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Potential Future Exposure for a Derivatives Position

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Potential Future Exposure (PFE) is a simple way to measure the riskiness of a derivatives portfolio, given some statistical assumptions about the distribution of future prices of the derivative portfolio’s underlying assets.  These assumptions are wrong, but not so wrong that the PFE will not provide some valuable information. The PFE uses the model of the underlying asset price process that the Black-Scholes option formula uses, and therefore shares the same assumptions, so the PFE can illustrate some of its limitations.

The PFE is easy to model in Excel.  We start with the asset price process,

ST = Ste(r – 1/2σ^2)(T-t) +/- σZ(T-t)^2

which is described here and here. For this example I have taken the WTI Crude Oil Cal13 prices as the underlying, meaning we have a portfolio of derivatives: futures, forwards, options, or a mixture of all of them with WTI as the underlying.

The r for each month will be the LIBOR rate of corresponding term, the sigma will be the implied volatility taken from the option on each contract month, and the Z will be a confidence level that we set.  Here we use 95%, or 1.65 (standard deviations).  In Excel, use NORMSINV(.95) to get 1.65.  If our assumptions were correct, which they aren’t, 95% of the time the portfolio’s worst loss would be inside the interval we create.

Apply the above formula to each contract month, adding the second term (with the Z factor) to get the upper interval and subtracting to get the lower, and using each month’s specific r, sigma, and time to expiration for each monthly contract (T-t), and we get this result:

It is a simple matter to get an exposure in dollar terms.  We take the portfolio’s exposure in barrels, net the longs and shorts for each month, and multiply each month’s underlying by each month’s corresponding price on the lower curve (since we would be losing if the underlying went down).  If the portfolio has options, treat them as being delta barrels long or short.  This works since the option delta is calculated using the same r, sigma, S, and (T-t) as our underlying process uses here.

Note that the upper bound is farther away from the current forward curve than the lower bound.  This is due to the lognormal distribution of asset prices.  The downside is floored at zero and the upside is infinite.

Garrison’s “Time and Money”, Chapter 4

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Macroeconomics and Secular Growth

Secular growth leads to the rate of savings and investment being greater than capital depreciation economy-wide.

Technological innovation, even when occurring in only a few markets, leads to an outward shift in the PPF as resources are re-allocated.  The demand for loanable funds shifts to the right as production increases, while the supply of loanable funds also shifts rightward due to higher incomes.

The IR changes under these conditions vary as different technology changes lead to different changes in current vs. future consumption.  The technology advance does, however, lead to an increase in the potential of investible resources, as if the subsistence fund had increased.

It is possible that IRs may rise as the existing subsistence fund is drawn on for the new production possible with the new technology.

New technology may shift resources to more time-consuming and capital intensive production methods.  The ability to shift resources to later stages might be less than is demanded, which will cause higher consumer goods. Scarce resources are sent to longer production times.  Higher prices will decrease savings, IRs will rise, and new technology will be under-utilized.  The effects of the technology change and the IR rise pull and push the production structure in opposite directions.

Eventually, the higher and more efficient production will push down consumer prices, savings and investment will increase, and IRs will fall.

Changes in Intertemporal Preferences

Sustainable growth, in addition to technology advances, can come about from changes in time preferences.

Labor based econ downplays time preference changes, seeing consumption as being strongly autocorrelated.  Capital based econ says that small changes in time preference can produce large results on resource allocation.

Resource misallocation can result if IR changes when no time preference change occurred, or vice versa

decr in C -> incr S -> incr supply of loanable funds and decr IR

Keynes said that a decrease in C in one period leads to a decrease in consumption in later periods, but if businesses’ expectations followed this line of reasoning, miscoordination would occur whenever S and C patterns changed.  since increased S now implies S for later consumption.

If investment, I, increases as C decreases, incomes don’t have to come down.  The economy can stay on the PPF.  Otherwise, Keynes’ “paradox of thrift” would come into play.

Keynes wrote in “Postulates of Classical Economics” that they all stand or fall together.  Capital based macro says they stand, even intertemporally.

