CHARTERED INSTITUTE OF
STOCKBROKERS
ANSWERS
Examination Paper 2.3
Derivative Valuation and Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
September 2013
Level 2
SECTION A: MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
D
C
C
B
A
D
D
A
D
C
C
A
A
A
B
A
B
C
D
A
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A
B
D
D
B
A
D
B
A
D
D
B
A
D
D
C
B
A
B
B
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SECTION B: SHORT ANSWER QUESTIONS
Question 2 – Derivative Valuation and Analysis
2(a):
As share price rises, call option value rises.
Q 2(b):
As exercise price rises, call option value falls.
Q 2(c):
As interest rate rises, call option value rises.
Question 3 – Portfolio Management
I. The investor benefits from the expertise of professional managers.
II. Transactions costs are lower.
III. A mutual fund achieves diversification that an individual small investor may not
easily achieve.
IV. Greater transparency through regular reporting of fund position.
Question 4 – Commodity Trading and Futures
This is a situation where an investor takes a long position in a futures contract in order to
hedge against future price volatility.
A long hedge is beneficial to a company that knows it has to purchase an asset in future and
wants to lock in the purchase price.
For example, assume it is January and a flour miller needs 100 tonnes of corn to produce
corn flour and fulfill a contract in May.
In January, the flour, miller would take a long position in May futures to lock in the price.
SECTION C: ESSAY TYPE, CALCULATION AND/OR CASE STUDY QUESTIONS
Question 5 – Derivative Valuation and Analysis
5(a):
Price of Put option using Put Call Parity.
Po= Co – So + Ke-rT
= 2.42 – 60 + 60e0.005 x 0.25
= 2.42 – 60 + 59.925
= N2.345
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Q5(b):
At maturity, the value of the call is:
C=S-K
TT = (Ps – K) – CP
= 65 – 60 = N5
Initial cost was C = N2.42
Total profit = 200 (5 – 2.42)
= N516.00
5(c):
Delta measures the sensitivity of an option price to a small movement in the price of the
underlying asset. Delta can be obtained by taking the partial derivative of the BlackScholes formula with respect to the stock price.
d1 = ln (S/K) + (r +
ᵟ √T
ᵟ
2
/2)T
d1 = ln (60/60) + (0.5% + (0.2)2/2)0.25
0.2 √0.25
= 0.0625
N(d1) = 0.5249
Hence, the delta of call option = 0.5249
Similarly, the delta of the put option is:
-N(-d1) = - [1 – N(d1)]
= - [1 – 0.5249]
= - 0.4751
The delta of a call is a positive number whereas the delta of a put option is a negative
number, because the put value moves in the opposite direction of the underlying
market. Also, since the option is at the money, the delta of a call option approaches
+0.5 and that of a put option approaches -0.5 as also seen in the above calculated
values.
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Q5(d):
Rho measures the sensitivity of an option price to a small change in the interest rate.
For any increase in interest rate, the price of the call option would increase.
Question 6 – Portfolio Management
6(a): The profit from the contract with the fast-food chain with respect to future
cocoa prices can be represented as a function of the future cacao price P c:
Profit = N520m – (N300m + 200 · Pc) = 220 - 200 · P c
(where Pc is the cocoa price per metric)
N Profit
or loss (‘000)
$ Profit/loss
140,000
1400000
120,000
1200000
1000000
100,000
800000
80,000
600000
60,000
400000
40,000
200000
CocoaPrice,
price,
metric
$NCacao
perper
metric
ton ton (‘000)
20,000
0
0
-200000 0
-20,000
-400000
-40,000
-60,000
-600000
-80,000
200
20
400
40
600
60
800
80
1000
100
1200
1400
140 1600
160
-800000
Purchasing one five-month cacao futures contract the chocolate producer locks in
the cacao costs for 10 metric tons. This contract can be viewed as a loss if the
market price of cacao in 5 months will be lower than N100,000 per metric ton.
The hedge is not perfect, because the producer locks in the costs for only 10 tons
out of 2,000 needed for production. The profit and loss on the purchase of one
futures contract is illustrated below:
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N Profit or$ Profit/loss
loss (‘000)
5000
50,000
4000
40,000
3000
30,000
2000
20,000
1000
10,000
00
200
400
600
-10,000
-1000 0
20
40 60 80
-20,000
-2000
80
-30,000
-3000
-40,000
-4000
-50,000
-5000
-60,000
-6000
N Cocoa price, per metric ton (‘000)
$ Cacao Price, per metric ton
800
1000
100
1200
120
1400
140
1600
160
It is obvious, that if the market price is equal to N100,000 per metric ton, the
profit from the futures contract is zero.
Q6(b):
To make a perfect hedge, the chocolate producing company has to buy 200 futures
contracts, because the production requires 2,000 metric tons of cocoa, and each futures
contract is for 10 metric tons only.
In this case the profit/loss line will look as follows:
N$ Profit
or loss
Profit/loss
1200000
1000000
800000
600000
400000
N Cocoa price, per metric ton (‘000)
200000
$ Cacao Price, per metric ton
0
-200000 0
200
400
600
800
1000
1200
1400
1600
-400000
-600000
-800000
-1000000
Analytically the profit/loss line can be described as:
Profit = N520m – N300m – 200 futures contract · 10 metric tons/contract x N100,000
per metric tons
= N520m – N300m – 200m
= N20m as initially planned.
Q6(c):
The benefits of hedging are that the costs for the cocoa are fixed. There is no chance to
pass the change in prices on Mr Biggs in case prices for cocoa suddenly rise. On the other
hand, if the prices decrease, the chocolate producer will still be obliged to purchase cacao
at N100,000, as fixed by the futures contract. In case its competitors do not hedge, they
will make more profit. It is important to note, that hedging mainly aims at providing
insurance against downside risk, but not about a strategy to derive profit.
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Q6(d):
There is a number of different strategies to benefit.
I.
Long Butterfly:

