1. G L O B A L A S S O C I AT I O N O F R I S K P R O F E S S I O N A L S
R I S K A N A LY S I S
Chess: A Valuable Teaching
Tool for Risk Managers?
How does chess resemble risk analysis? Are there similarities, for example, between the way a chess player
studies opponents’ games and the way a risk analyst studies clients’ portfolios? Igor Postelnik takes a
comprehensive look at chess strategy and discusses the lessons that risk managers can learn from chess.
ne of the most obvious features of financial Although chess has no randomness or concealed infor-
O markets is that prices move up and down
unpredictably. This has led to random walk
models that, in turn, suggest that practition-
ers should look for insight to games based on
randomization: e.g., coin flips, dice rolls and
card shuffles. In this article, I’d like to look at risk analysis
from a chess master’s perspective. I’ll try to compare chess
analysis to risk analysis and explain what risk management
might learn from chess.
mation, it is nonetheless unpredictable. If two players sit
down to play a game of chess, neither the game nor the
result is the same as the game the same two players played
yesterday.
Imagine a risk manager and a hedge fund manager trying
to decide an appropriate leverage level for a portfolio and
two opposing chess masters trying to decide how compli-
cated they want their positions to be. Are there no similari-
ties? Let’s see.
40 GLOBAL ASSOCIATION OF RISK PROFESSIONALS M A R C H / A P R I L 0 8 I S S U E 41

2. G L O B A L A S S O C I AT I O N O F R I S K P R O F E S S I O N A L S
R I S K A N A LY S I S
Just as higher leverage may enhance return or cause big- Humans vs. Computers
ger loss for a risk manager or a hedge fund manager, a A complicated chess position requires deep calculations
more complicated chess position may open unexpected and is more likely to cause a human player to make an
variations that will lead to first-prize money or leave a error. The players understand this general guideline, but
player without a prize at all. Each chess move has advan- also study their future opponents’ games and try to pick a
tages and disadvantages. While each move’s advantages style that is least familiar to their opponent. In 1997, for
include creating the possibility of a certain desirable future example, while Garry Kasparov was preparing to play a
line of play, there is a risk that each move will open up pos- computer, IBM programmers and chess advisers had
sibilities for (perhaps unforeseen) lines of play that are adjusted Deep Blue to better analyze Kasparov’s previous
desirable for the other side. Weighing the risks of this play games. The styles that are most effective for Kasparov are
and counterplay is the key to good judgment in chess and is known in the chess world, so the computer program was
really a type of risk management. fine-tuned to avoid playing such styles. By analogy, a com-
Before moving forward, let me dispel a myth that chess is puter risk model needs to be fine-tuned to better analyze
a deterministic game with full information available to styles a fund manager is more likely to use.
both players. In theory, this is true. However, in practice, it Deep Blue didn’t just play a game. It played against a
is hardly ever the case that a player sees all possibilities at specific opponent’s style, and Kasparov was embarrassing-
once. And even if he or she actually sees them, it’s hard to ly crushed in the last game as a result. Similarly, a computer
predict how well an opponent will program may not treat a leverage request as too high with-
react to them. So, it comes down to out human understanding of the investment style behind
probabilities: i.e., how likely is the the leverage request.
opponent to know a certain open- Now let’s discuss a “stress test.” It’s important to under-
ing or a certain type of a position? stand what happens when a chess player decides to sacri-
For example, I am a 2200-rated fice some pieces. The sacrifice is intended not to gain spe-
chess player. Against someone rated cific advantage but to create certain weaknesses in the posi-
below 2000, I definitely prefer to tion that the player will try to exploit later. A computer will
reach a simple position as soon as accept the sacrifice and evaluate the current position in its
possible. Against someone rated favor, rather than considering the intent of the sacrifice. As
above 2400, I want to keep the Igor the game progresses, the computer will treat an extra piece
position very complicated for as Postelnik as a positive, even as its position deteriorates.
long as possible. Consequently, the computer will not only miss the unex-
As more pieces come off the board, the less room there is pected sacrifice but will also be unable to determine where
for calculations. Why does it matter? A simple position the sacrifice would lead. Moreover, it certainly doesn’t give
doesn’t require deep calculations but does require a deep any thought as to why a human player would want to sac-
understanding of strategy. Chess players, as their strength rifice at all. A human player, in contrast, might not accept
grows, learn to calculate first and understand later. sacrifice in the first place, in order not to be exposed to the
In risk management, an analyst takes a first look at a opponent’s well-developed strategy.
fund's portfolio (chess position) and has to make a first Despite the fact that the world’s best chess players could
move (approve for leverage). Once a certain level of lever- barely manage to draw their matches against the best com-
age is approved (the first move is made), we have to consid- puter programs, average players are able to achieve decent
er how the portfolio manager will respond — as well as results against the same programs by selecting inferior
what factors will cause the trader to complicate the posi- openings that would be ridiculed if played against other
tion (increase risk in the portfolio) and, when that happens, humans. The sole purpose of such openings is to create
how the risk manager should respond. positions that rely more on deep comprehension of posi-
There are other similarities between chess strategy and tional nuances than on the rough calculating power of
risk analysis. Under time pressure in a tough position, a computers.
