Archive for November, 2012

Regression and Volatility-Based 1-Yr Apple Price Projections

Sunday, November 4th, 2012

Apple is in a bearish condition at the moment, with swirling questions about its management changes, product roll-outs, and competition, as well as the 2012 Christmas shopping season.  There is also the possibility that some of the current selling pressure may be due to an extra level of year-end selling due to upper income investors deciding to realize profits before the increased gains taxation expected in 2013.

This post looks at three perspectives on the future price of Apple (AAPL) out a year, based on price projections from historical charts using (a) regression trendlines and volatility-based price probability ranges, and simple trendlines drawn from recent tops and bottoms, (b) analyst 1-year target prices, and (c) price level probabilities based on options implied volatility for two contracts with expiration dates that straddle the 12-months ahead ending in November 2013.

The historical data by definition is backward looking, and is used in the statistical regression extensions and volatility-base price probability range to guesstimate the future assuming a continuation of past price behavior.  The options data is forward looking by traders placing their capital at risk now based on their assumptions about the future.

It is important to keep in mind that the options implied outcomes are likely to change more, and more frequently, than statistical projections based on historical data, and probably more than average analyst price targets. Options data does however reflect what people who are risking their capital believe about the future, whereas analysts may not be risking capital; and historical data incorporates less and less of an anticipation of the present situation and current future assessment as we go back in time.  We think it is a good idea to be aware of all three perspectives.

Figure 1 shows the history driven November 2013 projections (plus the average analyst projection), while Figure 2 shows the probability of those history driven projections being achieved sometime during the life of two options expiration dates (July 2013 and January 2014) that straddle the November 2013 year ahead projection

The average analyst 1-year target price of 56 analysts at 767 is almost 33% above the current market price.  The highest analyst 1-year target is 1,114  and the lowest analyst target is 271.

Figure 1:

The options volatility implied probability of each of the price levels cited in Figure 1 being touched sometime during the life of the option contract is shown in Figure 2.

There is no November 2013 options contract for Apple, so we can’t get an exact view of traders perspectives of the history-based projections. However visual interpolation suggests that the two option contracts that straddle November 2013 give the average analyst 1-year target price having about a 1 in 3 chance of being achieved.

Figure 2:

The probabilities in Figure 3 are for the price of Apple achieving prices at 5% increments from the current market price during the lifetime of the July 2013 and January 2014 options contracts.

Figure 3:

Disclosure: QVM has positions in AAPL as of the creation date of this post.


Regression and Volatility-Based 1-Yr GLD Price Projections

Saturday, November 3rd, 2012

The 1-year outlook for GLD (a gold bullion ETF) based on linear regression projections and volatility-based 96% price probability ranges, sees a spread of price possibilities from a high of about $204 to a low of about $134.  That relates generally to gold bullion prices of about $2,040 to $1,340.

One additional point would be based on a market disruption similar to the one in 2008 due to the fiscal cliff being bungled, or some other equally nasty macro event.  GLD declined 30% from its peak to its 2008 low.  A 30% decline from the 2011 high for GLD would bring the price down to about $125.

Note: Figure 1 below uses historical data, while Figures 2 and 3 use options derived data.  The historical data by definition is based on what has actually been happening with the security, and the projections assume more of the same. The options data is based on what traders think is going to happen, which is a forward looking view, and which tends to change more day-to-day than the projections based on historical data.

Figure 1:

Figure 1 uses historical price data and plots the linear regression trend lines and the volatility-based 96% probability price ranges for GLD.

The linear regression lines were plotted from (a) the fund’s inception in 2004, (b) the low in 2009, and (c) the high in 2011.

The price probability ranges were plotted using a 96% probability based on 252-day (1-year) and 63-day (3-month) historical price volatility.

The “96% probability” (for data points B, C, F and G) refers to the price falling within the upper and lower bounds of the probability cone, not the probability of the bounds being reached.

Overall the extremes of these statistical projections has a +/- price change from the current market price of about + 25% and about -23%.

The long-term trend lines are obviously up, and the intermediate-term trend line is moderately down, presumably due to concerns about possible recession in 2013 over the fiscal cliff, but that is just supposition.

Options Related GLD Price Levels at Various Dates and Volatility Levels:

Using options data from OptionsExpress, Figure 2 shows the prices that are  1, 2, and 3 standard deviations away from the current market price for GLD for these contract expiration dates; March 2013, June 2013, September 2013 and January 2014.  The upper matrix shows the prices at the standard deviation levels.  The lower matrix shows the percentage change in the price of GLD required to achieve the prices at each standard deviation level.

