CHARTERED INSTITUTE OF
STOCKBROKERS
ANSWERS
Examination Paper 1.3
Derivatives Valuation Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
September 2011
Level 1
1
SECTION A: MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
B
A
B
B
D
A
C
A
A
D
A
C
D
D
D
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
C
C
B
A
A
D
C
B
C
A
A
C
A
C
C
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
D
D
B
D
A
C
B
A
B
C
D
B
B
D
A
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
B
A
D
A
B
B
A
D
D
C
A
C
C
A
C
(60 marks)
SECTION B: SHORT ANSWER QUESTIONS
Question 2 - Derivative Valuation and Analysis
Futures contracts are generally liquid because they are highly standardized, usually
specifying, among others , the underlying assets, types of settlement, amounts and units
of underlying, delivery month e.tc.
(1½ marks)
On the other hand forward contracts are ‘tailor-made’ or customized. This makes them
flexible. It is easy to accommodate the peculiar needs of the parties involved in the
terms of the contract which are not rigid.
(1½ marks)
Total = 3 marks
Question 3 – Portfolio Management
The Required Rate of Return is the return that is required by an investor based on the
risk of the investment. It has three main components:
1. Risk Free Rate
2. Expected Inflation Rate Premium
3. Risk Premium
The basic theory is that the starting point for an investor’s expectation of return is the
amount they can earn on a risk free asset (usually a AA rated government bond yield),
plus the inflation expectation and finally (and most importantly) the perceived risk of the
investment.
2
Total = 4 marks
Question 4 – Commodity Trading and Futures
Market risk is the risk that the value of a portfolio will decrease due to changes in
commodities prices and /or their volatilities
Total = 3 marks
SECTION C: COMPULSORY QUESTIONS
Question 5 - Derivative Valuation and Analysis
5(a)
Given the following variables:
SO = N20
X = N20
r = 3% = 0.03
T = 3/12= 0.25
= 0.15
First compute d1 and d2
₁
ln
²
2
₀
√
= In (20/20) + (0.03 + 0.152/2)(0.25)
0.15 √0.25
₂
₁
= 0.1375
(1 mark)
√
= 0.1375 - 0.15√0.25
=
0.0625
Looking up the normal probability table:
₁ = 0.5547
(1 mark)
(1 mark)
₂ = 0.5249
Plugging into the option pricing formulae:
₀
₀
₁
= 20(0.5547) – 20e
=11.094 – 10.420
= 0.674
₂
- 0.03(0.25)
x (0.5249)
(1 mark)
= 4 marks
3
5(b)
The call matures in 3 months,, we apply a two –period binomial model.
Therefore , 1 period = 1.5 months.
U = 1.054464
D = 1/u = 0.948349
∏ = 0.52215
CU = 2.24 X 0.5221 +0 X 0.4779)/ exp (0.03 x 1.5/12) = 1.1641
Cd = 0
C
= (1.1641 x 0.5221 + 0 x 0.4779) / exp (0.03 x 1.5/12) =
0.6056
(4 marks)
5(c)
We will use the Black & Scholes result, 0.6737. The binomial method is not precise
enough with a two period model. Using infinite number of periods (Cox, Ross, Rubinstein
model), the result would strive towards the analytical (B&S) result.
The binomial model is only useful when you have a precise scenario during the lifepath
of the option (dividends, change in risk free rate or volatility ...).
(2 marks)
Total = 10 marks
Question 6 - Portfolio Management
6(a)
CML is the capital market line which represents the expected returns of the efficient
portfolios as a function of volatilities measured by the standard deviations of their
returns.
The SML is the security market line which measures the expected returns of individual
securities as a function of their sensitivity to market fluctuations.
The difference between the two lies in the fact that while a CML represents only efficient
portfolios, the SML represents all portfolios including inefficient portfolios as well as
individual securities. Thus all portfolios lying on the CML are also lying on the SML but
not all portfolios lying on the SML are efficient and hence need not lie on the CML.
(3 marks)
4
6(b1)
The expected returns of the stocks based on the CAPM theory are calculated using the
following formulae:
E(RJ = Rf + Pi' [E(RJ- Rf]
Hence the expected returns for the three stocks are calculated as:
E(RA)=Rf+PA .[E(RJ-Rf] =6%+ 1.36· [12%-6%] = 14.16%
E(Rs) = Rf + Ps . [E(RJ- Rf] = 6% + 0.52' [12% - 6%] = 9.12%
E(Rc) = Rf +Pc' [E(RJ- Rf] = 6% + 0.69' [12% - 6%] = 10.14%
(3 marks)
6(b2)
To reshuffle the portfolio within these three stocks, we need to know if the theoretical
returns using the CAPM theory are in accordance with the expected returns based on our
own forecasts. The difference between the two is calculated using alpha. Hence we first
need to calculate the alphas of each stock in order to find out which stocks are
underpriced / overpriced. Accordingly we will then decide which stocks need to be
bought / sold.
The equation for calculation of alpha of a stock is given by:
uj = Ri - [Rf + Pi (Rm - Rf)]
Hence,
uA = RA - [Rf + P A (Rm - Rf)] = 14% - [6% + 1.36 (12%-6%)] = - 0.16%
Us = Rs - [Rf + Ps (Rm - Rf)] = 9.4% - [6% + 0.52(12%-6%)] = + 0.28%
Uc = Rc - [Rf + Pc(Rm - Rf)] = 10% - [6% + 0.69(12%-6%)]
= - 0.14%
From the above calculations it is seen that stock B is underpriced as the expected return
of stock B is greater than the return calculated by the CAPM framework. On similar lines,
stock A and C are overpriced. Hence, from an expected return point of view, it is
advisable to buy more of stock B which is underpriced and sell more of stock A and C
which are overpriced.
(5 marks)
Total = 11 marks
5
Question 7 - Commodity Trading and Futures
7(a)
Profit/loss
+ve
0
1
2
3
4
5
6
7
8
Price at expiration
-ve
The above diagram shows that the long futures position generates profit when there is a
price advance, while losses would result when prices fall.
(5 marks)
7(b)
Key price drivers in agricultural commodities market include the following:
i.
ii.
iii.
iv.
v.
vi.
vii.
Industrial uses.
Oil prices and production/transportation costs.
Demand for biofuels.
Climate and weather.
Political situation affecting major producers.
Economic growth.
Market inelasticity.
(1 mark for each well-explained point = 4 marks)
Total = 9 marks
6