chess player has to choose a move, while a risk manager A human player knows that opening moves made are
has to choose a position in the portfolio to liquidate to inferior, and it’s generally just a matter of time until he or
meet a margin call when a portfolio is tanking. Chess play- she will eventually take advantage of them. A computer
ers also study opponents’ games trying to anticipate how doesn’t recognize inferiority and has to prove errors by
the next game will develop, while risk analysts study calculating. If calculations don’t reach far enough, the
clients’ portfolios trying to anticipate how the next trade computer won’t select the correct strategy. Based on
will affect the portfolio. recent events, computer risk models, just like computer
M A R C H / A P R I L 0 8 I S S U E 41 GLOBAL ASSOCIATION OF RISK PROFESSIONALS 41

3. G L O B A L A S S O C I AT I O N O F R I S K P R O F E S S I O N A L S
R I S K A N A LY S I S
chess models, tend to ignore a piece of analysis that is strategy before the game can be crucial to the end result.
not readily calculable — the piece that requires human This type of knowledge can also prove to be quite useful
understanding. in risk management. If we can determine, for example,
Keep in mind that all scenarios, at least in theory and no what strategy a portfolio manager will choose next, proac-
matter how improbable, are available on the chess board. tive steps can be taken to keep a firm’s current portfolio
Nevertheless, despite having superior quantitative ability, exposure reasonable (even when current exposure does not
computers can’t pick them all. So, then, how can they seem excessive) and to avoid unnecessary calculations.
account for all stress scenarios and calculate probabilities When models are insufficient, this knowledge can prove
of events that never happened in finance? particularly helpful. Say, for example, a fund sells deep
On the other hand, world champion chess players are OTM naked puts. A stress-testing model would assign a
known to make simple errors late in games because of value to a downside move and compare it to a fund's equi-
fatigue and/or mental lapses, and computers do an excel- ty. However, it wouldn’t know that the probability of the
lent job in avoiding such errors. move changes daily, and it also wouldn’t take into account
that something will always happen in the human world.
The Art of the Sacrifice Bobby Fischer was perhaps the best chess player ever, but
One last strategy that is worthy of consideration is why a not the greatest tactician. He proposed FischerRandom
player is more likely to sacrifice at the opening of a match chess, which reduces computer knowledge and calculating
with black pieces rather than with white pieces. It is impor- power in general by selecting starting setups at random.
tant to remember that with white pieces, he or she already Under such conditions, each human player will have more
has the advantage of the first move, and the goal is to keep and less favorable starting setups. A computer won’t make
that advantage and try to increase it. On the other hand, such a distinction.
with black pieces, he or she is already behind, so why not Computer programs are blind to human intentions and
sacrifice? It might help eliminate the first-move advantage. may not evaluate them correctly but do a great job in
Thinking about this from a risk management perspec- avoiding simple human blunders. Humans must specify
tive, if a fund is outperforming its benchmark, why use opponents’ intentions correctly and base computer calcula-
more leverage? But if it’s underperforming, why not use tions on those intentions, regardless of whether the oppo-
more leverage? nent is a chess grandmaster or a hedge fund manager.
A player may resort to sacrifices in time pressure, hoping
that an opponent will make a mistake by calculating. The Different Responses to Different Strategies
best way to avoid this is to exchange pieces. In the last In many ways, risks arising from randomness are the easi-
game of the 1985 world championship, the world champi- est to manage. If we flip a fair coin 100 times, for a $1 mil-
on had to win to tie the match. From the first move, he lion bet each time, we know the distribution of outcomes
launched an all-out attack. His opponent, Garry Kasparov, and can plan accordingly. With financial markets, it’s more
expected the attack and prepared in advance. Kasparov difficult, because the parameters of the distribution have to
won the game and the title. be estimated.
In the last game of the 1987 world championship, roles Risks arising from complex strategic interactions among
were reversed. Kasparov, as the world champion, had to competing (and in finance, but not chess, cooperating) enti-
win to keep the title. Not only did he not attack, he took a ties require more subtle management. It is tempting to treat
while to cross the middle of the board and stayed away everything as random and then set a powerful computer to
from exchanging the pieces. His opponent was consequent- crank through all the calculations. This can work, as com-
ly forced to spend time calculating. Whenever he tried to puter chess programs and successful program traders
simplify the position, Kasparov stayed back. As time began demonstrate. But it doesn’t always work.
to run out, Kasparov’s opponent committed a few small Sometimes you have to consider the intentions of other
errors that Kasparov was able to capitalize on, converting entities and their responses to your moves. Sometimes the
tiny positives into a decisive advantage. strategy that can be proven to be optimal with infinite com-
Thus, using very little leverage, the world champion puting resources (or perfect information) is a terrible strate-
retained the crown. This game turned into a very valuable gy in practice. In these situations, a chess master may have
lesson for many players on how to approach must-win situ- better insights than a poker, bridge, backgammon or gin
ations. The main lesson is that knowledge of an opponent’s rummy champion. ■
✎ IGOR POSTELNIK (FRM) is a national chess master and a vice president in Bear Stearns’s global clearing services risk control group. He
can be reached at ibpiar300@yahoo.com.
42 GLOBAL ASSOCIATION OF RISK PROFESSIONALS M A R C H / A P R I L 0 8 I S S U E 41