Transcript ccccc - OptiRisk Systems

Great investors and hedge fund managers: their methods and evaluation
Prof William T Ziemba
Alumni Professor of Financial Modeling and Stochastic Optimization
(Emeritus)
Mathematical Institute, Oxford University
ICMA Centre, University of Reading
William T Ziemba Investment Management Inc, Vancouver, BC
Dr Z Investments Inc, San Luis Obispo, CA and
Private International Wealth Management, BC Capital Group, Nassau
CARISMA Seminar, June 25, 2007
Session 1: What it takes to win and have smooth wealth paths
1. Some great investors: Buffett, Keynes, Benter, Thorp, the Harvard
Endowment and the Ford Foundation
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Keynes as a Hedge Fund Manager
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Unofficial, private hedge funds have been run for centuries using futures, equities,
and other financial instruments
Futures in rice trading in Japan date from the 1700s
Futures trading in Chicago was active in the mid-1800s
The Chest Fund at King’s College, Cambridge: an early hedge fund
Managed by the famous economist John Maynard Keynes from 1927–1945.
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November 1919 - Keynes appointed second bursar
Prior to 1919 King’s College invested only in fixed-income trustee securities
and the college’s own land and buildings.
June 1920 - Keynes convinced the college to start a separate fund containing
stocks, currency, and commodity futures.
1924 Keynes became first bursar and thus had final authority on investment
decisions
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Keynes (cont’d)
Keynes (1938) emphasized three principles of successful investing:
(1) a careful selection of a few investments (or a few types of investments), having
regard to their cheapness in relation to their probable actual and potential intrinsic
value over a period of years ahead and in relation to alternative investments at the
time;
(2) a steadfast holding of these investments in fairly large units through thick and thin,
perhaps for several years, until either they have fulfilled their promise or it is evident
that they were purchased by mistake;
(3) a balanced investment position (i.e., a variety of risks in spite of large individual
holdings and, if possible, opposed risks).
Keynes did not believe in market timing:
We have not proved able to take much advantage of a general systematic movement out of
and into ordinary shares as a whole at different phases of the trade cycle dots. . .As a result of
these experiences I am clear that the idea of wholesale shifts is for various reasons
impracticable and indeed undesirable. Most of those who attempt to sell too late and buy too
late, and do both too often, incurring heavy expenses and developing too unsettled and
speculative a state of mind, which, if it is widespread, has besides the grave social
disadvantage of aggravating the scale of the fluctuations. (Keynes, 1938)
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Keynes (cont’d)
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By emphasizing value, large holdings, and patience, Keynes’ ideas overlap those
used by Warren Buffett in his Berkshire Hathaway Fund.
Buffett has also added effective side businesses, such as insurance, and a greater
level of involvement in the management of his holdings.
Keynes’ approach of having a small number of positions even partially hedged
naturally led to fairly high volatility
Details of the holdings over time, as with hedge funds, are not known, but it is
known that in 1937, the fund had 130 separate positions.
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The record of The Chest Fund, King’s College, Cambridge, 1927-1945 (Keynes)
-w-0.25 (80% Kelly, 20% cash), see Ziemba (2003)
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Absolute and relative performance of the Chest Fund managed by J.M.Keynes,
1927-1945 Source: Updated from Chua and Woodward (1983)
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Keynes (cont’d)
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The returns do not include dividends and interest.
The income, which is not public information, was spent on modernizing and
refurbishing King’s College.
The index’s dividend yield was under 3 percent.
A capital asset pricing model (CAPM) analysis suggests that Keynes was an
aggressive investor with a beta of 1.78 versus the benchmark U.K. market return, a
Sharpe ratio of 0.385, and geometric mean returns of 9.12 percent a year versus –
0.89 percent for the benchmark. Keynes had a yearly standard deviation of 29.28
percent versus 12.55 percent for the benchmark.
