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.