorry, no free lunch!

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Random Walk Theory

The movement of stock prices from day to day DO NOT reflect any pattern.

Statistically speaking, the movement of stock prices is random (skewed positive over the long term).

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Random Walk Theory

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Efficient Capital Markets

Stock prices are in equilibrium or are “fairly” priced

If this is true, then you should not be able to earn “abnormal” or “excess” returns, in expectation. Investors cannot “beat the market” except through good luck or better information.

Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market.

They do mean that, on average, you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns.

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3 Levels of Market Efficiency

Weak Form Efficiency Market prices reflect all historical price

informationSemi-Strong Form Efficiency

Market prices reflect all publicly available information

Strong Form Efficiency Market prices reflect all information,

both public and private

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Efficient Market Theory

Last Month

This Month

Next Month

$90

70

50

Microsoft Stock Price

Cycles disappear

once identified

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Market return at announcement of takeover (or positive earnings news)

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-11

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39

Days Relative to annoncement date

Cu

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orm

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(%)

Announcement Date

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Weak-form efficiency

Can’t profit by looking at past price trends. A recent decline is no reason to think stocks will go up (or down) in the future. There is no predictable price pattern based on price path.

Evidence supports weak-form EMH, but “technical analysis” is still used by some people.

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Weak-form efficiency

Technical Analysts Forecast stock prices based on the

watching the fluctuations in historical prices (thus “wiggle watcherswiggle watchers”)

These guys do not believe in the weak form of market efficiency.

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Semi-strong form efficiency

All publicly available information is reflected in stock prices, so it doesn’t pay to over-analyze annual reports looking for undervalued stocks.

Largely true, but superior analysts can still profit by finding and using new information.

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Semi-strong form efficiency

Fundamental Analysts Research the value of stocks by delving

into detailed accounting and operating numbers.

These guys do not believe in semi-strong form of market efficiency.

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But how is their performance?

-40

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-20

-10

0

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Ret

urn

(%

)

FundsMarket

Average Annual Return on 1493 Mutual Funds and the Market Index

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(will not test) Hedge return across small and big stocks.

SMB Factor %

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0

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(Will not test) Hedge return across high B/M and low B/M stocks.

HML factor %

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(Will not test) Hedge return across low accrual stocks and high accrual stocks.

Size adjusted return between lowest and hiest accrual deciles

-0.3

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0

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69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01

Year of portfolio formation

Siz

e a

dju

ste

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etu

rn

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(Will not test) One-year-ahead hedge returns based on capital investment levels. ©Donglin Li 2004

Go long the lowest investment

stocks.

Go short the highest investment stocks.

12 month size adjusted buy and hold hedge returns after May each year.

Positive in 36 out of 39 years, average 12.6%

Pattern is consistent with market mispricing band against semi-strong efficiency.

1 year ahead hedge returns between lowest and highest deciles of investment (d_PPE) firms

-0.1

-0.05

0

0.05

0.1

0.15

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0.25

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0.35

1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

Year

Hedg

e Po

rtfol

io R

etur

n

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Strong-form efficiency

All information, even inside information, is embedded in stock prices. That is, one cannot profit even on private information.

Not true--insiders can gain by trading on the basis of insider information, but that’s illegal.

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Is the stock market efficient?

Empirical studies have been conducted to test the three forms of efficiency. Most of which suggest the stock market was: Highly efficient in the weak form. Reasonably efficient in the semistrong form. Not efficient in the strong form. Insiders

could and did make abnormal (and sometimes illegal) profits.

Behavioral finance – incorporates elements of cognitive psychology to better understand how individuals and markets respond to different situations.

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What Makes Markets Efficient?

There are many investors out there doing research As new information comes to market, this

information is analyzed and trades are made based on this information

Therefore, prices should reflect all available public information, and almost instantly.

If investors stop researching stocks, then the market will not be efficient.

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Lessons of Market Efficiency

Markets have no memory (you cannot tell whether stock is overvalued based on historical pattern.)

Trust market prices (example) Read the entrails (Price reflects valuable information.) There are no financial illusions (FIFO to LIFO, earnings

& price) Seen one stock, seen them all (The market is deep.

You can buy or sell in large quantities.)

When the market is not efficient, you can make money by arbitraging.

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Arbitrage

An arbitrage opportunity arises when an investor can construct a zero investment portfolio that will yield a sure profit.

To construct a zero investment portfolio, one has to be able to sell (go short on) some securities and use the proceeds to purchase (go long on) other assets.

Borrowing may be viewed as a short position in a risk free assets.

Arbitrage always means buying undervalued and selling the overvalued.

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Arbitrage Example 1

Suppose gold is trading at $250 per ounce in New York and £210.53 per ounce in London.

Current exchange rate is $1.425/ £. You can immediately buy (go long) gold at

$250 in New York and sell (go short) it at £210.53 in London.

Then you can change £210.53 into 210.53*1.425=$300 and make profit of a sure $50.

Arbitrage activities will drive gold price to be equal across two market, at a price in between.

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Arbitrage on several assets

If you can use one or more assets to replicate or exceeds the payoff from asset A, then the price of your replicating portfolio must be no lower than the price of A.

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Arbitrage Example 2

Bond A pays coupon rate of 6% and matures in 10 years. Price=$1000

Bond B pays coupon rate of 12% and matures in 10 years. Price=$1100

Bond C pays coupon rate of 9% and matures in 10 years. Price=$1060

Buy (go long) 1 share of Bond A and 1 share of bond B, go short 2 shares of bond C.

Make a profit of $20 immediately. In the next 10 years, use the cash inflows from

Bond A and Bond B to pay off your obligation under Bond C.

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Arbitrage

In every market that reveals arbitrage opportunities, there will be arbitrageurs operating. Arbitrage opportunities appear and disappear extremely quickly. (Example.)

Transaction cost (commission fee, bid-ask spread) may prevent people from taking arbitrage opportunities.