CHARTERED INSTITUTE OF STOCKBROKERS
ANSWERS
Examination Paper 2.3
Derivative Valuation and Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
March 2014
Level 2
SECTION A: SOLUTION MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A
C
B
C
D
B
A
A
D
C
C
C
D
D
B
C
B
C
C
D
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
A
C
C
D
B
A
D
C
D
B
D
A
B
D
A
B
D
B
A
B
(40 marks)
SECTION B: SOLUTION TO SHORT ANSWER QUESTIONS
Solution to Question 2 - Derivative Valuation and Analysis
i.
Conversion price:
=
Nominal value of convertible loan stock or debentures
Number of shares issued
=
N100
50
=
N2.00
This means that N2 of loan stock is needed to obtain each ordinary share.
ii.
Conversion ratio:
=
=
=
Number of shares issued
Nominal value of debentures
50
N100
0.50
This means that 0.50 ordinary share will be obtained from the conversion of N1 nominal
loan stock. It is generally found that the conversion terms vary over time, with the
conversion price increasing in line with the expected increase in ordinary share values.
(3 marks)
Solution to Question 3 – Portfolio Management
The above scenario reflects the Efficient Market hypothesis (EMH) which suggests that
at any given time, prices fully reflects all available information on a particular stock
and/or market.
According to this hypothesis, no investor has an advantage in predicting a return on a
stock price because no one has access to information not already available to everyone
else.
(4 marks)
Solution to Question 4– Commodity Trading and Futures
The spot price is affected by:
i.
ii.
the cost of carry and
the risk premium.
The cost of carry is the cost of storing an asset plus the interest foregone by investing
funds in the asset. The storage costs include the actual direct physical costs of storage
(rent, insurance, security, etc.).
The risk premium is the amount by which the expected future price is discounted to
compensate the person holding the asset for assuming the risk.
(3 marks)
SECTION C: SOLUTION TO ESSAY TYPE, CALCULATION AND/OR CASE STUDY QUESTIONS
Solution to Question 5 – Derivative Valuation and Analysis
Solution 5(a)
(Target β - Current β) *
Value of Exposure
Future β
(Value of Future * Contract Multiplier)
N = (β* - β) P/A
= (0.85 - 1.8) * 200,000,000
1
6,500 * 500
= (-0.95) * 20,000,000
6,500 * 500
= - 58.46
Sell = 58 contract short
That is, short 58 contracts.
(4 marks)
Solution 5(b1)
Initial Investment
Sell 1 put (N400 exercise)
Sell 1 call (N600 exercise)
Profit
N
6
15
+ 21
(2 marks)
Solution to Question 5(b2)
i. Index value at maturity
-N700
Call option holder - Exercises option (N700 - N600)
Put expires worthless
Initial gain on sale of put and call loss
Loss
ii. index at maturity
N
(100)
0
(100)
21
(79)
N450
Call expires worthless
Put expires worthless
Initial gain from sale of put and call
Profit
0
0
21
+ 21
(4 marks)
Solution to Question 5(b3) – Derivative Valuation and Analysis
Profit
21
0
379
400
600 621
Stock price
This is a limited profit, unlimited risk option strategy that is taken when the option trader
thinks that the underlying stock will experience little volatility in the near term.
Short strangles are credit spreads as a net credit in taken to enter the trade.
(4 marks)
Solution to Question 6 – Portfolio Management
Solution 6(a1)
Agree; Amaka’s conclusion is correct.
By definition, the market portfolio lies on the capital market line (CML). Under the
assumptions of capital market theory, all portfolios on CML dominate, in a riskreturn sense, portfolios that lie on the Markowitz efficient frontier because, given
that leverage is allowed, the CML creates a portfolio possibility line that is higher
than all points on the efficient frontier except for the market portfolio, which is
RLI’s portfolio. Because QFL’s portfolio lies on the Markowitz efficient frontier at a
point other than the market portfolio, RLI’s portfolio dominates QFL’s portfolio.
(3 marks)
Solution 6(a2)
Non-systematic risk is the unique risk of individual stocks in a portfolio that is
diversified away by holding a well-diversified portfolio. Total risk is composed of
systematic (market) risk and non-systematic (firm-specific) risk.
Disagree; Ema’s remark is incorrect.
This is because both portfolios lie on the Markowitz efficient frontier, neither QFL
nor RLI has any non-systematic risk. Therefore, non-systematic risk does not
explain the different expected returns. The determining factor is that RLI lies on
the (straight) line (CML) connecting the risk-free asset and the market portfolio
(RLI), at the point of tangency to the Markowitz efficient frontier having the
highest return per unit of risk. Ema’s remark is also countered by the fact that,
since nonsystematic risk can be eliminated by diversification, the expected return
for bearing nonsystematic risk is zero. This is a result of the fact well-diversified
investors bid up the price of every asset to the point where only systematic risk
earns a positive return (nonsystematic risk earns no return).