The drawdown from 100 in 1927 to 49.6 in 1931, with losses of 32.4 percent in
1930 and 24.6 percent in 1931, was more than 50 percent, but this drawdown
occurred during the depression, when the index fell 20.3 percent and 25.0 percent,
respectively.
The College’s patience with Keynes was rewarded in the substantial rise in the
index from 1932 to 1937 to 315.4.
Keynes’ aggressive approach caught up with him as Britain prepared for World
War II in 1938–1940, when the index fell to 179.9. Then, during the war, 1941–
1945, Keynes had a strong record.
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Keynes (cont’d)
• Keynes’ turning 100 into 480.3 in 18 years, versus 85.2 for the index, plus dividends
and interest given to the College, gives Keynes a good record as a hedge fund
manager.
• Keynes’ aggressive style (which is similar to the Kelly betting I discuss later) led to
great returns—and some losses and embarrassments.
• When a grain contract was not covered in time, Keynes had to take delivery and fill
up the famous King’s College chapel, which was fortunately large enough to store the
grain safely until it could be sold.
• The Sharpe ratios and CAPM results are based on normality, and a better way to
calculate Keynes’ B’s is through Leland’s (1999) B’s which applies for the fat tails that
Keynes had.
• For example, Keynes’ aggressive style is close to log utility, so a g relative risk
aversion of 1.25 approximates his behavior, which compares to 1/g = 80 percent in
the log optimal portfolio and 20 percent in cash.
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Gamblers as Hedge Fund Managers
• I have consulted for seven individuals who used investment market anomalies and
imperfections and hedge funds ideas to turn a humble beginning with essentially zero
wealth into hundreds of millions of dollars
• Five are billionaires.
• They shared several common characteristics
• a gambling background usually obtained by playing blackjack or other sports betting
professionally or a knowledge of the mathematics of gambling;
• a focused, fully researched, computerized system for asset-position selection;
• careful attention to the possibility of loss
• focusing more on not losing than on winning.
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Gamblers (cont’d)
• Four were relative value long–short managers who consistently eked out small edges.
• One was a futures trader who made bets on a large number of liquid financial assets and
some short term trading on a daily or almost instantaneous basis based on favorable
trends (interest rates, bonds, and currencies were the best then but not now).
He is now a multi-billionaire.
• The sixth was a Hong Kong horserace bettor (see Benter in Hausch, Lo, and Ziemba,
1994).
• The seventh does all sorts of trading and investing in superior hedge funds to make
billions.
Their gambling backgrounds led them to conservative investment behavior and excellent
results, both absolute and risk adjusted.
• They had their losses, but rarely did they overbet or lack sufficient diversification.
• Good systems for diversification and bet size were crucial in avoiding major blowouts.
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Ed Thorp
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Edward Thorp, a mathematician with a Ph.D. from the University of California at Los
Angeles (UCLA), became famous in 1960 after devising a simple-to-use cardcounting system for use in the card game blackjack.
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In 1966, Beat the Market, a follow-up to his book Beat the Dealer, outlined a system
for obtaining edges in warrant markets.
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Thorp was close to finding the Black–Scholes formula for pricing options, at least
from an approximate, empirical, and discrete-time point of view,
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Some of his ideas were used in his hedge fund Princeton Newport Partners (PNP).
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He ran this fund, with offices in Newport Beach, California, and Princeton, New
Jersey, from 1969 to 1988 and used a variety of strategies, many of which can be
classified as convergence or long–short strategies.
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A Nikkei put warrant risk-arbitrage trade that Thorp and I jointly executed based on
my ideas gives some idea of the approach. The basic idea is to sell A at an
expensive price, hedge it with the much cheaper close substitute A’ and then wait
until the prices converge and cash out, remembering not to overbet.
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Thorp wrote the foreword to my book, Beat the Racetrack written with Donald
Hausch. By using probabilities estimated from the simpler win market, we provided a
simple-to-use winning system for racetrack betting based on weak market
inefficiencies in the complex place and show markets.
