CHARTERED INSTITUTE OF STOCKBROKERS
March 2015 Examination Diet
Paper 2.3 Solution
Section “B” - Derivative Valuation and Analysis
Solution to Question 2 (Section B):
THETA measures the exchange in the value of an option because of
changes in the time until expiration for the option contract. That is, with the
passage of time, the value of an option contract will change. In most cases,
the option will experience a decrease in value with the passage of time. This
is known as time decay. Formally, THETA is the negative of the first
derivative of option pricing model with respect to changes in the time until
expiration. Since your father-in-law has constructed a portfolio with a positive
THETA, the passage of time should increase the value of his portfolio. Thus,
he should, all things being equal, return from his vacation to find that the
value of his portfolio has increased.
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Section “C” – Derivative Valuation and Analysis
Solution to Question 5:
5(a):
John should choose the long strangle strategy.
A long strangle strategy consists of buying a put and a call with the same
expiration date and the same underlying asset. In a strangle strategy, the
call has an exercise price above the stock price and the put has an exercise
price below the stock price. An investor who buys (goes long) a strangle
expects that the price of the underlying asset (KZ in this case) will either
move substantially below the exercise price on the put or above the exercise
price on the call.
With respect to KZ, the long strangle investor buys both the put and call
options for a total cost of N9.00, and will experience large profits it the stock
price moves more than N9.00 above the call exercise price or ₦9.00 below
the put exercise price. This strategy would enable John’s client to profit from
a large move in the stock price, either up or down, in reaction to the
expected court decision.
5(b1):
The maximum possible loss per share is ₦9.00, which is the total cost of the
two options = ₦5.00 + ₦4.00
5(b2):
The maximum possible gain is unlimited, if the stock price moves outside
the breakeven range of prices.
5(b3):
The breakeven prices are ₦46.00 and ₦69.00. The put will just cover costs
if the stock price finishes ₦9.00 below the put exercise price
(₦55.00 - ₦9.00 = ₦46.00), and the call will just cover costs if the stock price
finishes ₦9.00 above the call exercise price (₦60.00 + ₦9.00 = ₦69.00).
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5(c):
The following diagram provides support for the answers above.
12
10
8
6
4
2
0
-2
-4
-6
-8
-10
69.0
46.0
35
40
45
50
55
60
65
70
75
80
5(d):
The delta for a call option is always positive, so the value of the call option
will increase if the stock price increases. Specifically, if the stock price
increases by ₦1.00, the price of the call will increase by approximately
₦0.63:
∆Price call = 0.6250 x ₦1.00) = ₦0.625 increase
5(e):
Gamma is the second derivative of the option price with respect to the stock
price and measures how delta changes in the underlying stock price.
The gamma for the put option would increase if the stock price decreases to
₦57.00. Gamma is respectively small when an option is out-of-the-money
but becomes larger as the option approaches near-the-money, which is the
case as the underlying asset value moves down towards the put option’s
₦55 exercise price.
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5(f):
Delta of call = 0.625
Delta of put = 0.625 – 1 = -0.375
Current delta of short stock position = -1,500,000
Let
represent the number of puts required.
Total delta of puts = -0.375
Total delta of stock and put = -1,500,000 – 0.375
For delta neutrality:
-1,500,000 – 0.375
4,000,000 puts
Ms Funmi will therefore need to sell 4,000,000 puts.
5(g):
Practical problems with delta-neutral hedging strategy include:
i. The delta of an option changes even when the stock price does not
change. For example, as time to expiration changes, delta of an
option changes. Therefore, the delta hedge has to be adjusted
periodically – thereby incurring regular transaction costs.
ii. Although delta-neutral positions are hedge against changes in the
price of the underlying asset, they still are subject to volatility risk,
the incurred from unpredictable changes in volatility.
iii. Delta hedging is only effective for a very small change in the price of
the underlying asset. For a large change in price a delta-gammahedge will be required.
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Section “B” – Portfolio Management
3 (Section B):
The CAL has four segments.
The four segments are:
i. A is the point where the investor only hold the risk-free asst (X1 =0), hence
the standard deviation is zero.
ii. The segment from A to B is the locus of all portfolios, which are at the
same time long in risky and the risk-free asset (
x1
).
iii. In B all the portfolio is invested in the risky asset (x1 =1).
iv. Beyond B, the share of the risky asset is of over 100% of wealth of the
portfolio(that is, x1
x2 0). This means that the investor borrows at the
risk-free arte in order to buy risky assets.
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Section “C” – Portfolio Management
Solution to Question 6 (Section C):
6(a):
The major risks include:
 Political risk. Political actions, changes in governments, events or
instability, changes of tax law, currency or market regulations, all these
can affect the value or liquidity of an investment.
 Liquidity risk. Liquidity is the case with which one can sell an investment
without any loss of value. In smaller foreign stock exchange, liquidity risk
increases for thinly traded shares.
