CHARTERED INSTITUTE OF
STOCKBROKERS
ANSWERS
Examination Paper 1.3
Derivatives Valuation Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
September 2010
Level 1
1
SECTION A: MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
C
A
A
C
D
B
C
A
C
B
B
C
C
C
B
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
C
B
C
D
D
D
B
D
A
D
D
A
B
C
C
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
B
B
C
B
A
A
A
C
A
C
D
B
D
D
D
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
A
A
A
C
C
A
D
D
B
A
B
A
D
C
A
(60 marks)
SECTION B: SHORT ANSWER QUESTIONS
Question 2 - Derivatives Valuation and Analysis
2(a) Derivatives are referred to as a zero-sum game because the gains of one party
(say the seller) normally correspond to the loss of the other party (the buyer) in a
derivative contract – and vice versa. Therefore the net position of the two parties
is nil.
For example, the profit of the long position in a forward contract is exactly equal
to the loss of the short position and vice versa.
Long Profit (or loss) = Ft – F0
Short Profit (or loss) = F0 – Ft
(2 marks)
2(b) The put-call parity relationship for a non-dividend paying stock :
callprice + Exerciseprice . e - r T = putprice + Underlyingprice
(1 mark)
2
Question 3 – Portfolio Management
3(a) Active equity portfolio management strategies include:
i.
ii.
iii.
iv.
v.
vi.
vii.
Naira cost averaging
Contrarian investing
Momentum investing
Market timing
Investing in penny stocks
Value investing
Investing in growth stocks
½ mark for each example
(Maximum 2 marks)
3(b) A load fund is a mutual fund which charges a commission at the time of the
fund's purchase, at the time of its sale, or as a "level-load" for as long as the
investor holds the fund.
This is the opposite of a no –load fund in which shares are sold without a
commission or sales charge. The reason for this is that the shares are distributed
directly by the investment company, instead of going through a secondary party.
(2 marks)
Question 4 – Commodity Trading and Futures
4(a) Differences between forward and futures contracts.
Issue
Forwards
Futures
1
Terms and
conditions
Tailor-made to the needs of
the parties
Standardized
2
Trading platform
Over- the -Counter
Formal exchange
3
Default risk
Very high
4
Posting of margins
Not required
Low because the exchange acts
as counter party to both parties
involved
Required
5
Not done
6
Marking –to -the
market provision
Offsetting
7
Liquidity
Not very liquid
Offsetting of position is not
possible except by mutual
agreement with the other
party
Transactions are daily markedto-the market
Offsetting of positions before
contract maturity is relatively
easily done by engaging in an
opposite transaction of the
contract.
Very liquid because of its
flexibility and readily available
information on the exchange
½ mark for each point
(Maximum 2 marks)
3
4(b) Backwardation is a market condition where spot price exceed forward prices.
Contango is the opposite condition, where forward prices exceed spot prices.
(1 mark)
SECTION C: COMPLUSORY QUESTIONS
Question 5 - Derivatives Valuation and Analysis
5(a)
U=1.05 ; d= 0.95 ; r= 0.08;
T =1/12=
fu =3 ; fd = 0
p = erT – d = e0.08 x 1/12 - 0.95 = 1.006688938 -0.95 = 0.056688938
u –d
1.05- 0.95
0.1
0.1
= Approx
0.5669
f= e-rt [ pfu + (1- p)fd
f= e-0.08 x 1/12 [ 0.5669 (3) + (1 - 0.5669)0]
= 0.99335507 [(1.7007) + (0)] = N 1.69
(4 marks)
5(b) The following factors affect call option premium:
i.
ii.
iii.
iv.
v.
Underlying security price/ strike price
Time to expiration
Volatility
Risk-free interest rate
Dividend
Underlying security price/strike price - An option's premium (intrinsic value plus
time value) generally increases as the option becomes further in the money. Therefore
as the value of the underlying security rises, call option value will generally increase.
Time until expiration - Generally, as expiration approaches, the levels of an option's
time value, for calls, decreases or "erodes."
Volatility - Higher volatility estimates reflect greater expected fluctuations (in either
direction) in underlying price levels. This expectation generally results in higher option
premiums for puts and calls alike.
Risk-free interest rate – As interest rate rises, the value of call option increases.
Dividends – The value of call option is negatively related to the size of an anticipated
future dividend.
(5 marks)
4
Question 6 - Portfolio Management
6(a)
Expected rate of return
R (Apple) = 0.2 X 22 + 0.6 X 14 + 0.2 X (-4)
= 4.4 + 8.4 - 0.8
= 12
R (Grape)= 0.2 x 5 +0 .6 x 15 + 0.2 x 25
= 15
Variance
Apple = (22 -12)
2
x 0.2 + (14-12)2 x .60
+ (-4 -12)2 X 0.2
= 20 +2.4+ 51.2 = 73.6
Grape = (5- 15)
2
x 0.2 + (15 -15)2 x .60
+ (25-15)2 X 0.2
=
40
Standard deviation
Apple =
(73.6)1/2 =
8.6
Grape =
(40)1/2
6.32
=
(4 marks)
6(b) Grape share is comparatively less risky since its variance and standard deviation
are less than that of Apple.
(2 marks)
6(c)
We need to compute the portfolio standard deviation to be able to reach a
conclusion:
•
First compute the correlation coefficient between stocks of Apple and Grape
Ltd :
Correlation (A, G) =
Covariance (A,G)
S.d (Apple) x S.d (Grape)
Covariance (A, G) = Sum of…. Pi [Ai – E(A)][Gi –E(G)]
=(22-12)(5-15)x 0.2 + (14-12)(15-15) x 0.6 + (-4 -12)(15-25) x 0.2
= -100 x 0.2 + 0 + 160 x0.2
= -20 + 0 + 32 = 12
5
Correlation (A, G) =
12
= 0.22
6.3 x 8.6
Now determine the portfolio risk (measured by the standard deviation):
Portfolio Variance = (0.5)2 (40) + (0.5)2 (73.6) +2(0.5) x(0.5) x 22 x 8.6 x 6.3
= 34.4
Standard deviation = (34.4)1/2
=
5.86
Conclusion
Combining the stocks of Apple and Grape results in risk reduction, since the portfolio
risk at 5.86 is lower than the risk of investing in either the stocks of Apple (s.d of 8.6)
or Grape (s.d of 6.32) alone.
The reason for the risk reduction is that the securities have relatively low degree of
correlation.
(5 marks)
Question 7 - Commodity Trading and Futures
7(a) The difference between the initial margin requirement and the maintenance
margin requirement is N2. With initial futures price at N212, a margin call would
be triggered if the price falls below N210.
(2 marks)
7(b)
Day
0
Beginning
Balance
0
Funds
Deposited
200
1
200
0
2
180
3
Futures
Price
212
Price
Change
Gain/
Loss
Ending
Balance
200
211
-1
-20
180
0
214
3
60
240
240
0
209
-5
-100
140
4
140
60
210
1
20
220
5
220
0
204
-6
-120
100
6
100
100
202
-2
-40
160
(5 marks)
7(c) By the end of day six, the price is N202, a decrease of N10 from the purchase
price of N212. The loss so far is N10 per contract times 20 contracts. This equals N200
That is: (202 -212) X 20 = - N200
(2 marks)
6