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Thorp (cont’d)
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See PNP’s performance record - actual trades and positions used by Thorp and his
colleagues are not public information
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PNP gained 15.1 percent, net of fees (which were about 4 percent given the 20
percent profit fee structure), versus 10.2 percent for the S&P 500 and 8.1 percent for
T-bills.
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An initial index of 100 on 1 November 1969 became 148,200 at the end of
December 1988 versus 64,500 for the S&P 500 and 44,500 for T-bills.
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But what is impressive is that the risk control, by using various stochastic
optimization procedures, led to no years with losses and a high Sharpe ratio, which,
based on monthly data, approached 3.0.
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Of course, Thorp had an easier market to deal with than Keynes. For example, the
S&P 500 had negative returns only in 1973, 1974, and 1976.
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The record of Princeton Newport Partners, LP, cumulative results,
Nov 1968- Dec 1998 (Thorp)
This is ideal:
20 years,
3 losing months,
no losing quarters,
very smooth path.
The best smooth
wealth path
Downside Sharpe
measure = 13.8
It is this WTZIMI
tries to achieve.
See WTZ’s JPM
(2005) paper on
this
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PNP: 15.1% net vs 10.2% for the S&P500
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Growth of assets for various high-performing funds, Dec 1985 - June 2000
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Buffett’s Berkshire Hathaway
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Warren Buffett’s Berkshire Hathaway is a closed-end fund which is run like a hedge
fund with an emphasis on value investing, insurance businesses, and other
ventures.
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A comparison with Keynes’ and Thorp’s performance,shows his brilliant record from
December 1985 to [June 2000
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Buffett also had a great record from 1977 to 1985, turning the index value of 100 into
1,429.87 in 1985 and 65,852.40 in April 2000 and about 110,000 now.
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Also shown are the records of George Soros’ Quantum Fund, John Neff’s Windsor
Fund, Julian Robertsons’ Tiger Fund, and the Ford Foundation.
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Capital growth
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Capital growth or Kelly criterion fans, such as Thorp and I, prefer Buffett’s long-term
growth record.
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Indeed, Thorp (2006) has argued that Buffett largely uses Kelly-like strategies.
Keynes and Buffett have many common characteristics in addition to their
aggressive style, namely, an emphasis on value, large holdings, and patience.
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From January 1980 to March 2000, Buffett’s Sharpe ratio was 0.786, whereas the
Ford Foundation’s was 0.818.
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So, by the Sharpe ratio measure, the Ford Foundation beat Berkshire Hathaway
because it had good growth with little variation.
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But much of Berkshire Hathaway’s variation was on gains, and the total wealth at
the horizon was much greater. Using the symmetric downside risk measure provides
a fairer evaluation—with Berkshire Hathaway improved but not dominating, see §22.
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Starting from July 1977, Berkshire Hathaway’s Sharpe ratio was 0.850 versus Ford’s
0.765, and the S&P’s was 0.676, and geometric mean returns were 32.07 percent
(Berkshire Hathaway), 14.88 percent (Ford), and 16.71 percent (S&P 500).
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Buffett’s 39 Year Record: only one decline, $15 in 1965 --> $110,000 in June 2007
Increase in per share book value of Berkshire Hathaway versus returns on the S&P500 with
dividends included, 1965-2003, in percent. In Feb 2007 it’s about $110,000.
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The record of Bill Benter, the world’s greatest racetrack bettor.
Efficiency of Racetrack Betting Markets, Academic
Press (1994)
He made 400M+ in a market with >15% track take.
He had advantages such as computer betting into the pools, very poor bettors in
opposition and data updates every 12 seconds.
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A+ Performance: Harvard an in house hedge fund
Harvard boasts the largest endowment of any university in the nation,
in part because of the outstanding performance turned in by its inhouse portfolio managers...
