Polar Star Quantitative Commodity Fund

Dr Mauritz van den Worm, PhD

30 March, 2020

Overview

Outline

  • Portfolio manager background
  • Cyclic nature of commodity markets
  • Long term drivers of commodity prices
  • Philosophy of taking many small bets
  • The core strategies
  • Portfolio

Portfolio Manager Background

Education

  • PhD in Quantum Physics from Stellenbosch University - 2015

  • Thesis: Dynamics of Long-Range Quantum Spin Systems

  • Applications:

    • Rapid information transfer in quantum systems
    • Spreading of correlations in quantum systems
    • Theory of trapped ion quantum simulators
    • Wishlist: Development of quantum computers

Most Cited Peer Reviewed Fundamental Research

Citation History

Coauthor Network

Time at Polar Star

Cyclic Nature of Commodity Markets

Corn Life Cycle

Corn Calendar Spread Example

Lean Hog Calendar Spread Example

RBOB Gasoline Curve Example

Deliverable Wheat

Long Term Drivers of Commodity Markets

Curve Structure - Contango

Curve Structure - Backwardation

How the Curve Structure Affects Prices (1/4)

How the Curve Structure Affects Prices (2/4)

How the Curve Structure Affects Prices (3/4)

How the Curve Structure Affects Prices (4/4)

Backwardation and Annualised Return

Using the Curve in your favour

  • Each commodity has a different curve structure
  • You can think of the curve structure as a tide
  • It is much easier to swim with the tide than against it
  • For many commodities the curve structure has cyclical behaviour
  • Using Curve Carry we try to exploit this
  • Using the curve structure in a trend strategy helps in entering profitable long term trades

Philosophy of Taking Many Small Bets

Fundamental Law of Portfolio Management

\[ \large \text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}} \]

  • Skill measures your ability to find profitable opportunities
  • Breadth captures how many opportunities you have available

Coin Flipping Casino (1/5)

  • We know the coin is biased with \(P(\text{heads}) = 0.51\)
  • We have 1000 coins
  • The minimum wager is 1 coin
  • If you win you gain 1 coin
  • If you loose you loose 1 coin
  • There are 1000 tables with coin wagers

Coin Flipping Casino (2/5)

How do we place the bets?

Two extremes:

  • Bet 1000 coins on one coin flip
  • Bet 1 coin on 1000 coin flips

Coin Flipping Casino (3/5)

The same expected return:

  • Single bet: \(0.51 \times 1000 + 0.49 \times (-1000) = 20\)
  • Multi bet: \(1000 \times [0.51 + 0.49 \times (-1)] = 20\)

Totally different risk to loose it all:

  • Single bet: 49%
  • Multi bet: \(0.49 \times 0.49 \times \dots \times 0.49 = 0.49^{1000} \approx 0\)

Coin Flipping Casino (4/5)

Another way to look at risk is to use standard deviation of returns

  • Multi bet:

\[ \text{risk} := \text{std}\left\{1,-1,-1,1, \dots, 1 \right\} = 1 \]

  • Single bet:

\[ \begin{align} \text{risk} &:= \text{std}\left\{1000,0,0,0, \dots, 0 \right\} = 31.62 \\ \text{risk} &:= \text{std}\left\{-1000,0,0,0, \dots, 0 \right\} = 31.62 \end{align} \]

Coin Flipping Casino (5/5)

Risk Adjusted Returns (Sharpe Ratio):

  • Single bet: \(\text{SR}_{\text{single}} = \frac{20}{31.62} =0.63\)
  • Multi bet: \(\text{SR}_{\text{multiple}} = \frac{20}{1} =20\)

We rewrite the risk adjusted return as:

  • \(20 = 0.63 \times \sqrt{1000}\)
  • \(\text{SR}_{\text{multiple}} = \text{SR}_{\text{single}} \times \sqrt{\text{Bets}}\)
  • \(\text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}}\)

Law of Large Numbers and Long Term Horizons

Three Pillars of Diversification

  1. What you trade
    • Different commodities
    • Different calendar spreads
    • Different parts of the curve
  2. How you trade
    • Trend
    • Curve Carry
  3. When you trade
    • Different signals
    • Different times of the year
    • Roll methodology and timing

All of these add to the breadth of opportunities.

