Upper and lower breakeven prices are COW expiration prices that would result in a current delta spread with no profit or loss. Volatilities described by the breakeven spreads as percentage of strike prices, and implied volatilities calculated by the Black-Scholes option price model, show that the volatility curves are skewed — higher at each end and lower where the strike price equals the underlying asset price. A similar pattern of skewness appears on “Cattle volatility smiles” (below). Breakeven spread percentages for the different strikes follow smooth curves down toward a ratio of 0.96 for futures price-to-strike price.
When we analyze live cattle and lean hog call options for three expiration dates on Aug. 24, 2012, we see that the two highest curves belong to October and June lean hogs, while December live cattle forms the bottom curve. In the middle are December hogs as well as October and June live cattle. The cattle price curves are close enough together that the small difference may have suggested calendar spreads on Aug. 24, selling June live cattle futures and buying October.
Heights of the option price curves as a percentage of the strike price that equals the current December futures price indicate the comparative volatilities shown below:
|Expiration||Lean hogs||Live cattle|
“COW and combo” showed that the two price series move closely in terms of percentage price changes, so we should find that their volatilities are similar. On Aug. 30, 2012, a Black-Scholes option price evaluation resulted in the standard deviation of annual returns for the January 2013 COW calls of 0.120. A similar analysis of December 2012 live cattle and lean hog call options showed standard deviations of 0.111 and 0.215, respectively. A weighted average of the livestock implied volatilities is 0.152. Thus, the volatilities are similar as they should be, with the combo result perhaps elevated because of the recent movement in lean hog futures.
Continuing analysis of the COW, live cattle and lean hog price changes should produce profitable trades. The universe of ETNs is large, and the same analysis might be applied to an increasing number of exchange-traded securities whose values depend on a wide range of underlying assets. In any case, the objective is not a completely accurate matching of the ETN price movements, but instead an estimate that includes the primary causes of ETN price changes.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.