Background

A freight forwarder with a fleet of bulk carriers wants to optimize their portfolio in the metals markets with entry into the nickel business and use of the tramp trade. Tramp ships are the company’s “swing” option without any fixed charter or other constraint. They allow the company flexibility in managing several aspects of freight uncertainty. They have allocated $250 million to purchase metals. The company wants us to:

1. Retrieve and begin to analyze data about potential commodities to diversify into
2. Compare potential commodities with existing commodities in conventional metals spot markets
3. Begin to generate economic scenarios based on events that may, or may not, materialize in the commodities
4. The company wants to mitigate their risk by diversifying their cargo loads

Decision

Identify the optimal combination of Nickel, Copper, and Aluminium to trade

1. Product: Metals commodities and freight charters
2. Metal, Company, and Geography:
   1. Nickel: MMC Norilisk, Russia
   2. Copper: Codelco, Chile and MMC Norilisk, Russia
   3. Aluminium: Vale, Brasil and Rio Tinto Alcan, Australia
3. Customers: Ship Owners, manufacturers, traders
4. All metals traded on the London Metal Exchange

Business questions

1. How would the performance of these commodities affect the size and timing of shipping arrangements?
2. How would the value of new shipping arrangements affect the value of our business with our current customers?
3. How would we manage the allocation of existing resources given we have just landed in this new market?

Stylized facts of the Metals market

The London Metal Exchange (LME) is the world’s centre for commodity exchange and the majority of non-ferrous metal is conducted on its’ market.

• In 2016 the LME traded $10.3T USD notional, which included the exchange of 3.5B m/t
• Volatility is rarely constant and often has a structure (mean reversion) and is dependent on the past.
• Past shocks persist and may or may not dampen (rock in a pool).
• Extreme events are likely to happen with other extreme events.
• Negative returns are more likely than positive returns (left skew).

History speaks

• We will develop the value at risk and expected shortfall metrics from the historical simulated distributions of risk factors.

• Given these factors we will combine them into a portfolio and calculate their losses.

• With the loss distribution in hand we can compute the risk measures. - This approach is nonparametric.

• We can then posit high quantile thresholds and explore risk measures the in the tails of the distributions.

First we set the tolerance level \(\alpha\), for example, equal to 95%. This would mean that a decision maker would not tolerate loss in more than \(1-\alpha\), or 5%. of all risk scenarios under consideration.

We define the VaR as the quantile for probability \(\alpha \in (0,1)\), as

\[ VaR_{\alpha} (X) = inf \{ x \in R: F(x) \geq \alpha \}, \]

which means find the greatest lower bound of loss \(x\)(what the symbol \(inf\)= infimum means in English), such that the cumulative probability of \(x\)is greater than or equal to \(\alpha\).

Using the \(VaR_{\alpha}\)definition we can also define \(ES\) as

\[ ES_{\alpha} = E [X \lvert X \geq VaR_{\alpha}], \]

where \(ES\) is “expected shortfall” and \(E\) is the expectation operator, also known as the “mean.” Again, in English, the expected shortfall is the average of all losses greater than the loss at a \(VaR\)associated with probability \(\alpha\), and \(ES \geq VaR\).

Data and analysis to inform the decision

• Spot market prices of nickel, copper, and aluminium
• Nickel and Copper: correlation
• Nickel and Aluminium: correlation
• Copper and Aluminium: Correlation
• Nickel and Copper: Correlation sensitivity to copper dependency
• All together: correlations and volaitlities among these indicators
• Cross-section of rolling correlation will be visualize correlation

Data Definations

• Nickel: daily nickel price ($/per metric ton)
• Copper: daily copper prices ($/per metric ton)
• Aluminium : daily aluminium prices ($/per metric ton)

Metals Price Percent Changes

Initial Analysis of Nickel, Copper, Alluminium

Historical data 2012-2016

• Nickel has experienced a number of spikes in price and magnitude percentage change.
  
• Copper is less volatile in terms of price and magnitude percentage change
• Aluminium experienced some shocks of volatility in 2015 and 2016

Size of metals Price Percent Changes

Nickel.Copper

Nickel.aluminium

Copper.aluminium

Correlation

Skills and Tools

This analysis is carried out using R programming language with the following packages:

• ggplot2
• scales
• quadprog
• quantreg
• flexdashboard
• qrmdata
• xts
• matrixStats
• zoo
• QRM
• psych
• Moment

Data Insights

• Nickel value at risk with an alpa of 0.95 is 2.75 and its expected shortfall is 3.5 based on the historical data
• Copper value at risk with an alpa of 0.95 is 1.87 and its expected shortfall is 2.27 based on the historical data
• Aluminium value at risk with an alpa of 0.95 is 1.96 and its expected shortfall is 2.58 based on the historical data

History & Nature of exchange rates – key concepts:

• non-stationary trend
• volatility clustering
• peakedness & fat tails (kurtosis)
• positive / negative correlation

• persistence over time (ACF/PACF lags)

• There is a strong correlation (0.90) between nickel and aluminium.

• There is a strong correlation (0.88) between nickel and copper due to shared applications.

Business Remarks

• Creation of cupronickel alloy which is used for desalinisation due its high resistant to corrosion, minting, armaments, marine engineering, electrical applications, and many others, e.g. the repair of fan blades found in geothermal power plants.

• Another example would be purchasing Copper from Codelco in Santiago, Chile and tramping it to General Electric, Schnectady, NY as part of GE’s purchasing and procurement wing of their supply chain.

• Aluminium is a metal which is used in a plethora of industries and markets. It’s relatively stable price is testament to this. Moving aluminium from Brasil to West Coast USA for aircraft supply chains is a safe, long term freight line that ship owner’s can use to mitigate risk.

Reference Heavy Metals: Example project from the class syllabus.[FIN 654]