View of Current Book

Core Strategies

Curve Carry (1/n)

Aim of the strategy:

  • Harness the curve carry
  • Storable commodities have predictable cuve structure
  • Higher stock levels are associated with contango curves
  • Many commodities evolve into a contango as the front nears expiry

We define \(p\) as the ratio of the Front to the Deferred price \[ p := \text{Front}/\text{Deferred} \]

  • When \(p\) < 1 the Front is trading at a discount to the Deferred.
  • The smaller \(p\) the greater the contango

Curve Carry (2/n)

Curve Carry (3/n)

Curve Carry (4/n)

Curve Carry (5/n)

Curve Carry (6/n)

  1. From a fundamental point of view we

    • Identify commodity calendar spread pairs
    • With predictable behaviour during certain parts of the year
  2. For every month of the year we have a list of

    • Commodities,
    • Associated calendar spread we want to be involved with and
    • The side of the trade
  3. ML Technique to determine probability of the spread ending in the money

  4. Size positions according to the

    • Volatility and
    • Probability of profit
    • Lower volatility receives a higher allocation

Curve Carry (7/n)

Curve Carry - Risk and Return Statistics (8/n)

Risk/Reward Statistics
Sharpe Ratio 1.16
Sortino Ratio 2.04
Omega Ratio 1.56
Skewness 0.61
Kurtosis 2.50
Risk Statistics
Annualized Std.Deviation 17.70
Maximum Drawdown 27.81
Month to Recover 23.00
Worst Month -14.23
Losing Months (%) 37.45
Average Losing Month -2.91
Loss Deviation 2.90
Return Statistics
Last Month 3.35
Year To Date 13.33
3 Month ROR 13.33
12 Month ROR 14.65
36 Month ROR 73.80
Total Return 4291.44
Compound ROR 20.54
Best Month 20.74
Winning Months (%) 62.55

Curve Carry - Time Windown Report (9/n)

Time Window Analysis:

1 Month 3 Month 6 Month 1 Year 2 Year 3 Year 5 Year
Best 20.74 42.58 96.52 153.25 268.48 450.79 754.88
Worst -14.23 -27.81 -19.57 -24.12 -10.67 -5.15 10.39
Average 1.69 5.17 10.73 23.88 59.19 107.30 263.66
Median 1.11 3.82 8.42 16.86 37.87 58.54 136.32
Last 3.35 13.33 12.92 14.65 35.91 73.80 88.74
Winning (%) 62.55 73.03 81.09 86.21 87.27 99.52 100.00
Avg. Pos. Period 4.45 8.69 14.81 29.31 68.31 107.85 263.66
Avg. Neg. Period -2.91 -4.34 -6.81 -10.11 -3.33 -5.15 NaN
# Of Periods 243.00 241.00 238.00 232.00 220.00 208.00 184.00

Drawdown Report:

Depth (%) Length (Months) Recovery (Months) Start End
-27.81 23 20 2014-01-31 2015-11-30
-24.31 23 19 2003-08-29 2005-06-30
-15.75 27 18 2000-06-30 2002-08-30
-9.83 3 2 2007-07-31 2007-09-28
-9.38 7 3 2013-06-28 2013-12-31

Trend Following (1/n)

Aim of the strategy:

  • Trade medium to long term commodity trends profitably
  • Lookback windows ranging from a couple of weeks to one year
  • Breakout, Donchain and Exponential Moving averge signals
  • Target volatility 20%
  • Diverse universe of commodities
  • Multiple parts of the futures curves
  • Roll structure created from fundamental understanding

Essence: Cap your losses and let the winners run

Trend Following (2/n)

Build the strategy on fake data:

  • Create data with trends
  • See if we can trade it profitably
  • Investigate price behaviour that cannot be traded profitably

Why is this preferred:

  • No overfitting of the underlying market data
  • Datamined lookbacks and models perform great in sample
  • Majestic performance is difficult to follow up on new data

Trend Following (3/n)

Trend Following (4/n)

Trend Following (5/n)

Trend Following (6/n)

Trend Following - Risk and Return Statistics (7/n)

Risk/Reward Statistics
Sharpe Ratio 1.07
Sortino Ratio 2.12
Omega Ratio 1.43
Skewness 1.14
Kurtosis 6.27
Risk Statistics
Annualized Std.Deviation 21.13
Maximum Drawdown 34.99
Month to Recover 42.00
Worst Month -21.87
Losing Months (%) 39.63
Average Losing Month -3.33
Loss Deviation 3.09
Return Statistics
Last Month 4.88
Year To Date 9.13
3 Month ROR 9.13
12 Month ROR 2.46
36 Month ROR 2.14
Total Return 432495.07
Compound ROR 22.65
Best Month 44.67
Winning Months (%) 59.96