Figure 2:

The $204 November 2013 regression projection from the 2009 bottom (Figure 1 : A) falls between the 1 and 2 standard deviation price levels for the September 2013 and January 2014 options contracts.

The $182 November 2013 regression projection from the inception of the fund (Figure 1: D) lies below the 1 standard deviation price levels for the September 2013 and January 2014 options contracts.

The $197 and $188 November 2013 upper projections based on 1-year and 3-month historical volatility (Figure 1: B and C) lie between those two regression projections (Figure 1: A and D).

The $156 November 2013 regression projection from 2011 high (Figure 1: E) falls significantly below the 1 standard deviation price levels for the September 2013 and January 2014 options contracts.

The $141  November 2013 lower projection based on 3-month historical volatility (Figure 1: F) lies very close to the 1 standard deviation price level for the September 2013 and January 2014 options contracts.

The $134  November 2013 lower projection based on 1-year historical volatility (Figure 1: G) lies between the 1 and 2 standard deviation price levels for the September 2013 and January 2014 options contracts, but closer to the 1 standard deviation level.

The $125 30% offset from the 2011 high (Figure 1: H) lies essentially on the 2 standard deviation level for the September 2013 options contract, and between the 1 and 2 standard deviation level for the January 2014 contract.

Options-Based Probability of Price Levels For Various Contract Expiration Dates:

Figure 3 shows the probability of the price of GLD touching the indicated levels sometime during the life of the options contract for the contracts expiring in March 2013, June 2013, September 2013 and January 2014.  The probabilities are based on the volatility implied by those options contracts at this time.  The upper matrix shows touch probabilities for prices at $10 increments.  The bottom matrix shows the touch probabilities for prices from the A-H indicators in Figure 1.

Figure 3:


Disclosure:  QVM has some long positions in GLD and sells covered Calls and cash secured Puts on GLD.

Exploring Relationship: Currency In Circulation, Treasury Gold Holdings and Gold Price

Friday, November 2nd, 2012

Some investors believe that gold is the “real” money (and some believe that is nonsense).  Some of those who believe it is real money express that belief in terms of currency debasement through an ever expanding quantity of currency in circulation.

Their argument is that the wealth of a nation at any moment is a fixed value, and that by merely printing more fiat currency (paper money declared by government to be legal tender with no asset backing required), the currency is worth less and less and gold worth more and more — Weimar Republic hyperinflation and Zimbabwe hyperinflation being the extremes of that.

Historical Narrative Perspective:

In 1900 the U.S. Dollar became convertible and redeemable into gold for any holder, both citizens and foreign governments.  During 1933, the Dollar was made convertible into gold only by foreign governments, not U.S. citizens.  In 1971, the U.S. Dollar was made not convertible into gold by any party.

Here is how it is explained by the Richmond Federal Reserve Bank.

“March 14, 1900 – The Gold Standard Act officially placed the United States on the gold standard…. H.J. Res. 192, approved by President Roosevelt on June 5, 1933, provided that obligations payable in gold or specific coin or currency are contrary to public policy, and that those obligations could be discharged dollar for dollar in legal tender. After that resolution was adopted, currency of the United States could not be converted into gold by United States citizens, but the Treasury would convert dollars into gold for foreign governments as a means of maintaining stability and confidence in the dollar. Because the dollar was no longer freely convertible, one could consider that the United States was no longer on the gold standard at that time. If, however, one considers the gold standard as a monetary system in which the unit of money is backed by gold even if the monetary unit cannot be converted into gold, one could argue that the United States went off of the gold standard on August 15, 1971 when President Nixon announced that the U.S. dollar would no longer be convertible into gold in the international markets. The President was able to suspend the ability to convert the dollar into gold because there was no legal requirement that the United States exchange gold for dollars.

 … when the United States stopped selling gold to foreign official holders of dollars at the rate of $35 an ounce in 1971, it brought the gold exchange standard to an end. In 1973, the United States officially ended its adherence to the gold standard. Many other industrialized nations also switched from a system of fixed exchange rates to a system of floating rates. In August 1974, President Ford repealed the prohibition on the public’s owning gold or engaging in gold transactions. Today, no country bans private ownership of gold.”

Prior to 1968, the U.S. was committed to maintain 25% gold reserves versus the conversion privileges of the paper currency.  There is no such requirement today.

Beginning and Ending Data:

According to the US Treasury’s “US International Reserve Position” the 10/12/2012 US gold hoard is 261,497,506 ounces.  According to the Federal Reserve Bank, the September 1, 2012 quantity of  U.S. currency in circulation is $1.064 Trillion. The price of gold on September 1 was $1,692.  The ratio of currency in circulation per ounce of gold held by the U.S. based on this data was $4,079 (let’s term that the “conversion ratio”).  We should point out that the European Union has nearly the same conversion ratio.  Japan, however, has a much higher conversion ratio (indicating a greater currency debasement on their part than in the U.S. and in Europe).