A decrease in IR -> Hayekian triangle moves to a longer hypotenuse with a shallower slope, which represents longer, more efficient production process.

During this change, resources will move from later stages, where demand is falling with consumption, to earlier stages, where the increased savings are being channeled through investment (signaled by the lower IR).

Some firms may increase investment due simply to their input/output spreads in relation to the new, lower IR and cost of borrowing.  The general business sentiment will be expecting increased future consumption and will be favorable to investment.

A businesses hurdle rate for a particular deal will now be lower.  If the IR truly reflects time preferences, the project has a higher chance of working than if the IR is manipulated lower.  The manipulated lower IR increases the chance for a “cluster of errors”.

As savings and investment increase in the secularly expanding economy, the rate of increase of consumption may slow while the production structure is changing, but it will eventually move higher than the initial rate of increase as increased production leads to higher incomes and more consumption.

Labor demand is a “derived demand”, meaning its demand is derived from the demand to consume its product.  Labor will shift to earlier stages, where demand for its product is increased during the lengthening of the production structure.

Labor is valued at a discount, which is less as IR decrease.  The effect is greatest farthest away from the final good.  See Hayek’s Prices and Production where he mentions a “family of discount curves”, and Walter Block’s The DMVP-MVP Controversy.

The “derived demand” effect and the discounting effect work in opposite directions on wages.

Labor must be lured with higher wages, due to lower IR and discounting and increased demand for labor, to move to earlier stages.  The supply curve for labor is upward sloping in the short run and flat in the long run.  The demand curve shifts out, supply increases, then the supply curve shifts out as labor is drawn to the new stage’s market.

This assumes labor is non-specific.  Workers with specific skills to a market are considered human capital, and would probably not move to a new stage.  They would see a wage change, up or down depending on demand for their specific skills.

Non-specific capital will also move between stages.  Specific factors see a price change, non-specific see a quantity change in specific markets.

The Macro of Boom and Bust

During the period of sustainable growth described above, if the money supply is stable, prices will fall due to decreased consumption and increased savings and investment.

The business cycle, however, is created when the central bank, in the US the Fed, increases the money supply and the supply of credit, thereby lowering interest rates.  These lower rates are not the product of increased saving due to lengthened time preferences and hence are a false signal of increased future demand for consumption.

The Fed’s injection of new money will lead to relative price changes which will in turn signal, falsely, that new investment in the direction of the higher prices is warranted.  Macroeconomics usually focuses on the amount of the new money and its affect on the overall price level, but Austrian theory focuses on the point of entry of the new money and its subsequent movement through the economy and the affect this has on relative prices.

Unlike the intertemporal capital changes brought on and made possible by societal time preference changes, which are complementary and sustainable, the changes brought on by money and credit creation is not.  Money, the facilitator and numeraire, is the loose joint in the indirect exchange economy and a change in its supply not due to market forces sets in motion disequilibrating forces.

Austrian business cycle theory (ABCT) sees money and credit as the trigger and mechanism of propagation of the business cycle since newly created money and credit create the relative price changes which are the false investment signals which lead to malinvestment.

The boom phase of the cycle is characterized by lower IRs not corresponding to increased time preferences.  The supply of loanable funds is equal to savings + new funds created by the Fed.  This new money enters the system through the credit markets.

The Fed has three tools to influence the supply of money and credit and hence interest rates:  1) setting the reserve ratio for commercial banks, 2) setting the discount rate for Fed lending, and 3) Fed open market operations where the Fed borrows from the government by buying Treasury securities.

All three of these tools allow the Fed to lend newly created money and to put downward pressure on IRs.

Policy induced, as opposed to preference induced, booms utilize newly created credit in place of savings.  New credit, like increased savings, puts downward pressure on IRs, but the natural rate and the market rate will diverge.

Savings and investment move in opposite directions due to the lowered IRs during the credit expansion.  Savings decrease while consumption increases.  The simultaneous increase in investment and consumption cause the PPF to shift outward to an unsustainable level.

