RSK4805
notes.
, RSK 4805 Notes
You enter into a futures contract to buy white maize for R1845 per tonne. The contract is for
delivery of 1000 tonnes. The initial margin is R200 000 and the maintenance margin is R60 000. You
receive a margin call as R140 000 was lost from the margin account. What change in the futures
price led to this margin call and what will happen if you do not meet the margin call? (5
marks)
The price of white maize decreased by R140 per tonne to R1705 per tonne:
140 000 = R140 per tonne
R(1 845 -140) = R1 705
If you do not make the margin call, the broker will close out your position.
An investor enters into a short forward contract to sell 100,000 British pounds for U.S.dollars at an
exchange rate of 1.3000 U.S.dollars per pound. How much does the investor gain or lose if the
exchange rate at the end of the contract is (a)1.3900 and (b) 1.3200?
(a) The investor is obligated to sell pounds for 1.3000 when they are worth 1.2900.
The gain is (1.3000− 1.2900)× 100,000 = $1,000.
(b) Theinvestorisobligatedtosellpoundsfor1.3000whentheyareworth1.3200.
The loss is (1.3200− 1.3000)× 100,000 = $2,000.
A trader enters into a short cotton futures contract when the futures price is 50 cents per
pound.The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if
the cotton price at the end of the contract is (a)48.20 cents per pound and (b) 51.30 cents per
pound?
(a) Thetradersellsfor50centsperpoundsomethingthatisworth48.20centsperpound.
Gain = ($0.5000 − $0.4820) × 50,000 = $900.
(b) Thetradersellsfor50centsperpoundsomethingthatisworth51.30centsper
pound.Loss = ($0.5130 − $0.5000) × 50,000 = $650.
The current price of a stock is $105, and three-month European call options with a strike price of
$107 currently sell for $5.20. An investor who feels that the price of the stock will increase is
trying to decide between buying 100 shares and buying 1,500 call options. Both strategies
involve an investment of $10,500. What advice would you give if the stock price increased to
$120? How high does the stock price have to rise for the option strategy to be more profitable?
(5 marks)
The investment in call options entails higher risks but can lead to higher returns. If the stock price stays at
$105, an investor who buys call options loses $10 500 whereas an investor who buys shares neither gains
nor loses anything. If the stock price increases to $12, the option strategy is much more profitable. An
investor who buys call options gains:
Profit = 1 500 x (120 – 107) – 10 500
= 1 500 x 13 – 10 500
= 19 500 – 10 500
= $9 000
An investor who buys shares gains:
Profit = 100 x (120 - 105)
= 100 x 15
Page 1 of 17
, RSK 4805 Notes
= $1 500
The strategies are equally profitable if the stock price rises to a level s:
100 X (s – 105) = 1 500 x (s – 107) – 10 500
100s – 10 500 = (1 500s – 160 500) – 10 500
100s – 1 500s = (-10 500 – 160 500) + 10 500
-1 400s = -171 000 + 10 500
-1 400s = -160 500
s = -160 500 / -1 400
= $114.64
Therefore, the option strategy is more profitable when the stock price moves above $114.64
An analyst for Bloom Ltd gathered the following information about a futures contract:
Current spot or market price of R60
Risk-free interest rate of 8.87% per annum
The six-month future contract is priced at R62.60
Given that the actual futures price of the contract is R59, describe the strategy an arbitrageur could
follow.
Actual price < Theoretical price
Futures price is too low (under-priced)
Arbitrage:
Buy futures contract at R59
Sell the underlying R60
Invest that amount at the risk-free rate for six months:
Risk-free rate = R60 (1.0887)0.5
= R60 x 1.043407878
= R62.60
Profit = Risk free rate - buy futures
= R62.60 – R59
= R3.60
A company’s investments earn LIBOR minus 0.5%. (5 marks)
Table 1: Swap quotes made by market maker (percent per annum)
Maturity (years) Bid Offer Swap rate
2 2.55 2.58 2.565
3 2.97 3.00 2.985
4 3.15 3.19 3.170
5 3.26 3.30 3.280
7 3.40 3.44 3.420
10 3.48 3.52 3.500
Explain how the company can use the quoted rates to convert the investments to a two-year fixed
rate investment.
LIBOR (London Inter-bank Offered Rate) is the floating or variable rate.
Bid (fixed rate received from market maker)
Offer (fixed rate paid to market maker)
Page 2 of 17
notes.
