Question 1: Dry Market Hedging
A shipowner operates a 7-year old 172,000 mt dwt capesize vessel. Currently, on 25 July 2013,
the vessel is chartered on a period contract and she will be re-delivered to her owner between
1 and 5 January 2014 in the Far East. The owner is worried about the possibility that the market
may soften when the time comes to fix the vessel and thus he decides to hedge the vessel’s
earnings for the entire calendar year of 2014.
Given the FFA report from Freight Investor Services (FIS) and the freight rates from the
spreadsheets accompanying this coursework (tabs: TC Freight Rates and BFA_BCI_4TC),
identify the FFA contracts that can be used to hedge this exposure and calculate the P&L from
the combined paper and physical cash flows for 2014. You may assume that the rate at which
the vessel is fixed in the physical market is the same as the spot Baltic assessment on that
date. Comment on your findings and on the performance of the hedge.
Question 2: Wet Market hedging
You are a VLCC operator and currently, on 9 September 2011, you have one your vessels fixed
until early January 2012. You are concerned about freight rates softening in 2012, and thus
considering the use of FFAs on BDTI TD3 route to hedge your freight income for the next
calendar year. Given the following FFA rates and the freight rates from the spreadsheets
accompanying the coursework, show how FFA contracts can be used to hedge your freight
exposure in 2012 and calculate the corresponding cash flow position. You may assume that
the rate at which you fix your vessel in the physical market is the TD3 spot Baltic assessment
at the date of the fixture. You may also assume the following; TD3 Voyage Duration: 45 days;
TD3 Flat Rate: 22.60 $/mt
FFA Quotes for TD3 Route on 9/09/2011
Maturity FFA Rate
Sep 11 10.400
Oct 11 11.011
Nov 11 11.925
Dec 11 12.415
Q4 11 11.784
Q1 12 12.440
Q2 12 12.582
Q3 12 12.692
Cal 12 12.715
Source: Baltic Exchange
Question 3: Freight Options and Bunker Swaps
A) Consider the following option quotes on BCI 4TC (Date: 11 October 2013 – Figures in blue
correspond to call option premia (prm) and deltas and figures in red to put options):
Source: FIS – 11 October 2013
1. Given the option quotes show, with the help of a diagram, how a shipowner and a
charterer can use options to hedge their freight income or cost for the first six months
of 2014. Determine the cost of the option hedge in each case. Using the data from the
realised spot Baltic assessment in 2014 determine the payoff of those option positions
at the expiration of the contracts
2. One of the issues associated with using options is that the cost of the option premium
may be too high. One way of reducing the cost of the hedge is to use Collars. Using the
option quotes construct a collar that guarantees the freight cost for 2014 for a
charterer to be between 22,000 and 12,000 $/day. Using the data from the realised
spot Baltic assessment in 2014 determine the payoff of those option positions at the
expiration of the contracts.
B) It is 30 May 2016 You are interested in negotiating the price to hedge your bunker exposure
for the next 12 months (July 2016 to June 2017). You observe the following forward rates for
bunker forwards for 5,000 mt of 380cts high sulphur fuel oil deliverable in ARA.
a) Assuming a flat interest rate term structure of 5% for each of the next 12 months,
calculate the swap rate for a 12-month fixed for floating swap.
European 3.5% Fuel Oil Barges FOB Rdam (Platts) Forward Quotes
Maturity Forward Rate Maturity Forward Rate
July 2016 284.31 January 2017 295.90
August 2016 285.77 February 2017 297.78
September 2016 287.19 March 2017 299.78
October 2016 288.79 April 2017 291.72
November 2016 290.267 May 2017 293.65
December 2016 291.97 June 2017 295.21
b) Briefly discuss what other risks are involved in using a series of forward or a swap
contract to hedge your bunker exposure in this case.
Question 4: Risk Analysis and Value at Risk
Given the Baltic Assessments of FFA values (in US$/mt) for two major clean tanker routes TC2
and TC5 in Excel file “Baltic Tanker FFA 2014-16”.
TC2_37 Continent to US Atlantic coast (CPP, UNL) 37000mt
TC5 Middle East Gulf to Japan (CPP, UNL, naphtha condensate) 55000mt
a) Estimate the Rolling Volatility (annualised standard deviation) of the series from July
2014 to December 2015 using a six-month (126 day) window.
b) Estimate the Exponentially Weighted Average Volatility (RiskMetrics approach) for the
series over the same period as in part a), and plot the two (Rolling and EWAV)
volatilities, assuming λ=0.94.
c) Estimate and plot the 1%-1day VaR for each of the FFA prices over 2016, using the
Exponentially Weighted Average Volatility as well as the Rolling Volatility estimates.
d) Estimate and plot the 1%-1day VaR for a portfolio of 1 long TC5 position and 2 short
TC2 contracts over the 2016, based on EWAV.
t 1 (1 ) t σ =λσ + −λ r +
Question 5: Credit Risk Assessment
An investor is involved in negotiating with your bank to arrange a one year loan for the
purchase of an Aframax vessel whose current market value is $35m. The arrangement is that
this ship is going to operate on a one-ship-one-company basis and the company would like to
borrow as much as it can up to the full price of the vessel. However, your bank has a strict
policy of taking the vessel as collateral and only approving loans with a maximum default
probability of 20%, in order to reduce its credit risk exposure. It is also known that the
borrower has a good business and credit history; therefore, according to credit rating of this
borrower, default may occur if value of the asset falls 5% below the amount borrowed.
a) Assuming that the volatility of the value of this type of ships is 30%, and the risk free
rate is 3%, determine the maximum amount of funds that you are permitted to
provide to this shipping company for the purchase of this Tanker vessel.
b) What would be the yield on this asset-backed loan and its recovery rate?
c) What would be the loan amount, yield on the loan if it was sold in the market, and
recovery rate, if the bank increases the acceptable level of probability of default for
this loan to 15% or 25%?
d) Discuss what other alternatives the bank has to reduce its credit risk exposure to this
e) Optional: build a GBM model for the evolution of ship prices and find the probability
of default at the end of year 1, using simulation.