WTZIMI

Great investors and hedge fund managers: their methods and evaluation

Session 3: Anomalies, security market imperfections and behavioral biases

11. The various efficient/inefficient market camps: why Buffett wants to endow university chairs in efficient market theory.

Prof William T ZiembaAlumni Professor of Financial Modeling and Stochastic Optimization (Emeritus)

Mathematical Institute, Oxford UniversityICMA Centre, University of Reading

William T Ziemba Investment Management Inc, Vancouver, BCDr Z Investments Inc, San Luis Obispo, CA and

Private International Wealth Management, BC Capital Group, Nassau

CARISMA Seminar, June 25, 2007

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Efficient Markets (E):

• current prices are fair and correct except possibly for transactions costs

• commissions, bid-ask spread, price pressures - for small caps the latter can be large

• 4.6% on average for a $50,000 sale according to a Barra study

• Fama et al, 1960s to 80s

• Sharpe index funds - they still beat about 75% of active managers

• DFA - manage > $25 billion passive funds

Risk Premium (RP):

• markets are basically efficient but one can realize extra return by bearing additional risk

• if returns are above average, then the risk must be there somewhere; you cannot get higher returns without bearing additional risk

• for example, beating the market index S&P500 is possible but not risk adjusted by the CAPM

• Beta must then be greater than one (Fama et al 1990s, Frank Russell, DFA)

The Camps: Can you beat the stock market?

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Genius (C)

• superior investors exist who are brilliant or geniuses but you cannot determine in advance who they are: the Samuelson argument

• you can determine them ex ante and to some extent they have persistent superior performance, Soros did this with futures with superior picking of futures to bet on; traders are “made not born” philosophy

Efficient markets is hogwash (D)

• by evaluating companies and buying them when their value is more than their price, you can easily beat the market by taking a long term view

• find these stocks and hold them forever

• find a few such stocks that you understand well

• forget about diversification,only buy winners, use some of your money to endow chairs in the efficient market hypothesis. Buffett et al,

• bet on insurance etc when the odds are greatly in your favor

Camps (cont’d)

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Markets are beatable (A)

• through behavioral biases, security market anomalies using computerized superior betting procedures

• construct risk arbitrage situations with positive expectation

• research the strategy well and follow it for long periods of time repeating the advantage many times

• factor models are useful and show that beta is not one of the most important variables to predict stock prices

• very focused,disciplined, well researched strategies with superior execution and risk control

• focus on not losing

• they rarely have blowouts: Thorp, Benter, Blair Hull, Harry McPike, James Simons (Renaissance Hedge Fund), David Swensen (Yale Endowment)

• blowouts occur more in hedge funds that do not focus on not losing and true diversification and over-bet; when a bad scenario hits them,they get wiped out: LTCM

Camps (cont’d)

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All can be multimillionaires but the centimillionaires are in (C), (D) and (A) (like the six listed with the exception of Swensen)

• WTZ was fortunate to work/consult with four of these and was also the main consultant to the Frank Russell Research Department for nine years

• (A) people earn money by winning and taking a percent of the profits, Thorp returned 15.8% net with $200 million under management; fees $8 million/year

• (E) and (RP) people earn money from fees by collecting assets through superior marketing and sticky investment decisions

How do investors and consultants do in all these cases?

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Fundamental Factors in U.S. and Japanese Stock Returns

Schwartz and Ziemba (2000) Predicting returns on the Tokyo stock exchange

• No quantitative strategy including mispricings will work all the time;the aim is to use strategies that add value on average over time

• Model developed for Yamaichi Research in Tokyo in 1989

• Similar model used by Buchanan Partners, a London hedge fund

Idea: use many factors to predict the best stocks and the worst stocks

• Ranking 1, ..., N.

• Then use this in various types of trading and investing

• especially long cheap warrants, short bad stocks

• Shorting cost 4%/year for many stocks.

For references see Ziemba and Ziemba (2007)

12. Fundamental anomalies: Jacobs and Levy (US model), Ziemba (Japan model), use in long/short strategies

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Jacobs/Levy study (1988a,b)• They turned this into a multibillion dollar investment company in Philadelphia• First paper to use factor model to separate out best from worst stocks

25 factors

1500 largest capitalized stocks

monthly revisions of most variables, Jan 1978 to Dec 1986

normalized factors

excess return vs factor exposure

cumulative effects relative to benchmark (S&P500)

univariate naive effects

multivariate pure effects

Which Factors are the Most Important on the NYSE?