For contrast, they reported the a July 199 gold holdings slightly greater than now at 261,615,927 ounces, and a quantity of currency in circulation of $0.488 Trillion.  The price of gold back then was $258 per ounce. The conversion ratio then was $1,864.

Currency In Circulation Changes:

From 1969 through now, the average annual rate of change of currency in circulation was 6.98%.  Figure 1 shows that data, with more significant variation since about 1990.  Figure 2 presents the same data for the shorter period from 2000, since which the average annual currency expansion has been 6.28%

Figure 1: Long-Term Rate of Change Of USD In Circulation

Figure 2: Intermediate-Term Rate of Change of USD In Circulation

Indexed Currency In Circulation vs. Indexed Gold Price:

Starting in July 1999, we indexed the amount of currency in circulation and the price of gold to see what that might reveal.  The gold price really took off after 2003 (which happened to be the bottom in the stock market).

Figure 3: Indexed Change in M0 (M Zero) vs Indexed Gold Price

M0 (M zero) is the letter designation for total currency in circulation.

Gold Price vs. Conversion Ratio:

The price of gold and the conversion ratio seem to move in parallel as shown in Figure 4, but by starting at different base levels had quite different growth patterns (as shown in Figure 3).

Figure 5 shows the spread between the price of gold and the conversion ratio.  Interestingly, the spread has been roughly steady with an average spread of $2,221. The spread went above the average in 2008 when gold declined 30%, and above the average when gold surged during the stock market recovery, now is closer to average.  If the average persists, the current price of gold might be expected to be about $1,860.

Figure 4: Actual Gold Price vs USD Currency/Treasury Gold Holdings

Figure 5: Gold Price and Conversion Ratio Spread

According to the “gold is real money” advocates, there should be some kind of long-term relationship between the price of gold and the conversion ratio [ remember, the conversion ratio shows the price of Treasury gold per ounce that under a hypothetical full conversion regime would result in no outstanding fiat currency and no gold in the Treasury ].  From that perspective, how then could the  gold price vary so much versus the conversion ratio from 1999 to now, given there was plenty of time between 1971 and 1999 for the gold market price to adjust to the fiat currency world regime?

If the real money theory holds water (and it may or may not be adequate as a single variable to explain gold price movement over the long-term), the likely explanation would be that ebbing and flowing of investor interest and trust in the stock market and government, and fears of deflation or inflation, and exchange rates the put the Dollar higher and lower at times; all added layers of upward and downward pressure on gold, causing it to fluctuate around a more central value based on the concept of gold being real money that in the end would be based on how much gold was potentially behind it.

Other Factors Potentially Better Related To Gold Price:

We think there should be some metric or some set of metrics that can be tracked to help establish when gold is overvalued or undervalued.  Fiat currency per ounce of central bank gold is the most logical fist suspect since that is actually the way it was under the legal system as one time in the past.

There may be others, and we are looking for them.  Our prior blog post did an historical chart review of the relationship between the price of gold and several other assets and did not find any essentially better metric.  That doesn’t make the conversion ratio a good or the best metric, but it doesn’t knock it out of consideration either.

Perhaps there is a polynomial metric that we will find with further research, but pending that we are inclined to think that, all other things being constant (which they seldom are), gold is likely to find a current center around $1,860, advance at least 6% per year as the currency base appears likely to do, and perhaps break with its multi-year spread behavior and approach $4,000 per ounce to reach the conversion ratio. Then again it could drop into bear market territory under recession/deflation conditions.

As time goes by and the likely 6% currency expansion continues, the $1,860 center and the $4,000 price potential would probably increase proportionately.

Gold could, of course go well beyond the currency growth adjusted $4,000, but the rationale would need to be established to understand it or manage around it (e.g a collapse in the exchange rate of the Dollar, which is the global price base of gold; or currency printing presses gone crazy).

Temporary Gold Price Decline Scenario:

As we have noted in other posts, there is also a realistic chance of gold at least temporarily declining to something like $1,300 if it goes down 30% from its recent peak, as it did in the 2008 market crash.  That possibility arises because (a) gold is in a decline at the moment, and (b) the fiscal cliff has the potential to be market disrupting and deflation fear generating as was the case in 2008.

Figure 6: Current Daily Chart For GLD (gold ETF) for 1 Year:

The leading physical gold fund is GLD.  For who do not own bullion directly or do not traded in gold futures, this fund is a popular alternative.  Other physical gold ETFs are IAU, SGOL and AGOL, but GLD is the largest and most liquid, with liquid stock options available.