A long butterfly consists of buying 2 call options, one with a strike price XL, lower
than $1,000 and one with a strike price XH, higher than $1,000. Then one writes 2 calls
with an intermediate strike price $1,000. This results in a payoff pattern as shown below:
$ Profit or loss
N Profit or loss
XL
XH
1,000
Stock price at
expiration
II.

Short Straddle. This is a combination of a short put and a short call, with the same
strike price.
$ Profit or loss
N Profit or loss
1,000
Stock price at
expiration
III.

Short Strangle. Short strangle is similar to a short straddle, but the strike price of
the short call (XH) should be higher than that of the short put (XL), and the forecasted
price of $1,000 being in between.
$ Profit or loss
N Profit or loss
XL 1,000
XH
Stock price at
expiration
(any 2 strategies for 2 marks each)
Q6(e):
(2 marks)
The chocolate producing company’s main activity is not speculation. If the assistant’s
forecast is not true, the company will be subject to huge losses, because short positions on
options involve unlimited risk. The only strategy among the three mentioned above, that
limited the downside risk is the long butterfly. If cacao price rises dramatically, the
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chocolate producing company will suffer considerable losses not only due to the loss on
option contracts, but also due to the sharp increase of production costs of the main activity.
(2 marks)
stock and expiration date”.
Question 7 – Commodity Trading and Futures
7(a):
Profit
or
Loss
0
Stock Price at Expiration
The strategy is an option strategy used to simulate the payoff of a long stock position.
It is an unlimited profit, unlimited risk strategy that is taken when the option trader is
bullish on the underlying security but seeks a low cost alternative to purchasing the stock
outright.
Q7(b1):
This is an illegal and unethical practice of a Stockbroker trading an equity, taking advantage
of advance knowledge of pending orders from his customers.
Q7(b2):
This is an arbitrage strategy employed when the market price of the futures contract is
overpriced relative to its theoretical price.
The investor executes it by borrowing at the market free rate to buy the asset and by taking
a short position in the futures contract. At maturity, the asset is solid under the terms of
the futures contract, the loan is repaid, and a net profit can be realized.
Q7(b3):
This is a settlement method used in some commodities trade whereby upon expiry or
exercise, the seller of the financial investment does not deliver the actual.
Q7(b4):
This is the maximum number of contracts a trader (especially speculators) may hold. Some
exchanges may establish position limits as part of their rules.
This is to prevent one firm, individuals or related group of individuals from establishing a
dominant and potentially destabilizing position in a market.
The limit prevents the creation of a position in which a manipulation of the market can take
place. Position limits are particularly useful in the market with limited liquidity.
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