**You work for a Chinese domestic airline called JetSafe**

- In April 2019 JetSafe generated revenues of CNY 100 million i.e. 500 flights producing (on average) CNY 200,000 each. Revenues are partly determined by demand from international visitors to China who is sensitive to currency movements
- Assume that the percentage change in flights in the current month has a delta of 0.8 with respect to returns in the USD/CNY exchange rate in the previous month. For example, the USD appreciated by 0.75 % in April so flights in May will be 0.60% (i.e. 0.75%*0.8) higher at 503 after rounding. We assume that there is currently plenty of capacity to meet any increase in demand for flights.
- Every month JetSafe has fixed costs of CNY 50 million (this includes depreciation and debt servicing with interest costs fixed).
- The most significant variable cost is jet kerosene. Each flight requires (on average) 13 metric tonnes of jet kerosene.
- We assume that the USD price of jet kerosene at the end of the month will apply to all users of jet kerosene during the following month (i.e., USD 640 per metric tonne as of 30 April 2019 will apply for the entire month of May). To convert to CNY, we convert at the spot exchange rate applying at the end of the previous month.
- Other variable costs are CNY 35,000 per flight.
- So in May (i.e. month 0) the Earnings Before Tax (EBT) for JetSafe will be CNY 4,657,799
- Cash at hand is currently CNY 2,500,000.
- Jetsafe has a liquidity covenant built into its debt facility such that liquid assets (i.e. cash) must not fall below CNY 1,000,000 at any time.

**Q 1)** Examine the assignment data file which you may download from the course iLearn site (under Assignment). Here you will find monthly price data for both jet kerosene and the USD/CNY. Log returns have been calculated for you. Complete the following table:

Jet Kerosene returns in USD

USD/CNY returns

Volatility per month

(using all available data)

Volatility per annum

(using all available data)

Mean per month (using all available data)

Mean per annum (using all available data)

Correlation per month

(using all available data)

**Q 2)** Correlation is changing over time so you decide to investigate this using overlapping samples where each calculation uses 24 months of returns. For example you first calculate the correlation between jet kerosene and USD/CNY returns on 30 April 1996 using the first 24 returns observations. You then recalculate on 31 May 1996 and so on. Produce a graph showing how correlation changes over time.

**Q 3)** Since volatility is also changing over time, you perform a similar analysis with overlapping samples for volatility (expressed as standard deviation per annum) for the returns of jet kerosene and the returns of USD/CNY. Present both series in the same graph.

**Q 4)** Simulate 1000 paths of monthly prices for the next 12 months for jet kerosene in USD and the USD/CNY assuming that:

• the mean of log returns for both series is zero,

• the volatility of the jet kerosene returns is 10% per month,

• the volatility of the USD/CNY returns is 0.7% per month, and

• the two series have a correlation of -0.12.

Produce two histograms (one for jet kerosene and the other for USD/CNY) showing the distribution of prices at the end of 12 months. Hint: there is a Histogram tool in the free Data Analysis Add-in For the first path you should show all your workings (no other calculations to be presented). Your starting point (month zero) should be the prices as of 30 April 2019. Show sufficient calculations so that the marker can identify the source/nature of any errors. Comment on the shape of the histograms and why they take this shape.

**Q 5)** For each path, calculate the total EBT over the next 12 months (no need to adjust for time value). Now analyse the distribution of 12-month earnings across all the simulated paths using appropriate risk measures.

Each time you hit the F9 button or the Enter key, Excel will recalculate everything with a new set of random numbers. If at any time you want to stop this from happening you can change the calculation options under the Formulas tab. Try recalculating everything ten times and discuss/explain what you observe.