The dashed gold line is the 200-day average.  The pink shaded area is the 3-month price channel.  The green shaded area is the 1-month price channel.

Figure 7: Weekly GLD Prices Since Inception

Figure 8: Daily Price Ratio of GLD to Gold

The ratio of the prices of GLD and gold are not constant, although GLD trades in the vicinity of 1/10th the price of gold.  The daily fluctuations in the ratio, represent the inefficiencies in the arbitrage process that is intended to keep the price and the NAV close.  The gradual decline in the ratio probably represents the drag effect of fund expenses.

Figure 9:  GLD and GOLD Plotted Side-by-Side:

The price ratio might give a more severe interpretation of the price relationship than this chart, which plots GLD and gold prices on the same chart.  The gold price scale is on the left, and the GLD price scale is on the right.  The plots are minimally different and virtually on top of each other.

Disclosure: We have positions in GLD and positions in Puts and Calls relating to GLD.




Graphical View Of Long-Term Relationship Between Gold and Other Assets

Friday, November 2nd, 2012

There is a substantial debate about what asset, if any, gold price relates to or responds to.  We think its price is more responsive to perceived changes in its monetary alternative potential than to changes in its jewelry or industrial demand (including that a significant portion of the jewellery demand in some countries is as much a form of investment as decoration).

We think the most logical factor in its price as a form of money would be the ratio of the currency in circulation versus the amount of gold that could be associated with that currency (most probably, the amount of currency in circulation for the dominant currencies versus the amount of gold held in the central banks that issue those dominant currencies).

We have heard some strong opinions to the contrary ranging from that is no basis for gauging the value of gold because it just is what it is — as one gold dealer said “price doesn’t matter”; its a “philosophy” and an “insurance policy against government foolishness”.  Of course, that logic goes nowhere toward establishing a current value, but perhaps some other assets other than currency in circulation could be used to explain gold price behavior, and therefore provide some gauge of over and under valuation in the market price.

Price and value are not the same thing, but as investors it is helpful to strive to tell the difference.

Our Preferred Gold Valuation Metric:

We like the ratio of the currency in circulation in the United States and Europe to the gold held in their combined central banks.  That number is around $4,000; and would grow as the issued paper money increases, assuming no increase in the gold held by the central banks.

That $4,000 round number comes from summing the US dollar equivalent of all Dollar and Euro currency in circulation ($2.64 Trillion) and dividing it by the sum of the gold held by the US and European Monetary Union central banks (667.4 million ounces), which comes out to be $3,955 per ounce.

In other words, if there were ever a return to full convertibility to gold, that is the price at which all currency if converted would cause the payout of all central bank gold holdings.  We don’t think convertibility will return, but so long as central banks continue to hold gold, they keep the concept of potential convertibility alive, and as long as a large number of gold buyers think gold is a “real money” alternative to fiat currency, this convertibility calculation has some bearing on the current investment value of gold at any time.

We should also note that if another major market problem like that in 2008 should arise (say in the next few months if the fiscal cliff issue is bungled), gold could drop as much as it did in 2008.  That drop was 30%.  If you take 30% off of the most recent high for gold, you get $1,300. That is plausible, not probable, and would likely be temporary, but it could happen.

Other Investments Versus Gold:

You may disagree and you may  feel that other assets are better correlates or value drivers, so we put together this batch of charts that show gold versus various other investments on an indexed basis that may help you think through which, if any, you find to be a good yardstick to help you know when gold is priced too high or too low versus some sense of value.

The data is either from the US Federal Reserve or from  Data is from 1969 for most of the Federal Reserve charts and for 20 years for most of the charts from StockCharts.  In each case we present the data on an indexed basis so the relative change in each plot is more easily discernible.

The comparisons may be interesting if nothing else.

Gold vs. US Currency In Circulation

Gold vs. M0 (currency), M1 and M2

Gold vs. US Federal Debt

Gold vs. Combined Federal, State and Local Debt

Gold vs. Federal, State and Local Debt, Plus Household Debt

Gold vs. GDP

Gold vs. Cost of Living (as measured by “all items” CPI)

Gold vs. US Stocks (S&P 500)

Gold vs. US Dollar Index


Gold vs. West Texas Crude Oil

Gold vs. Copper

Gold vs. Silver

Gold vs. Corn and Soybeans

Gold Versus 10-Year Treasury Yield

Gold vs. Dow Jones AIG Commodity Index (includes gold)

Directly Related Gold ETFs:  GLD, IAU, SGOL, IAU