Trend Following - Time Windown Report (8/n)

Time Window Analysis:

1 Month 3 Month 6 Month 1 Year 2 Year 3 Year 5 Year
Best 44.67 88.63 114.33 142.94 238.83 341.48 643.48
Worst -21.87 -17.48 -19.76 -21.19 -30.54 -27.88 -5.06
Average 1.89 5.78 12.02 25.94 59.54 101.99 215.38
Median 1.19 4.31 8.83 21.68 52.27 96.27 217.82
Last 4.88 9.13 7.17 2.46 -0.61 2.14 -4.06
Winning (%) 59.96 67.55 75.56 82.74 89.55 92.34 98.61
Avg. Pos. Period 5.36 10.88 17.97 32.93 67.76 111.36 218.45
Avg. Neg. Period -3.33 -4.84 -6.39 -7.55 -10.91 -10.95 -3.27
# Of Periods 492.00 490.00 487.00 481.00 469.00 457.00 433.00

Drawdown Report:

Depth (%) Length (Months) Recovery (Months) Start End
-34.99 42 9 2011-03-31 2014-08-29
-25.58 50 NA 2016-03-31 NA
-21.87 7 6 1980-12-31 1981-06-30
-17.83 16 4 2004-08-31 2005-11-30
-16.15 7 1 2008-03-31 2008-09-30

Why Curve Carry and Trend Following? (1/n)

Why Curve Carry and Trend Following? (2/n)

Why Curve Carry and Trend Following? (3/n)

Why Curve Carry and Trend Following? (4/n)

Portfolio

Portfolio View

Portfolio View - Risk and Return Statistics

Risk/Reward Statistics
Sharpe Ratio 1.09
Sortino Ratio 2.19
Omega Ratio 1.39
Skewness 0.74
Kurtosis 2.52
Risk Statistics
Annualized Std.Deviation 15.03
Maximum Drawdown 19.62
Month to Recover 15.00
Worst Month -9.75
Losing Months (%) 40.08
Average Losing Month -2.45
Loss Deviation 2.17
Return Statistics
Last Month 5.38
Year To Date 14.99
3 Month ROR 14.99
12 Month ROR 13.65
36 Month ROR 43.38
Total Return 2048.96
Compound ROR 16.43
Best Month 20.01
Winning Months (%) 59.92

Portfolio View - Time Windown Report

Time Window Analysis:

1 Month 3 Month 6 Month 1 Year 2 Year 3 Year 5 Year
Best 20.01 46.51 81.33 100.70 165.95 296.47 438.92
Worst -9.75 -18.29 -13.78 -16.37 -7.71 9.41 23.01
Average 1.37 4.10 8.31 17.77 41.26 71.46 162.49
Median 0.83 3.13 5.71 13.65 25.89 35.89 96.92
Last 5.38 14.99 14.19 13.65 20.08 43.38 46.22
Winning (%) 59.92 70.00 81.86 87.45 98.63 100.00 100.00
Avg. Pos. Period 3.92 7.27 11.10 21.02 41.89 71.46 162.49
Avg. Neg. Period -2.45 -3.29 -4.29 -4.82 -4.46 NaN NaN
# Of Periods 242.00 240.00 237.00 231.00 219.00 207.00 183.00

Drawdown Report:

Depth (%) Length (Months) Recovery (Months) Start End
-19.62 15 5 2013-06-28 2014-08-29
-17.19 15 11 2003-08-29 2004-10-29
-11.39 5 3 2008-06-30 2008-10-31
-9.75 6 5 2006-06-30 2006-11-30
-9.26 4 2 2010-06-30 2010-09-30

Correlation with Polar Star Limited (1/n)

Correlation with Polar Star Limited (2/n)

Correlation with Polar Star Limited (3/n)

Summary

What we hope to achieve

  • Long term positive returns
  • Exploit fundamental knowledge and curve structure
  • Diversified quantitative commodity product
  • Low correlation to
    • other Polar Star funds,
    • equities and
    • commodity indices

Next meeting: On the stream…