Category Archives: Volatility

Natural gas winter volatility p-value simulation

Natural gas prices are more volatile during the winter heating season. I’ve adapted the code from Data Analysis for the Life Sciences to use natural gas daily price change and simulate a p-value.

Actual monthly natural gas volatility since 2010:

ng1 %>% group_by(month) %>% summarize(st.dev = sd(ng.diff)) #find the st. dev. of each month’s prices

Separate daily natural gas prices into winter and not winter:

ng.not.winter <- ng1 %>% dplyr::filter(!month %in% c(“1”, “2”)) #control group
ng.winter <- ng1 %>% dplyr::filter(month %in% c(“1”, “2”)) #treatment group

Find the real difference in price volatility (standard deviation of price):

month.diff <- sd(ng.winter$ng1) – sd(ng.not.winter$ng1)

Create a null distribution by sampling:

set.seed(1)
n <- 10000
samp.size <- 12
null <- vector(“numeric”, n) #create a vector for the null distribution, holding the differences between means of samples from the same population

for(i in 1:n) {
ng.not.winter.sample <- sample(ng.not.winter$ng1, samp.size) #sampling from population of control
ng.winter.sample <- sample(ng.not.winter$ng1, samp.size) #sampling from population of control
null[i] <- sd(ng.winter.sample) – sd(ng.not.winter.sample)
}

mean(null >= month.diff) #p-value

Not below 5%, but not bad. The p-value would decrease if we increased the sample size.

10% of samples from the control group (non-winter) have differences greater than the true difference. This is the p-value.

hist(null, freq=TRUE)
abline(v=month.diff, col=”red”, lwd=2)

The histogram looks normal, so using a normal approximation should give a similar answer:

1 – pnorm(month.diff, mean(null), sd(null))

Interest Rates and High Oil Prices

I came across this FT article from several months ago which gives a good picture of where we might be headed in the oil market, as well as in other commodities.  As I described a couple of posts back, the low nominal/negative real interest rates we have been experiencing have incentivized the holding of oil in storage (either in storage tanks or in the ground by not extracting) due to the negative returns available for money which would be received in exchange for the oil.  It has been less expensive to keep the oil in storage than to sell it, especially if one does not have any profitable new business to invest in. 

As rates have flat lined close to zero, oil prices have stayed up in the $95-$100 range since mid-2011.   The forward curve, which was in contango almost continuously from October 2008 until June 2013 (front month minus third month), is now backwardated.  This makes it more expensive for inventory holders to hedge as they have to sell forward to hedge the physical oil they own.  Until June 2013 they were able to capture a hedge profit by selling the higher priced forward and holding it until expiration, when they could buy it back cheaper and roll their hedge forward.  Couple this incentive to hold with the poor alternatives for the cash they would receive from selling their inventories, and the price support becomes obvious. 

Now, however, the forward market for WTI is backwardated and inventory holders must incur a hedge cost when they sell forward at lower prices than spot.  This alone should put downward pressure on spot prices as inventories are sold.  Indeed, inventories at Cushing, Oklahoma continue to decline as oil is sent to the Gulf Coast for either refining or storage.  If refining, this represents demand; if storage, it is just a change in location without affecting the overall level of crude inventories in the US. 

But WTI prices are holding up at around $100.  The normal mechanism would be for the increased supply on the market, induced by a backwardated curve, to push spot prices down until the curve structure is such that holding inventories is cheap enough to slow the selling down.  This hasn’t happened yet.  Is a rate rise what is needed to send prices down to a level more in keeping with what are believed to be supply/demand fundamentals?

 

Forecasting or Risk Management?

“There’s a chapter in the new book on what I think economics should be about, which is not forecasts. It’s about not taking the wrong risks. You don’t know what’s going to happen but you can avoid excessive risk-taking and this, unfortunately, has not been the policy of the Federal Reserve.”

So says Andrew Smithers in the FT.  He’s right.  The ability to make economic forecasts is highly dubious from both theoretical and empirical viewpoints.  Theoretically, human behavior and interaction is not governed by any stable rules or relationships.  This leads to almost infinite combinations of events, and the possible combinations are always changing.  Empirically, economists are usually wrong in their forecasts.

It is probably a better idea to focus on positioning oneself with the probable current, not try to guess where that current will take you.  In today’s world this usually means trying to understand the likely effects of government, especially central bank, policy on markets.  Free markets with free banking would offer weaker and shorter lived currents.  Better for average people, but worse for speculators.

Unfortunately, reducing one’s goals to simply being on the right side, probabilistically speaking, is not easy.  We are not talking about probability in the sense it is used in the natural sciences.  There are no stable distributions in economics.  Indeed, the most common distribution used in economics and finance, the normal distribution and its offshoots, is based on coin tossing where the probability of each of two possible outcomes is known and stable.  This is not the case when dealing with human beings, whose value scales, tastes, hopes, fears, time preferences, moods, etc. are in constant flux.  This means their reactions to events, which are themselves usually the result of other peoples’ reactions, are unstable from a probability standpoint.  Gambling probability, from which much of financial probability takes its inspiration, deals with large classes of events governed by the same probabilistic laws.  Human behavior, on the other hand, deals with individual cases, each of which has never happened before and which will never happen again, and hence are not governed by any knowable probability distributions.  The a priori distributions we put on them in order to understand them sometimes deviate from the results a posteriori.  This is the danger.

Another quote from Smithers in the article:

 “Prior to the great crash, Ben Bernanke wrote a paper claiming that central bankers have been responsible for what he called the ‘great moderation’. I thought he was right but I thought it was a disaster: in the process of moderating the swings of economies, they were also moderating the perceived riskiness of debt.”

Making economies appear less volatile than they are makes markets riskier.  The price stabilizing policies only serve to mask the true price changes, which makes economic calculation more difficult.  In this case, debt is underpriced in light of the true risk inherent in the economy.  People only see things through a monetary lens.  They see and react to nominal prices, not real prices.  This is when the miscalculation happens.

Volatility and Interest Rates

Volatility is low across many asset classes.  If volatility is a measure of uncertainty, then this is a bit strange.  These seem to be some of the most confusing economic times in recent history, with ever present calls for market crashes while stock markets move up, bonds stay very high, and oil moves sideways.

Central bank policy has provided strength to most markets, as they are designed to do.  This has in effect reduced downside volatility.  Oil is trading at less than 20% implied volatility, well below historic levels, even as economic uncertainty is high.  Oil production in the U.S. is growing and should be putting downward pressure on oil, but prices have been moving sideways since 2011.  Why would $100 WTI, with rising supply and economic crashes always around the corner, be trading at <20% implied put side volatility?

At least part of the answer seems to involve central bank policy.  Low interest rates have sent money out to non-traditional markets in search of yield.  Commodities like oil benefit from this.  Low interest rates also incentivize oil producers to keep oil in the ground.  If their option is to put their proceeds from oil sales into low to negative real rate paying treasuries, then why not wait?  Lastly, the money used by central banks to buy the bonds that keep interest rates low needs a home.  The new money is a wealth transfer from savers to the receivers of the new money, so there is a constant flow of real, not nominal, savings to the bondholders.  They will be looking for somewhere to invest the money.  These three factors, put in place because of the uncertainty the world faces, have led to the paradox of lower volatility in the face of greater uncertainty.

Below is a chart showing the Goldman Sachs commodity index with real 6 month interest rates:

image001