An n ual Returns**
School
1-Ye ar,%
10-Ye ar, %
Harvard
21.1
15.9
Yale
19.4
16.8
Stanford
18.0
15.1
Princeton
16.8
15.5
Columbia
16.9
11.6
25 Largest
17.1
12.8
Endowments*
*Median return is shown
Sources: Harvard; Yale; Princeton; Stanford; Colum bia
Barron’s, January 31, 2005
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S iz e (bi l)
$22.6
12.7
10.0
9.9
4.5
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...who have racked up impressive gains in many investment sectors.
Harvard's Hol dings
An n ual Returns**
W eigh t In
By Se ctor
1-Ye ar, %
10-Ye ar, %
En dowment, %
Domestic Equities
22.8
17.8
15
Foreign Equities
36.1
8.5
10
Emerging Markets
36.6
9.7
5
Private Equity
20.8
31.5
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Hedge Funds
15.7
n.a
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High Yield
12.4
9.7
5
Commodities
19.7
10.9
13
Real Estate
16.0
15.0
10
Domestic Bonds
9.2
14.9
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Foreign Bonds
17.4
16.9
5
Inflation-indexed
4.2
n.a.
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Bonds
Total Endowment
21.1
15.9
105%***
**Period ended June 2004, ***Equals 105 because of slight leverage.
Sources: Harvard; Yale; Princeton; Stanford; Colum bia
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The top 25 US university endowment funds, 2003-4, 2004-5 and 2005-6
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Yale’s endowment, 1950-2006 YEC (2006)
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Yale’s endowment, asset classes (YEC, 2006)
Changing allocations,
1985-2006
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Alternative asset returns exhibit significant dispersion (YEC, 2005)
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Yale growth, 1905-2005 (YEC, 2006)
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University revenue by source, 1905-2005 (YEC, 2006)
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2.
The Importance of getting the mean right. The mean dominates if the
two distributions cross only once.
Thm: Hanoch and Levy (1969)
• If X~F( ) and Y~G( ) have CDF’s that cross only once, but are otherwise arbitrary,
then F dominates G for all concave u.
• The mean of F must be at least as large as the mean of G to have dominance.
• Variance and other moments are unimportant. Only the means count.
• With normal distributions X and Y will cross only once iff the variance of X does not
exceed that of Y
• That’s the basic equivalence of Mean-Variance analysis and Expected Utility Analysis
via second order (concave, non-decreasing) stochastic dominance.
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Errors in Means, Variances and Covariances
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Mean Percentage Cash Equivalent Loss Due to Errors in Inputs
When RA is very low such as with
log u, then the errors in means
become 100 times as important.
Conclusion: spend your money
getting good mean estimates and
use historical variances and
covariances
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Average turnover: percentage of portfolio sold (or bought)
relative to preceding allocation
• Moving to (or staying at) a near-optimal portfolio may be preferable to incurring the
transaction costs of moving to the optimal portfolio
• High-turnover strategies are justified only by dramatically different forecasts
• There are a large number of near-optimal portfolios
• Portfolios with similar risk and return characteristics can be very different in
composition
In practice (Frank Russell for example) only change portfolio weights when they change
considerably 10, 20 or 30%.
WTZIMITests
show that leads to superior performance,
see Turner-Hensel paper in ZM (1998).
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Effect of the Risk Premium: Differing Future Equity Mean Returns: InnoALM
Siemens Austria Pension fund Multiperiod Model
• mean of US stocks 5-15%.
• mean of European stocks constrained to be the ratio of
US/European
• mean bond returns same
• case NM (normal distribution and mixing correlations).
• As expected, [Chopra and Ziemba (1993)], the results are very
sensitive to the choice of the mean return.
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If the mean return for US stocks is assumed to equal the long
run mean of 12% as estimated by Dimson et al. (2002), the
model yields an optimal weight for equities of 100%.