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Equity attributes

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Cumulative return to trends in earnings estmates

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Size and PER effect are intertwined

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Small size Low PE

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Beta was not a particularly good variable once other variables are considered

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All the factors - together and separate

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Monthly average returns to anomalies, January vs non-January

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Small Caps beat Large Caps, 1942-1999

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But if you start in 1926 then large caps beat small caps which never catch up after the 1929 crash

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Typical Value Line/S&P500 spread for cash and futures for the 1997-1998 turn of the year

See Rendon-Ziemba (2007) for plots like this for the Value Line/S&P spread and Russell 2000/S&P spread for 1982-2005

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Small cap minus large cap returns for December 1926-1997 (Noise)

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Small cap minus large cap returns for January 1926-1998

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Strong variables are

• Low PE

• Small size

• sales/price

• Trend in earnings estimateslagged 1, 2, 3 months

• current earnings surprise

• earnings torpedo

• relative strength

• residual reversallagged 1 or 2 months

In January also

yield

short and long term tax

low price

book/price

neglect

Some conclusions

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• Jacobs-Levy manage about $20 billion using these and other ideas

• WTZ long term student/trader in January effect, major change in 1990s especially 1996-8; so called January effect exists but only for short time in December and mostly in futures markets, so January results are probably unreliable??

• See Rendon-Ziemba (2007) for update on January effect in futures markets

Conclusions (cont’d)

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Ziemba study at Yamaichi Research Institute, Tokyo

Data• June 1979 to September 1989 (some tests to 1969)• All, 1163, stocks on first section of TSEReturns• Cumulative effect relative to TOPIX• Univariate naive effects• Multivariate pure effects• Rotate stocks month by month• Normalized effects of 30 factors• Research completed in fall 1989• Published in Ziemba-Schwartz (1991) Invest Japan, Probus and Schwartz

and Ziemba (2000)• Did Yamaichi use??• Buchanan hedge fund in London used similar model

1991-1998 for hedge warrant arbitrage portfolios with good success

Which factors were the most important on the Tokyo stock exchange up to 1989 and in the early 1990s?

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Definition of Fundamental and Technical Variables D=difference, A=acceleration, P=price BV=book value, Div= dividend

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Variables (cont’d)

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Future earnings growth (average of 3 forecasting services) over price is the best variable

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One of the most important theoretical ideas in the theory of finance.

Generally finance theories assume no arbitrage.

Buy for A, sell for B where B>A at the same time: cannot lose

Risk Arbitrage

Buy for A at time t, sell for B where B>A at time >t: could lose

Arbitrage exists but is rare

Prediction markets through betting exchanges show some current examples of arbitrage and risk arbitrage

13. Arbitrage: A typical Thorpian risk arbitrage trade: buy A for a low price, sell A’ for a high price: wait for them to converge, application to Nikkei puts 1989-90

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Two such examples are:

B Construct the arbitrage with a sequence of investments the net result yields the arbitrage

B Find mispricings in different localities that yield the arbitrage - today’s betting exchanges are like this.

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Track take (transactions costs) are

1. % of betting pool

2. Rounding down to nearest 10 or 20¢

Payoff per dollar bet on i for an ijk finish (in any order) is

Locks at the Racetrack: Constructing an arbitrage; similar analysis applies to the stock market

1QS Si S j Sk

3Si where S Si

i1

n

Minimum payoff 2.10 or 2.20 per $2 bet to win, place and show

Suppose there is a super horse, then if one bets a lot on that horse and a little bit on all the other horses, then one can construct a lock or arbitrage: you cannot lose

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Scenario 1: If DD is in the money, all 3 horses pay off $1.05/$ bet; this is more than we lost on the other two horses.

Scenario 2: If DD is out of the money, then we want bets so that then we do not lose money.

Alabama Stakes, Saratoga, August 11. 1979

The public’s win odds and show bets. The conversion of win odds to win probabilities accounts for the public’s biases, see reading 15.

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We bet x on the favorite

k = fraction of S pool on favorite by the crowd

(1-k)/(n-1) = fraction of S pool on all the other n-1 horses by the crowd

We bet an equal amount y on all the other horses.

Our total wager = x+(n-1)y

S1: If favorite is in $, we collect 5% on x and 2 of the y bets but lose (n-3)y on the (n–3) losers

Strategy: make same profit regardless of the finish

1 .05(x 2y) (n 3)y

S2: If favorite is out of the $, assume so far our bets do not influence the odds (prices)

2 3QS

3(1 k)Sn 1

3

y

(1 k)S /(n 1) x (n 4)y

profit on the 3 horses in the moneyloss on the favorite

loss on the other n-4 losses

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To guarantee a particular payout regardless of the finish

1 2 x

y 2

Q(n 1)

(1.05)(1 k)

This yields a profit of

.05yQ(n 1)

1.05((1 k) (n 3)y

0 k 1 Q(n 1)

21(n 3)

The bets are actually not quite equal and the bets may influence the odds

Q.85 and n 5 k .92

DD had k= .955

Bet is $2364 on DD

$34 on the other 4 horses

How it works

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S1: 1 = $53.60

S2: if bets were equal 2 would be $53.60 but the bets were not equal

The 2 depends on the finish of the top 3 finishers

Average=53.60

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x= bet on DD

y1= bet on Its in the Air

y2= bet on Mairzy Doates

y3= bet on Poppycock

y4= bet on Croquis

R=guaranteed return

Use a linear program

What if the bets are different?