 Information risk. The information released by foreign companies to their
shareholders may also be more difficult to access by non-local investors,
and may not always be available in English. Thus, investors may find it
difficult to obtain timely information needed to locate and invest in the
under-valued stocks of foreign companies offering the greatest discount
to their long-term values, or to adequately monitor their investments in
such companies.
 Trading costs. Traditional brokerage cost – as well as exchange fees,
custodial fees, taxes, and other charges – considerably increase the cost
of buying and selling foreign securities. Investing in foreign markets also
involves higher portfolio management costs (greater cost of research,
etc). This can have a negatively impact on returns.
 Currency risk. International diversification automatically brings with it
currency risk and requires expertise to manage this risk.
6(b1):
Hedging is not necessary – a rebounding cedi is a positive event – for
the investor.
6(b2):
Total value in cedi = 5,00 10 = 50,000
Exchange rate (cedi/naira) = 0.02
Total cost in naira = 50,000/0.02 = N2, 500,000
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6(b3):
Revised stock value in cedi = 50,000 1.08 = 54,000
Current Value of 1 cedi =1/0.02 = N50
Revised value of 1 cedi = N50 1.1 = N55
Current value of investment in naira = 54,000
= N2, 970, 000
Percentage gain
Note:
A faster approach is simply:
(1.08 1.10) – 1
N55
= 18.80%
(3 marks)
6(b4):
The variance is:
Standard Deviation
This is only an approximation because we are not using continuously
compound return.
(3 marks)
6(c):
Assume the initial investment = ₦100
CF0 = CF1
+
CF2
+
2
1+IRR
(1+IRR)
CF3
(1+IRR)3
100 = - 35
(1.0609)1
-
+
CF3
(1.0609)3
100 -
-
+
CF3
(1.0609)3
32.99
20
(1 +1.0609)2
17.77
=
=
0
0
CF3 = (1.0609)3 X 150.76 = 180.01
The return in third year is
Note: Any assumed initial investment should generate the above
result.
(4 marks)
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Section “B” – Commodity Trading and Futures
4 (Section B):
Most farmers who hedge would not deliver against the futures. Often the
wheat would not be deliverable due to difference in grade or type of wheat.
Also, wheat is probably distant from an approved delivery point, and trying
to deliver the wheat would involve prohibitively high transportation cost.
Instead of actually delivering, the farmer would be much more likely to sell
to the harvested wheat to the local grain elevator and offset the futures
position.
Section “C” – Commodity Trading and Futures
Solution to Question 7 (Section C):
7(a):
i.
Hedgers
Commodity prices can be volatile and are difficult to forecast, which is a
problem for any firm that produces or uses commodities. Such companies
may wish to take on an opposite position in the futures markets in order to
protect the firm from the impact of commodity price changes. An entity
that has an exposure to commodity prices and takes on an offsetting
position in the futures market to lower risk is called a hedger.
Commodity producers have a natural long position in the commodity that
they produce. A wheat farmer may wish to lock in the selling price of
wheat using a short hedge (known as “forward selling”). This allows a
farmer to fix the selling price (and profit) at the beginning of the growing
season.
Commodity consumers (e.g., manufacturers) have a natural short position
in the commodities that they use. Such users of commodity may wish to
fix the purchase price of their inputs with a long hedge. An airline faces
this situation: fuel costs are a major component of operating costs, so an
airline may want to take a long futures position in crude oil to offset
potential rising fuel prices.
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ii.
Speculators
When commodity hedgers use futures to lower risk, it is generally the
speculators that accept the risk by taking the opposite. Because they do
not have an offsetting physical commodity position, speculators are
exposed to significant risk of loss (or gain). In exchange for providing
liquidity to hedgers and for taking on this risk, speculators will on average
demand a premium.
iii.
Arbitrageurs
Commodity arbitrageurs try to create riskless profits from price difference
over time, between locations, or from difference between futures and spot
prices. Riskless profits are possible when price difference exceed the
frictions such as shipping costs, insurance premiums, and interest rates.
The actions of arbitrageurs act to keep the relationship between spot and
futures prices in line.
One example of a potential arbitrage trade is cash and carry arbitrage,
which is possible when the future price for a commodity is too high
relative to the spot price. An arbitrageur will buy the physical commodity
at the spot price, store it, and simultaneously enter into a futures contract
to sell the same commodity at a higher price in the future price and the
spot price (after subtracting storage, financing, and other costs).
7(b1):
The expected return on gold, as theoretically derived by the CAPM, is:
E(Rgold)
= 7% + βgold + 4%
= 7% - 0.3 (4%) = 5.8%
7(b2):
Given its negative beta, gold is likely to perform well when the overall
market performs poorly. Thus, our investment in gold is likely to offset
some of the loss on the rest of the portfolio. Investors should be willing to
accept an overall lower expected return on gold because, in periods of
financial distress, gold tends to do well.
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