CHARTERED INSTITUTE OF
STOCKBROKERS
ANSWERS
Examination Paper 2.3
Derivatives Valuation Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
September 2012
Level 2
1
SECTION A: MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
C
A
B
D
A
D
B
C
C
C
B
B
A
D
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
D
B
B
D
D
B
B
D
D
C
D
D
31
32
33
34
35
36
37
38
39
40
B
D
A
B
C
C
D
A
D
D
C
A
(40 marks)
SECTION B: SHORT ANSWER QUESTIONS
Question 2 – Derivative Valuation and Analysis
Credit risk of ABS depends on the likelihood of the borrower paying the promised cash
flow. Generally, the credit rating of ABS is high because of credit enhancement.
(11/2 marks)
In several ABS, at every point in time, the borrower has the possibility of refinancing his
loan. This is called prepayment.
Prepayment is a risk for the ABS investor because it tends to occur when the floating
rates drop and the fixed income on the ABS would be more valuable.
(11/2 marks)
2
Question 3 – Portfolio Management
i.
Low correlation with traditional investments like shares and bonds.
ii.
Relative illiquidity.
iii.
Difficulty in determining current value.
iv.
Limited historical risk and return data.
v.
Extensive investment analysis required before buying.
vi.
Transaction costs could be relatively high.
(1 mark each, any four points)
(4 marks)
Question 4 – Commodity Trading and Futures
Electricity cannot be stored.
(1 mark)
The implication is that the price of electricity fluctuates widely in response to changes in
demand and supply.
(1 mark)
If demand exceeds supply in a deregulated market, price will increase. When demand
and supply reach equilibrium again, the price will return.
(1 mark)
(Maximum 3 marks)
3
SECTION C: COMPLUSORY QUESTIONS
Question 5 – Derivative Valuation and Analysis
5(a)
Compute d1 and d2
d1 = 1n (S0/X) + [r + 0.5 δ2s] t
δ s √t
= 1n (180/150) + [0.1 + 0.5 (0.5)2] 0.25
(2 marks)
0.5 √0.25
=
0.1823 + 0.05625
0.25
= 0.95
(11/2 mark)
d2 = d1 - δs √ t
0.95 – 0.5 x √0.25
(1 mark)
= 0.70
(1 mark)
Step 2: Find N (d1) and N (d2) using normal distribution tables
N (d1) = 0.8289
(1/2 mark)
N (d2) = 0.7580
(1/2 mark)
Step 3: Plug these figures into the Black – Scholes formula
Pcall = So N (d1) – X e
-rt
N (d2)
= 180 (0.8289) – 150 e
-(0.1 x 0.25)
x 0.7580
(2 marks)
= 149.20 – 110.89
= N38.31
(1/2 mark)
A call option on 8,000 ordinary shares will be quoted at:
8,000 x N38.31 = N306, 480
4
5(b)
Delta hedging for client Q who purchased 20,000 shares.
Delta = N (d1) = 0.8289
0.8289
(1 mark)
=
20,000
Number of calls sold
Number of calls =
20,000
0.8289
(1 mark)
= 24,128 call options
(1 mark)
5(c)
Using put – call parity to value put option
S0 + P0 = C0 + X e
-rt
180 + P0 = 38.31 + 150 e
P0 = 38.31 - 150 e
-(0.1 x 0.25)
-(0.1 x 0.25)
– 180
= N4.61
4,000 puts would therefore cost
4,000 x N4.61 = N18, 440
Question 6 – Portfolio Management
6(a1)
Small Value:
2 + (0.85 x 8) + (0.8 x – 2) + (1 x 0.1) = 7.3%
(1 mark)
Small Growth:
2 + (0.95 x 8) + (1.3 x -2) + (1 x 0.1) = 7.1%
(1 mark)
Large Value
2 + (0.90 x 8) + (2 x -2) + (8 x 0.1) = 6.0%
(1 mark)
Large Growth
2 + (1.10 x 8) + (3 x -2) + (10 x 0.1) = 5.8%
(1 mark)
We choose the ‘Small Value’ portfolio.
(1 mark)
5
6(a2)
Using the weight of each portfolio in the market against the expected return:
5% x 7.3 + 5% x 7.1 + 40% x 6.0 + 50% x 5.8
= 6.02%
(3 marks)
6(a3)
Using E(r) = Rf + (Rm – Rf) β
(1/2 mark)
SV: 2 + (10 – 2) 0.85 = 8.8%
(1/2 mark)
SG: 2 + (10 – 2) 0.95 = 9.6%
(1/2 mark)
LV: 2 + (10 – 2) 0.90 = 9.2%
(1/2 mark)
LG: 2 + (10 – 2) 1.10 =10.8%
(1/2 mark)
The competitor would choose Large Growth
(1/2 mark)
6(a4)
Let proportion invested in small value = Y
Proportion invested in Large growth = (1 – Y)
Y x 0.85 + (1 - Y) 1.1 = 1
(1 mark)
0.85 Y1 + 1.1 – 1.1 Y = 1
1.1 – 1 = 1.1 Y – 0.85 Y
0.1 = 0.25 Y
Y=
0.1
/0.25 = 0.4
(1 mark)
1 – Y = 0.6
(1 mark)
He invests 40% in SV and 60% in L.G
6
6(b)
If the index goes to 3,000:
N
Value of stock portfolio = N7million x 3000 = 6,000,000
3,500
Plus premium on call option
sold (which expires worthless)
452, 154
(1 mark)
(1 mark)
6,452,154
The return is -7.83% =
6452,154 – 1
7,000,000
(1 mark)
The premium acts as a cushion against the loss.
If the index goes up to 4,000
Value of stock portfolio N7,000,000 x 4,000 =
3,500
8,000,000
(1 mark)
Premium on call option
452,154
(1 mark)
Value of call option which will be exercised
by the buyer = (20 x 500 x N100)
(1,000,000)
Portfolio final value
7,452,154
Return = 6.46% =
(1 mark)
7,452,154 – 1
7,000,000
The upside potential is capped as the call option are exercised.
(Maximum 6 marks)
Question 7 – Commodity Trading and Futures
7(a)
This is a contract involving the exchange of difference between the pre-agreed price and
closing price of the underlying instrument (such as an index or a share price).
It involves cash settlement.
(2 marks)
7(a2)
This means execute the whole quantity of the order if the market conditions permit,
otherwise cancel the whole order. It is also called ‘immediate’ or ‘cancel’ order.
(2 marks)
7
7(a3)
This is the number of contracts that have not been closed-out by being offset. It is an
important indicator of contract liquidity.
(2 marks)
7(a4)
An option’s value that represents it’s time to expiry and the volatility of the underlying
asset’s cash price. It is the option premium, less any intrinsic value.
(2 marks)
7(b1)
This type of strategy is called “bull call spread”. That is, buying a call with lower strike
(550) and selling a call with higher strike (600) simultaneously.
It is used when the investor is moderately bullish.
(2 marks)
7(b2)
Here both calls are in-the-money and would be exercises. The Investor exercised the
550 call and is obliged to deliver coffee at 600.
N
Profit on long call 605 – 550 – 37 = + 18
Profit on short call 600 – 605 + 19 = + 14
Profit
+ 32
(2 marks)
Profit
32
550
600
Underlying price at
expiry
18
Loss
(Total 15 marks)
8