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• Locks or true arbitrages exist but not very often.

• They are exploitable but work is involved.

• The gain is about 2% on money invested.

• My friends Jackson and Waldron in Dublin found a flaw in the British/Irish betting rules similar to this, published in Economics of Gambling,L Vaughn Williams, ed, 2004

• WTZ spotted it in the 1987 book but they wrote it up and did it to the tune of 50,000 pounds before the rules changed.

• Betting exchanges make such arbitrages more likely as there are more readily accessible markets.

Discussion

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Different prices in different places so: 6.44% riskless profit

Arbitrage

By taking risk you go to risk arbitrage but you usually make more

Betfair/Betdaq/Mansion/Matchbook/Tradesports; different prices can be used to construct real arbitrages and risk arbitrages.

WTZ papers on this in Hausch, Lo and Ziemba (1994) Efficiency of Racetrack Betting Markets, Academic Press (available from WTZ)

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www.betfair.com

FOMC – February FOMC

Tot al selections:(6) GBP Back Lay- 0.50-£200

100£2

- 0.25-£200

3£2

9£20

100£2

No Change-£200

14£2

19£4

24£8

27£2

+ 0.25£24.02

1.01£7

1.03£44

1.07£50

1.08£251

1.09£2

+ 0.50-£200

6£2

6.2£2

10£5

40£10

50£2

90£2

Any Other Change-£200

110£2

wtz +0.25 200£ @ 1.12

If I win +24.02£

If I lose -200£

I could cover at 1.07/1.08 and lock in a risk arbitrage

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www.betfair.com

wtz £200 @ 1.04 so this replaces 1.05 lay £30, so it now reads

1.04 1.05£200 £30WTZ £150 @ 1.04 Jan 31, 2006; maybe ?? the last hike?

ECB – February ECB

Tot al selections:(6) GBP Back Lay- 0.50 50

£2400£2

- 0.25 28£6

200£2

No Change 1.02£50

1.03£151

1.04£200

1.05£30

1.07£9

+ 0.25 30£8

200£2

400£2

+ 0.50 1.3£1381

34£2

40£2

Any Other Change 34£2

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A typical convergence trade: the Nikkei put warrant market of 1989-90

Buy A, Sell A’ cheaper and exit when the prices of A and A’ are within a transaction band

• Ed Thorp and I, with assistance from Julian Shaw, did a convergence trade based on differing put warrant prices on the Toronto and American stock exchanges.

• The trade was successful and Thorp won the over $1 million risk adjusted hedge fund contest run by Barron's in 1990.

• There were risks involved and hedge fund risk management care was needed. What follows is a brief description of the main points.

• Additional discussion and technical details appear in Shaw, Thorp and Ziemba (1995).

• Japanese stock and land prices were astronomical and very intertwined, see Stone and Ziemba (1993) for more on this.

Risk Arbitrage in Action

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• Tsukamoto Sozan Building in Ginza 2-Chome in central Tokyo is the most expensive land in the country with one square meter priced at ¥37.7 million or about $279,000 U.S. at the (December 1990) exchange rate of about ¥135 per U.S. dollar.

• Downtown Tokyo land values highest in the world, about $800 million an acre

• Office rents in Tokyo are twice those in London yet land costs 40 times as much

• Japanese stock market up 221 times in yen and 553 in dollars as measured by the Nikkei stock average from 1949 to end of 1989.

• Despite this huge rise, there had been twenty declines from 1949 to 1989 of 10% or more. Plus two more in 1990 and two more in 1991. So the market was volatile. Also both stocks and bonds were highly levered with debt.

• There was a tremendous feeling in the West that the Japanese stock market was overpriced as was the land market. For example, the Emperor's palace was reputed to be worth all of California or Canada. It took me 15-20 minutes to walk across it.

• Japanese land was about 23% of world's non-human capital. Japanese PE ratios were 60+.

The historical development leading up to the NSA put warrants, 1989

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• Various studies were made by academics and brokerage researchers to argue that the high prices of stocks and land were justified by higher long run growth rates and lower interest rates in Japan versus the US. See for example, Ziemba and Schwartz (1991) and French and Poterba (1991).

• However, similar models predicted a large fall in prices once interest rates rose from late 1998 to August 1990.

• Hence both must crash!

• There was a tremendous feeling in Japan that their economy and products were the best in the world.

