Tutorial 2

Q1.

• Exposure of the price of gold going down

You are exposed to spot gold prices falling over teh next few months. To manage this risk, you would short the Aug, Sep, Oct futures contract.

• You produce 1 ton (1,000,000g). Each contract is over m = 1000g
• $\therefore$ you should short $h=1000$ contracts for each month

Q2. What is the risk of the buyers?

• Risk of the price going up

Chinese buyers are exposed to the risk of the spot gold prices increasing. To manage this risk they would go long on the same number of contracts as you would go shorted.

Q3.

August, September and October prices are far lower

$$K_{Aug} = 558.76$$

$$K_{Sep} = 558.72$$

$$K_{Oct} = 560.64$$

short payoff= $K − S_{T}$

• $m$ = 1000
• $h$ = 1000

August payoff:

$$1000(558.76-575)\cdot 1000 = -16, 240,000$$

Sep Payoff:

$$1000(558.72-600)\cdot 1000 = -42, 280,000$$

Aug payoff:

$$100 \cdot (560.64 - 625) \cdot 1000 = -64, 360, 000$$

• These amounts represent how much money you missed out on buy locking in the gold price via futures contract
• The gold price went up which would have benefitted us
• You're not particularly happy about it, and all you can say to your board is 'what if gold went down?'

Equities Question 2

• look at last traded value
• contract multiplier is 100 (100 shares per contract)

• You own 10,000 tencent shares, and 1 futures contract is over $m=100$ shares
• We would short $h=100$ september contracts

Payoff of combined position (portfolio and futures position)

$$= 10,000\cdot S_{T} + h(K-S_{T})m$$

$$= 10,000 \cdot S_{T} + 10,000(K-S_{T})$$

$$= 10,000S_{T} + 10,000K -10,000S_{T}$$

$$=10,000K = 10,000\cdot 357.5 = 3,575,000_{HKD}$$

Q2.

• You go long on futures

long payoff = $(S_{T} − K)m$

$$= 10(S_{T} - 367.3)\cdot 100$$

Q3.

-- You profit from going long at $k=367.3_{HKD}$ and the close out by going short at $K_{t} = 500$

Payoff:

$$= 10(500 - 367.3)\cdot 100 = 132,700_{HKD}$$

(About $25,964 AUD)

Q3 - Currencies

1.

• No different to the above

• 1 contract is worth 0.1 bitcoin, you would short 100 (10/0.1) at the price in September

2.

• In this case you go long 100 December contract for $K = \$69,600$

3.

• think it is going to fall - take a short position on the 10 bitcoin

• To hedge against Elon, we short 100 september contracts for $K = \$68,910 \; \; \text{USD}$

Q6.

• interest rate goes down, am going to get a lower yield

• You are exposed to the risk of interest rates decreasing, resulting in a lower investment yield on your money

  • (the interest your getting paid will be less)

• FV of a 90 bank bill is always $1m

$$F=1,000,000$$

• To manage this risk you enter into $h=3$ BAB futures at the fixed rate receiver
• Effectively locking in the interest rate on investing in BABs with a face value of $5,000,000 in December

Payoff

• The face value of 1 BAB futures is $F=1,000,000$, so we're entering $h=5$ as fixed rate receiver

$100$ = last trade

$100-95.6 = 4.4$

The last traded December BAB futures price was 95.6, $\therefore$ a fixed rate of $K=4.4$