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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Research note / markets and cycles

Study of Financial Cycles

A 2011 note on short mood swings, 30 year and 60 year cycles, the end of the bond bull market and the case for gold.

Written around 2011Stocks and bondsGold

It has occurred to me that financial time series are far from simple random walks, even with fat tails. Financial markets exhibit cycles. My focus is on stocks, bonds and inflation, with gold as the inflation hedge. Two cycles are particularly interesting.

Mood swing cycles

These are short cycles that run for 2 to 5 years. The word quadrennial approximately describes them. They appear in sentiment, valuation and the rhythm of policy response.

Long run cycles

There appear to be two major long run cycles of about 30 years and 60 years. The longer cycle is visible in the relationship between stocks, bonds and gold. At the time of writing I had only random thoughts and articles, not a finished model.

Note on datingThis essay was written around 2011. The forecasts and market references below belong to that period. They are not updated claims about the present.

Overvalued stocks

Robert Shiller and Jeremy Grantham of GMO argued that the stock market was overvalued. My take in 2011 was that the correction that began in 2000 had to run into the middle of the 2010s. The fat tailed data in the data atlas makes such long adjustments easier to accept than a smooth random walk would.

Bonds ran out of steam

Bill Gross argued that the 30 year bull market in bonds was approaching its end as of 2011. A 30 year rate cycle is long enough to look permanent to one generation of investors.

A case for gold

When both stocks and bonds are out of favor in a decennial assessment, gold is the remaining major asset class. The case was obvious after the 2008 financial crisis damaged the balance sheets of major governments. The decade of the 2010s looked like a decade of inflation. The US government would not defend inflation while Treasury interest rates were low. It could let inflation reduce the debt burden and the overvalued stock and home prices.

How high could gold go? My assessment was $5,000 to $10,000 per ounce. One day in the following years, I expected the SPDR Gold ETF to become one of the largest ETFs, with a $500 billion cap. That would be a signal that gold's time was up.

Many people compare gold and the Dow over the last 110 years and conclude that gold is inferior. That is generally correct for a century of buy and hold. Most people, including professionals, rarely hold an investment for more than 3 to 5 years. Gold is the last resort safe haven of money, and it exhibits very long and simple cycles. From 1972 to 1980, gold rose from $43 to above $600, with a peak at $843 on January 21, 1980. A 15 fold appreciation is not inferior to the Dow bull market from 1950 to 1966 or from 1980 to 2000.

Gold stayed around $400 in the 1980s and 1990s and dropped to $250 in 2001. It then took off in a decennial rally to above $1,000 in 2010. Once gold broke its previous high of $800 in 1980, I expected it to move to the next level. That indicated a range of $5,000 to $10,000 within another 6 to 10 years. At the high end, the US government would be in better shape again.

The same scaling discussion appears in the N^3/2 law note. The distribution can also be explored in the simulator. The link between random growth and long cycles is set out in the Double Pareto note.

Source shelf

Data and further reading

11 entries
  1. Robert Shiller dataLong run US stock market data from Yale.
  2. GMO research libraryResearch and market commentary from GMO.
  3. World Gold Council researchResearch on gold as a financial asset.
  4. Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
  5. Bank for International SettlementsStatistics and research on global financial markets.
  6. IMF dataInternational financial and economic data.
  7. Lihn 2008 on SSRNThe 2008 working paper on the scale invariant Brownian motion model.
  8. Lihn 2009 on SSRNThe working paper on higher order lognormal cascade distributions.
  9. Fernholz 2002Stochastic portfolio theory and the diversity index.
  10. Gold standardHistorical background on the gold standard.
  11. US TreasuryDaily Treasury yield curve and interest rate data.