, RSK 4805 Notes
You enter into a futures contract to buy white maize for R1845 per tonne. The contract is for
delivery of 1000 tonnes. The initial margin is R200 000 and the maintenance margin is R60 000. You
receive a margin call as R140 000 was lost from the margin account. What change in the futures
price led to this margin call and what will happen if you do not meet the margin call? (5
marks)
The price of white maize decreased by R140 per tonne to R1705 per tonne:
140 000 = R140 per tonne
R(1 845 -140) = R1 705
If you do not make the margin call, the broker will close out your position.
An investor enters into a short forward contract to sell 100,000 British pounds for U.S.dollars at an
exchange rate of 1.3000 U.S.dollars per pound. How much does the investor gain or lose if the
exchange rate at the end of the contract is (a)1.3900 and (b) 1.3200?
(a) The investor is obligated to sell pounds for 1.3000 when they are worth 1.2900.
The gain is (1.3000− 1.2900)× 100,000 = $1,000.
(b) Theinvestorisobligatedtosellpoundsfor1.3000whentheyareworth1.3200.
The loss is (1.3200− 1.3000)× 100,000 = $2,000.
A trader enters into a short cotton futures contract when the futures price is 50 cents per
pound.The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if
the cotton price at the end of the contract is (a)48.20 cents per pound and (b) 51.30 cents per
pound?
(a) Thetradersellsfor50centsperpoundsomethingthatisworth48.20centsperpound.
Gain = ($0.5000 − $0.4820) × 50,000 = $900.
(b) Thetradersellsfor50centsperpoundsomethingthatisworth51.30centsper
pound.Loss = ($0.5130 − $0.5000) × 50,000 = $650.
The current price of a stock is $105, and three-month European call options with a strike price of
$107 currently sell for $5.20. An investor who feels that the price of the stock will increase is
trying to decide between buying 100 shares and buying 1,500 call options. Both strategies
involve an investment of $10,500. What advice would you give if the stock price increased to
$120? How high does the stock price have to rise for the option strategy to be more profitable?
(5 marks)
The investment in call options entails higher risks but can lead to higher returns. If the stock price stays at
$105, an investor who buys call options loses $10 500 whereas an investor who buys shares neither gains
nor loses anything. If the stock price increases to $12, the option strategy is much more profitable. An
investor who buys call options gains:
Profit = 1 500 x (120 – 107) – 10 500
= 1 500 x 13 – 10 500
= 19 500 – 10 500
= $9 000
An investor who buys shares gains:
Profit = 100 x (120 - 105)
= 100 x 15
Page 1 of 17
, RSK 4805 Notes
= $1 500
The strategies are equally profitable if the stock price rises to a level s:
100 X (s – 105) = 1 500 x (s – 107) – 10 500
100s – 10 500 = (1 500s – 160 500) – 10 500
100s – 1 500s = (-10 500 – 160 500) + 10 500
-1 400s = -171 000 + 10 500
-1 400s = -160 500
s = -160 500 / -1 400
= $114.64
Therefore, the option strategy is more profitable when the stock price moves above $114.64
An analyst for Bloom Ltd gathered the following information about a futures contract:
Current spot or market price of R60
Risk-free interest rate of 8.87% per annum
The six-month future contract is priced at R62.60
Given that the actual futures price of the contract is R59, describe the strategy an arbitrageur could
follow.
Actual price < Theoretical price
Futures price is too low (under-priced)
Arbitrage:
Buy futures contract at R59
Sell the underlying R60
Invest that amount at the risk-free rate for six months:
Risk-free rate = R60 (1.0887)0.5
= R60 x 1.043407878
= R62.60
Profit = Risk free rate - buy futures
= R62.60 – R59
= R3.60
A company’s investments earn LIBOR minus 0.5%. (5 marks)
Table 1: Swap quotes made by market maker (percent per annum)
Maturity (years) Bid Offer Swap rate
2 2.55 2.58 2.565
3 2.97 3.00 2.985
4 3.15 3.19 3.170
5 3.26 3.30 3.280
7 3.40 3.44 3.420
10 3.48 3.52 3.500
Explain how the company can use the quoted rates to convert the investments to a two-year fixed
rate investment.
LIBOR (London Inter-bank Offered Rate) is the floating or variable rate.
Bid (fixed rate received from market maker)
Offer (fixed rate paid to market maker)
Page 2 of 17
