### Many Colors of Risks

When equity investing first started, risk was a relatively
simple concept: your notional investment was your “value at
risk.” Then came the academians who
would apply the theory of normal distribution to asset prices. Now people apply the concept of “standard
deviation” on “value-at-risk”. With
that, people start to associate 4 or 5 or higher standard deviations as “almost
impossible” (traders and risk managers will sometimes cut corners here). Unfortunately, normal distribution is not a
good model for many equities, and statistics on a time series (like the asset
prices) implied history may repeat itself, which may be a very bad assumption to
start with.

Furthermore, when aggregating many stocks, long and short,
into a “book”, another risk management technique is employed: correlation. Relationship of price changes is assumed
through some implied correlation between assets, and the coefficients (or the
magnitudes of correlation pairs) are estimated through historical data. If two stocks are correlated statistically,
you long one and short the other, it seems you offset the risk and thus can
control risks in this way. Bad
idea. Correlation may be a good trading
idea-generation concept, but it is bad as a measure for risk management. Correlation that is simply based upon
historical data can breakdown at any moment, and thus, two seemingly offsetting
assets can actually suffer losses at the same time. Statistics based correlation does not reduce
risk, but simply hides it and make it more dangerous – it can be knowingly or
unknowingly turned into a corner-cutting trick in risk management.

When options join the mix, there is a multitude of risks
that do not exist in a stock only portfolio.
Each first-degree Greek is risk.
Delta is obviously a risk. Vega,
either long or short, is a risk, even though for some, long Vega is associated
with owning insurance (but insurance can get much cheaper very quickly, and
thus, is a risk). Theta is something very interesting and is often
misunderstood. Since its driver only
goes in one direction (as time always goes forward), it causes some to regard
collecting theta decay as a profit opportunity, rather than a risk. For us with volatility strategy, Theta is
always associated with Gamma. Either
long or short Theta is risk.

Though option pricing is based on statistics, many relations
in options can be expressed analytically, not by historical statistics. The Greeks, the vol surface, skew, are all
based on analytic functions, while the relation between implied vol and
realized vol is based on historical statistics.
Such analytical forms give us a much more solid foundation to risk
management.

Even with analytic relationships, large offsetting positions
still pose an elusive risk. A vertical
spread or calendar spread has a much reduced Vega risk, nevertheless, they
expose the skew and term structure risks, which require additional analysis. Even a reversal or conversion position which
has no major Greek risks, are exposed to other substantial risks such as dividends,
interest rate and early exercise.
Detecting hidden risks inside a conventional risk control parameters is
an art for risk managers and traders for a complex option book.

Statistics are unavoidable, but it is important to
understand whether a relationship is based on statistics or analytics. Pair trading, relative value strategies are
all statistical based. While skew or
term structure spread, or vol surface arbitrage, are analytical based. When the
opportunity cost and chance of returns are similar, no doubt we should opt for
the latter.

Sum it up in 2 short rules:
(1) Statistics may be good for trading idea, but bad for risk
management; (2) A large quantity of anything is usually a risk.