The money and credit creation allows the decisions of consumers/savers and borrowers/investors to be out of sync for a while.  This conflict causes overproduction of both consumer and capital goods during this period.

At first, increased investment spending is of a greater magnitude than consumer spending because of the easy credit.  But the credit expansion leads to both more long term projects and more consumer spending.  The boom consists of malinvestment and over consumption.  Described geometrically, the Hayekian triangle has two simultaneous hypotenuses with different slopes.

The lack of real savings causes the boom to be unsustainable.  IRs increase as resource prices are bid up.  Investment in the earlier stages of production eventually leads to price increases of complementary goods in later stages.

Projects which are now seen to be unprofitable are abandoned and incomes and employment decrease.  This causes a reversion to the original PPF, but to a different point.  The new point has a higher level of investment and a lower level of consumption than before the boom.  This is because the capital structure has been lengthened by the credit expansion.  The new C and I mix on the PPF is not sustainable.  Malinvestment, rather than simply over investment, occurred.

The newly lengthened production structure cannot be sustained by society’s saving and consumption patterns.  The long term and specific nature of the new capital investments is not conducive to a quick restructuring.

As incomes and consumption decrease, the economy moves inside the original PPF.  The bust phase increases risk aversion and increases liquidity preference, causing a second deflationary force to act on the economy.

Ron Unz’s “China’s Rise, America’s Fall”

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The American Conservative recently ran an article by Ron Unz which is a response to Acemoglu and Robinson’s “Why Nations Fail”, which argues that China’s growth will falter and America’s will resume because of the corrupt, “extractive”, one party rule in China versus the open, democratic rule of the benign American bureaucratic State.

Criticism of the American system of government-big business-bank partnership, in other times and places called fascism, has for too long been the exclusive domain of leftists, with soi disant conservative publications mocking any criticism of the corrupt symbiosis of government and the corporate world, especially “conservative” corporate sectors like weapons manufacturers and private prison operators.  Defense.  Law and order.  Those are conservative values, right?  Who other than a liberal would be against them?  So it is good to see a magazine with the word “conservative” in its title actually criticize our corporate welfare state.

Unz documents the rapid growth of the Chinese economy against the stagnant American median incomes of the last 40 years, and lists several areas where the Chinese have surpassed American business.  Despite this, China’s rise does not need to be seen as a threat since the global standard of living is increased by Chinese production.

Of course, China has its share of corruption and social problems with such a quick ascent, but this is a lot easier to take when real per capita income has risen by over 1,300 percent in 30 years.  The stagnant American worker seems much more resentful of his elites.

While China’s masses are benefiting from this progress, the United States is becoming more unequal, with the top one percent controlling about as much wealth as the bottom 95 percent.  The Chinese and American Gini coefficients are about equal now, and moving in opposite directions.  Thirty five percent of the last few years’ economic recovery in America has gone to the top .01 percent.  The government-corporate partnership funnels money upward.

The central message of the article is this:

“…although American micro-corruption is rare, we seem to suffer from appalling levels of macro-corruption, situations in which our various ruling elites squander or misappropriate tens or even hundreds of billions of dollars of our national wealth, sometimes doing so just barely on one side of technical legality and sometimes on the other.

Sweden is among the cleanest societies in Europe, while Sicily is perhaps the most corrupt. But suppose a large clan of ruthless Sicilian Mafiosi moved to Sweden and somehow managed to gain control of its government. On a day-to-day basis, little would change, with Swedish traffic policemen and building inspectors performing their duties with the same sort of incorruptible efficiency as before, and I suspect that Sweden’s Transparency International rankings would scarcely decline. But meanwhile, a large fraction of Sweden’s accumulated national wealth might gradually be stolen and transferred to secret Cayman Islands bank accounts, or invested in Latin American drug cartels, and eventually the entire plundered economy would collapse.

Ordinary Americans who work hard and seek to earn an honest living for themselves and their families appear to be suffering the ill effects of exactly this same sort of elite-driven economic pillage. The roots of our national decline will be found at the very top of our society, among the One Percent, or more likely the 0.1 percent.”