# 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

• Applications:

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

# Long Term Drivers of Commodity Markets

## 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)

• 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:

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

## Three Pillars of Diversification

• Different commodities
• Different parts of the curve
• Trend
• Curve Carry
• Different signals
• Different times of the year
• Roll methodology and timing

# 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 (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 - 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 - 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

# Portfolio

## 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

# 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