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a mean return for US stocks of 9% implies less than 30%
optimal weight for equities
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Optimal Asset Weights at Stage 1 for Varying Levels of US Equity Means
Observe extreme sensitivity to mean estimates
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The Effects of State Dependent Correlations (Geyer and Ziemba, 2007)
Optimal Weights Conditional on Quintiles of Portfolio Wealth at Stage 2 and 5
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Different approaches to estimating means
• Econometrics
• Factor models
• Technical analysis
• Crash models
• History
• Mean reversion
James-Stein means shrink the historic mean towards the grand mean
Bayes-Stein means shrink the historic mean towards the min Var portfolio
• Truncation estimators
Foster, MacLean, Ziemba, 2002, 2005
If you get the mean right and do not overbet and truly diversify, you should win.
Truly means: in ALL scenarios.
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Zenit Stockholm Multi-Billion Hedge Fund - data
Getting the right mean/hedge ratio
-0.60 all in US
Two of WTZ crash models signaling
downturn in 2002  tilt scenarios
If you do the most important thing right
and watch your risk control, you can
win big time.
They were long when models said to
be long, then went short when models
said to be short.
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Zenit graph: 35%/year 1996-2003
Crash models +then WTZIMI
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3. Avoiding the recipe for disaster: overbetting, non-truly diversifying and
then being hit by a bad scenario
Do not overbet.
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The recipe for disaster
It is clear that hedge funds got into trouble by overbetting and not being
truly diversified, and vulnerable, they then got caught by low probability
but plausible disaster scenarios that occurred.
It is exactly then - when you are in trouble - that you need access to new
cash and since that is usually not available, it makes more sense to plan
ahead for such contingencies by not overbetting and by being truly
diversified in advance.
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Markets are understandable most (95%+) of the time. However real asset prices
have fat tails because extreme events occur much more than lognormal or normal
distributions indicate.
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Keim-Ziemba (2000) Security Market Imperfections in Worldwide Equity Markets,
Cambridge University Press, much of asset returns are NOT predictable.
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Must have way to use conventional models, options pricing, etc and the irrational
unexplainable aspects once in a while.
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Whether the extreme events are predictable or not is not the key issue - what is
crucial is that you consider that they can happen in various levels with various
chances.
How much should one bet on a favorable investment situation?
It’s clear that hedge funds got into trouble by overbetting and having plausible but low
probability disastrous scenarios occur.
It is exactly then - when you are in trouble - that you need access to new cash.
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Hedge Funds: Some Directional Strategies
• Macro - an attempt to capitalize on country, regional and/or economic change affecting
securities, commodities, interest rates and currency rates. Asset allocation can be
aggressive, using leverage and derivatives. The method and degree of hedging can
vary significantly.
• Long – a “growth”, “value”, or other model approach to investing in equities with no
shorting or hedging to minimize market risk. These funds mainly invest in emerging
markets where there may be restrictions on short sales.
• Long Bias – similar to equity convergence but a net long exposure.
• Short – selling short over-valued securities attempting to repurchasing them in the
future at a lower price.
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Long Term Capital Management
That’s about 1% of all the world’s derivative positions
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The bad scenario
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Kelly and fractional Kelly - explaining the overbetting that led to the
LTCM disaster
More on these strategies in section 6
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If returns are lognormal then fractional Kelly is just the negative
power coefficient otherwise approximate
Ref MacLean, Ziemba and Li, Time to Wealth (2005)
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Fractional Kelly has less growth and less variability, it lowers the bet to give a
smoother wealth path.
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What is the optimal fractional Kelly? -w, >0, what  is good?
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MacLean, Sanegre, Zhao and I, JEDC (2004) solve this in a continuous time model where
you check discretely and use a Var type criterion on the wealth path.
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With Kelly, the better the bet is the more you bet and thus the more you lose when you
lose so it’s very hard to stay above a wealth path.
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Theory developed under restrictive assumptions; calculations: algorithm exists but
computations lengthy.
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Better to penalize with a convex penalty for falling below the path
implemented for a gold hedge fund in London
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The more you are below the target, the more you are penalized as in Russell Yasuda
on this and slide 64
WTZIMI Kasai and Vienna models; see papers
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