• There was a natural trade in 1989, early 1990

• Westerners bet Japanese market will fall

• Japanese bet Japanese market will not fall

Historical development (cont’d)

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Various Nikkei put warrants which were three year American options were offered to the market to fill the demand by speculators who wanted to bet that the NSA would fall.

The various NSA puts and calls were of three basic types. Let NSA0 be today's NSA and E0 be today's exchange rate. Then Ee is the strike price and NSAe be the exchange rate on expiry for Canadian or US dollars into yen. The symbol (X)+ means the greater of X or zero.

Our convergence trades in late 1989 to early 1990 involved:

• selling expensive Canadian currency Bankers Trust I's and II's and buying cheaper US currency BT's on the American Stock Exchange; and

• selling expensive Kingdom of Denmark and Saloman I puts on the ASE and buying the same BT I's also on the ASE both in US dollars.

• This convergence trade was especially interesting because the price discrepancy was based mainly on the unit size (0.5 vs 0.2 of an NSA)

NSA puts and calls on the Toronto and American stock exchanges, 1989-1992

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• We performed a complex pricing of all the warrants which is useful in the optimization of the positions size, see Shaw, Thorp and Ziemba (1995).

• The table gives insight into this in a simple way.

• For example, 9.8% premium year year means that if you buy the option, the NSA must fall 9.8% each year to break even.

• So selling at 9.8% and buying 2.6% looks like a good trade.

• A stochastic programming optimization model helps in determining how much to sell give the risks and your wealth level.

Relative values of the put warrants

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• Large price discrepancy across Canadian/U.S. border• Canadians trade in Canada, US's trade in U.S

• Different credit risk

• Different currency risk

• Difficulties with borrowing for short sales

• Blind emotions vs reality

• An inability of speculators to properly price the warrants

The market was confused; % unit became important, BT U.S. cheapest even though

its nominal price was highest.

Some of the reasons for the different prices were:

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• A simulation in Shaw, Thorp and Ziemba (1995) showed that for similar parameter values, I's were worth more than II's, which were worth more than III's.

• But many investors preferred the currency protected aspect of the II's and overpaid (relative to hedging that risk separately in the currency futures markets) for them relative to the I's.

• Look at figures of the two convergence trades.

• Relative Cost = (Actual Cost - Theoretical Cost)/Theoretical Cost when =20% is plotted rather than implied volatility since the latter did not exist when there were deep in the money options trading for less than intrinsic as in this market.

• Fair value at 20% NSA volatility and 10% exchange rate volatility is zero on the graph. At one, the puts are trading for double their fair price.

• At the peak, the puts were selling for more than three times their fair price.

Simulation

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• The BT-I's did not trade until January 1990 and in about a month the Canadian BT-I's and BT-II's collapsed to fair value and then the trade was unwound.

• To hedge before January 1990 one needed to buy an over the counter put from a brokerage firm such as Salomon who made a market in these puts.

• The NSA decline in 1990 is also shown on the graph.

• Additional risks of such trades is being bought in and shorting the puts too soon and having the market price of them go higher.

• We had only minor problems with these risks.

Risks

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• For the second trade, the price discrepancy lasted about a month.

• The market prices were about $18 and $9 where they theoretically should have had a 5 to 2 ratio since one put was worth 20% and the other 50% of an NSA and trade at $20 and $8.

• These puts were not identical so this is risk arbitrage not arbitrage.

• The discrepancy here is similar to the small firm, low price effect (see Keim and Ziemba, 2000).

Size Effect

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• There was a similar inefficiency in the call market where the currency protected options traded for higher than fair prices; see the figure.

• There was a successful trade here but this was a low volume market.

• This market never took off as investors lost interest when the NSA did not rally.

• US traders prefered Type II (Salomon's SXZ) denominated in dollars rather than the Paine Webber (PXA) which were in yen.

• The Canadian speculators who overpaid for these put warrants that led to our risk arbitrage made $500 million Canadian since the NSA's fall was so great.

• The issuers of the puts also did well and hedged their positions with futures in Osaka and Singapore.

• The losers were the holders of Japanese stocks.

• This case example illustrates many of the aspects of hedge fund trading risks.

The call market

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14. A model to rank countries for long-short portfolios based on short term momentum, long run mean reversion and value

One year return based on short term momentum, long-run mean reversion, and value.

Source: Arrowstreet Capital (John Campbell, Harvard Economics Professor)

Model +b1(return)-1 - b2(10-year cumulative return) + b3(dividend yield)-1

Worst - Finland

Poor- US, Japan

Best - Asia ex Japan, including New Zealand, Australia

• Short term - momentum

• Long term - mean reversion

• Value

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NASDAQ 1990-2002: Mean Reversion

Mean reversion

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Refining our expectations

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Insert Siegel’s Stocks for the Long Run