(4 marks)
Solution 6(b1)
Expected return:
X, 5 + 0.8(14-5)
= 12.20%
Y. 5 + 1.5(14-5)
= 18.5%
Alpha:
X, 14 – 12.20
= 1.8%
Y, 17 – 18.50
= 1.5%
(4 marks)
Solution 6(b2) (i)
For a well diversified investor, the appropriate measure of risk is beta. On the basis of
this stock X should be recommended because it has a positive alpha, it is currently
undervalued. Stock Y with negative alpha is currently overvalued.
(3 marks)
Solution 6(b2)(ii)
In this case, Stock Y should be recommended because it has higher expected return and
lower risk. The respective Sharpe ratios are:
X:
(14-5)/36
= 0.25
Y:
(17-5)/25
= 0.48
Market Index: (14-5)/15
= 0.60
The market index has an even more attractive Sharpe ratio than either of the individual
stocks, but, given the choice between Stock X and stock Y, Stock Y is the superior
alternative.
When a stock is held as a single stock portfolio, standard deviation is the relevant risk
measure. For such a portfolio, beta as a risk measure is irrelevant. Although holding a
single asset is not a typically recommended investment strategy, some investors may
hold what is essentially a single-asset portfolio when they hold the stock of their
employer company. For such investors, the relevance of standard deviation versus beta
is an important issue.
(2 marks)
Solution 6(c)
Total return = dividend yield + capital gain yield
Dividend yield:
Stock K,
₦0.75/₦22.50
= 3.33%
Stock P,
₦0.75/₦15.00
= 5%
Expected capital gain:
Stock K,
12.20% - 3.33%
= 8.87%
Stock P,
17.20% - 5%
= 12.20%
Therefore, expected price:
Stock K,
₦22.50 × (1.0887)
= ₦25.50
Stock P,
₦15 × (1.122)
= ₦16.83
(4 marks)
Solution to Question 7 – Commodity Trading and Futures
Solution Q7(a1)
In the case of Raw Cocoa commodity futures the cocoa farmers are willing to
sacrifice some returns in order to hedge themselves against the risk of price
fluctuations during the production period. As a result, in a market dominated by
producers, substantial producer hedging pressure could cause the futures price of
certain commodity futures contracts to fall to a discount to the spot commodity
price and result in a downward sloping forward curve. The futures curve is in
Backwardation: futures price < spot price.
In the case of coffee futures, the commodity consumers take long positions to
receive the commodity in the future at a guaranteed price, and speculators are at
the short side of the contract. Therefore, if net long-hedging exceeds net shortspeculation, futures prices must be overpriced relative to their true value to
encourage speculators to sell futures. We therefore have an upward sloping
forward curve. The futures curve is in contango: futures price > spot price.
(5 marks)
Solution Q7(a2)
b)
The situation in the Raw cocoa futures, where we have a downward sloping
forward curve is called normal backwardation and it provides a positive roll yield.
As investor can (i) buy a futures contract at a lower price than the spot; (ii) as
the contract matures, sell it to close the position; (iii) re-establish a position in a
new contract with a longer maturity at a lower price. Stated differently, an
investor who buys “discounted” commodity futures contracts may expect to earn
a return due to taking on price risk that inventory holders wish to lay off.
(3 marks)
Solution 7(b1)
The cost of carry or carrying charge is the cost of storing a physical commodity, such
as grain or metals, over a period of time. The carrying charge includes insurance,
storage and interest on the invested funds as well as other incidental costs. In interest
rate futures markets, it refers to the differential between the yield on a cash instrument
and the cost of the funds necessary to buy the instrument.
If long, the cost of carry is the cost of interest paid on a margin account. Conversely, if
short, the cost of carry is the cost of paying dividends, or rather the opportunity cost;
the cost of purchasing a particular security rather than an alternative.
Storage costs (generally expressed as a percentage of the spot price) should be added to
the cost of carry for physical commodities such as corn, wheat, or gold.
(2 marks)
Solution 7(b2)
Riskless arbitrage is the act of buying an asset and immediately selling the same asset
for a higher price. For example, one may execute two orders at once, one to buy
a security at N10 and one to sell the same security at N12. The short time frame
involved means that riskless arbitrage occurs without investment; there is no rate of
return or anything like it because the asset is immediately sold. One simply makes
a profit on the deal.
If the market prices do not allow for profitable arbitrage, the prices are said to constitute
an arbitrage equilibrium or arbitrage-free market.
(3 marks)
Solution 7(b3)
The initial margin requirement is the amount required to be collateralized in order to
open a position. Thereafter, the amount required to be kept in collateral until the
position is closed is the maintenance margin. This is the minimum amount to be
collateralized in order to keep an open position and is generally lower than the initial
requirement. This allows the price to move against the margin without forcing a margin
call immediately after the initial transaction.
It is a set minimum margin per outstanding futures contract that a customer must
maintain in their margin account.
When the total value of collateral after haircuts dips below the maintenance margin
requirement, the position holder must pledge additional collateral to bring their total
balance after haircuts back up to or above the initial margin requirement.
On instruments determined to be especially risky, however, the regulators, the
exchange, or the broker may set the maintenance requirement higher than normal or
equal to the initial requirement to reduce their exposure to the risk accepted by the
trader.
(3 marks)