CHARTERED INSTITUTE OF
STOCKBROKERS
ANSWERS
Examination Paper 1.3
Derivatives Valuation Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
March 2011
Level 1
1
SECTION A: MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
D
C
C
A
A
C
A
D
A
B
D
D
B
C
A
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
B
A
B
A
B
D
A
D
C
C
A
D
B
C
D
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
A
C
B
B
B
D
C
C
D
D
A
D
B
C
A
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
C
C
A
A
B
B
C
B
B
C
C
A
A
B
B
(60 marks)
SECTION B: SHORT ANSWER QUESTIONS
Question 2 - Derivative Valuation and Analysis
2(a)
i. They are highly leveraged instruments, with potential to generate huge losses or
returns as the case may be.
ii. Some derivative contracts expose investors to counter-party risk.
iii. Derivatives massively leverage the debt in an economy, making it ever more difficult
for the underlying real economy to service its debt obligations, thereby curtailing real
economic activity, which can cause a recession or even depression.
iv. They are complex instrument not easily understood by inexperienced investors.
(½ mark for each point)
Total 1½ marks
2(b)
Cheapest-to-deliver bond is the least expensive bond that can be delivered upon expiry
to satisfy the requirements of a Treasury bond futures contract.
This is applicable because Treasury bond futures contracts give the holder of the short
position the right to deliver different grades of underlying bonds at maturity.
(1½ marks)
Total = 3 marks
2
Question 3 – Portfolio Management
3(a)
Capital market line (CML) is a line used in the Capital Asset Pricing Model (CAPM) to
illustrate the rates of return for efficient portfolios depending on the risk-free rate of
return and the level of risk (standard deviation) for a particular portfolio.
The CML is derived by drawing a tangent line from the intercept point on the efficient
frontier to the point where the expected return equals the risk-free rate of return.
(2 marks)
3(b)
Investment horizon is simply the total length of time that an investor expects to hold
a security or portfolio. The investment horizon is used to determine the
investor's income needs and desired risk exposure, which is then used to aid in security
selection.
(1 marks)
For example, a young professional could afford to invest mostly in equities because his
time horizon could be 30 years or more. However, for someone nearing retirement,
preservation of capital becomes much more important; so fixed-income investments
become more attractive.
(1 marks)
Total = 4 marks
Question 4 – Commodity Trading and Futures
Hedging generally involves establishing a position in one market in an attempt to offset
exposure to price changes or fluctuations in some opposite position, with the goal of
minimizing one's exposure to unwanted risk.
(1½ marks)
Example: A flour miller who has a contract to supply 1,000 bags of corn flour in six
month’s time takes a long position in corn futures to lock in the purchase price, thereby
protecting himself from future adverse price movements. This is referred to as a long
hedge.
(1½ marks)
Note to assessors
Other examples using short or long hedges are equally acceptable.
Total = 3 marks
3
SECTION C: COMPULSORY QUESTIONS
Question 5 - Derivative Valuation and Analysis
5(a)
Given the following variables:
SO = N68.50
X = N65
r = 4% = 0.04
T = 110/365= 0.3014
= 0.38
First compute d1 and d2
ln
₀
²
+ 2
+
₁=
√
= In (68.5/65) + (0.04 + 0.382/2)(0.3014)
0.38 √0.3014
= 0.4135
(1 mark)
₂= ₁− √
= 0.4135 - 0.38√0.3014
=
0.2049
Looking up the normal probability table:
( ₁) = 0.6591
(1 mark)
(1 mark)
( ₂) = 0.5793
Plugging into the option pricing formulae:
₀ = ₀ ( ₁) − = 68.5 (0.6591) – 65e
( ₂)
-0.04(0.3014)
(0.5793) = 7.95
(1 mark)
= 4 marks
5(b)
Using put-call parity relationship:
So + P = C + Xe –rt
68.5 + P = 7.95 + 65 e -0.04(0.3014)
P = 7.95 + 65 e -0.04(0.3014) - 68.5 = 7.95 + 64.22 - 68.5 = 3.67
(1 mark)
(1 mark)
(2 marks)
= 4 marks
5(c)
Option delta measures the rate of change of option value with respect to changes in the
underlying asset's price.
(1½ marks)
For example, with respect to a call option, a delta of 0.7 means that for every N1
increase in the underlying stock, the call option will increase by N0.70.
(½ marks)
= 2 marks
Total = 10 marks
4
Question 6 - Portfolio Management
6(a)
Neither of the two portfolios dominates each other. For the higher level of returns
recorded by portfolio X, a corresponding higher level of risk was undertaken.
(2 marks)
6(b)
KE
= Rf + (Rm – Rf) B
= 6% + (8% - 6%) 1.2
= 6% + 2.4% = 8.4%
(1 mark)
The return of portfolio Y is not in line with the CAPM. While the CAPM model predicts
8.4% return, the actual return is 10%.
(2 marks)
= 3 marks
6(c) Computation of Treynor ratios
Portfolio
X
Y
Market
:
=
−
Treynor ratio
15% - 6% = 6.43%
1.4
10% - 6% = 3.33%
1.2
8% - 6% = 2%
1
Ranking
1st
2nd
3rd
1½ marks for each correct ratio= 4 ½ marks
Correct ranking
= 1½ marks
6 marks
Total = 11 marks
5
Question 7 - Commodity Trading and Futures
7(a)
F0 = S0er. T = 45,000 . e
0.06 x 90/365
= N45,671
(2 marks)
7(b)
There is an arbitrage opportunity, as the theoretical futures price is far lower than the
futures market price.
(1 mark)
To exploit the arbitrage trade, the following steps can be taken:
Now
i.
ii.
iii.
Borrow money at the risk free rate
Buy gold at the spot price
Sell gold futures at the market price
Cash flow (N)
45,000
(45,000)
-
In 90 days
i.
ii.
iii.
Deliver gold at maturity and receive cash
Repay borrowed fund (principal)
Pay interest on loan (90 days @ 6% c.c)
Cash flow (N)
46,500
(45,000)
(671)
N 829
(3 marks)
7(c)
7(c1) Clearing house
A clearing house acts as a third party to all futures contracts - as a buyer to every
clearing member seller and a seller to every clearing member buyer. It is responsible for
settling trading accounts, clearing trades, collecting and maintaining margin monies and
reporting trading data.
(1 mark)
7(c2) Variation margin
This is the amount of cash or collateral that brings the account up to the initial margin
amount once it drops below the maintenance margin.
(1 mark)
7(c3) Cash settlement
A settlement method used in certain future and option contracts whereby, upon expiry or
exercise, the seller of the financial instrument does not deliver the actual but transfers
the associated cash position.
(1 mark)
Total = 9 marks
6