PAPER 2.3
QUESTIONS AND SOLUTIONS
SEPTEMBER 2014 DIET
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Question 2 – Derivative Valuation and Analysis
“Hedging is the inverse of speculation”. Do you agree? Justify?
(3 marks)
Solution 2 – Derivative Valuation and Analysis
Hedging involves taking an offsetting position in a derivative in order to balance any gains
and losses to the underlying asset. Hedging attempts to eliminate the volatility associated
with the price of an asset by taking offsetting positions contrary to what the investor
currently has. The main purpose of speculation, on the other hand, is to profit from betting
on the direction in which an asset will be moving.
Hedgers reduce their risk by taking an opposite position in the market to what they are
trying to hedge. The ideal situation in hedging would be to cause one effect to cancel out
another. Speculators make bets or guesses on where they believe the market is headed.
For example, if a speculator believes that a stock is overpriced, he or she may short sell the
stock and wait for the price of the stock to decline, at which point he or she will buy back
the stock and receive a profit. Speculators are vulnerable to both the downside
and upside of the market; therefore, speculation can be extremely risky.
Overall, hedgers are seen as risk averse and speculators are typically seen as risk lovers.
Hedgers try to reduce the risks associated with uncertainty, while speculators bet against
the movements of the market to try to profit from fluctuations in the price of securities.
(1 mark for each relevant point)
Total = 3 marks
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Question 3 – Portfolio Management
Which of the following phenomena would be either consistent with or a violation of the
efficient market hypothesis? Explain briefly.
Question 3(a)
Money managers that outperform the market (on a risk-adjusted basis) in one year are
likely to outperform in the following year.
(2 marks)
Solution 3(a)
Inconsistent. This would be the basis of an “easy money” rule: simply invest with
last year’ best managers.
Question 3(b)
Stock prices of companies that announce increased earnings in January tend to
outperform the market in February.
(2 marks)
Solution 3(b)
Inconsistent. The abnormal performance ought to occur in January when earnings
are announced.
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Question 4 – Commodity Trading and Futures
Imagine a baker who has the opportunity to bid on a contract to supply a local
military base with bread for an entire year. The problem is the baker must commit to
a price today and hold to that price for the entire year.
Identify the risk faced by the baker, and explain how the use of a futures contract
could transfer the risk.
(3 marks)
Solution 4
The baker faces the problem of not knowing what the future price of flour (wheat)
will be. He may feel quite comfortable developing a price for the bread based on the
current prices of wheat, but if the price of wheat should increase the bread making
profits will fall and may turn into significant losses. Without the ability to transfer this
risk the baker would probably have to pass on this opportunity. Fortunately the
baker could purchase a wheat futures contract that would expire in a year, giving
him the right to purchase some quantity of wheat at a price reflecting today's market
price. If the market price of wheat does increase he will lose on the baking operation
but the value of his futures contract will increase. If the price of wheat falls, his
futures contract loses value but his baking profits will increase.
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Question 5 – Derivative Valuation and Analysis
NSE B5 Index is currently quoted at 500 points [1 Index point = N100] and the current
price of a forward contract to purchase the Index after 6 months is 502 points. The 6month risk free interest rate is 5% p.a. Mr. Gongola, an investor, perceives an arbitrage
opportunity between the NSE B5 Index and the 6 months forward contract on NSE B5
Index and desires to perform an arbitrage trade. Ignore tax and transaction costs, and
assume that there are no restrictions on both long and short positions in the Index and
the forward contract.
5(a) Describe a strategy that makes use of the arbitrage opportunity and will necessarily
earn a riskless profit, indicating the profit to be derived from that strategy [Note:
work on one Index]. Assume that the dividends from NSE B5 Index are zero.
(4 marks)
Solution 5(a)
The theoretical forward price is: F theo  S  1  R   500  1.050.5  512.35 .
t
{Or, with continuous compounding: F theo = S. ert = 500. e 0.05 x 0.5 = 512.66 }
By contrast, the forward contract price is 502, so you perform a reverse cash and carry strategy:
(borrow and sell short) the index and buy it forward in 6 months. The proceeds of the short sale
are N500, that in 6 months become 512.35; in 6 months you buy the Index at 502. The difference
of N10.35 is the profit.
(4 marks)
Description
Short NSE B5 Index
Purchase F
Invest the proceeds
Total
Cashflow Today
+500
In 6 months
-X
0
＋ X-502
-500
＋ 512.35－502
(Forward settlement)
0
＋10.35 profit
Question 5(b)
Assume that NSE B5 Index cannot be shorted and that you cannot take a short position
in the forward contract. All other assumptions remain the same. An investor who is
already long the NSE B5 Index will be able to make use of an arbitrage opportunity in
this situation.
Describe what he needs to do in order to exploit this opportunity [Note: work on one
Index].
(4 marks)
Solution 5(b)
An investor who is already long the NSE B5 Index can sell it spot and buy it back forward
through the forward. He receives N500, invests the proceeds in the risk free asset at 5% for
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6 months, obtaining at maturity 512.35, and in 6 months he buys back the index paying 502. In
6 months he will be long the NSE B5 Index plus N10.35.
(4 marks)
Question 5 (C)
Now assume that following 6-month European options on the NSE B5 Index are available
for both purchase and sale, as shown in the table below:
Strike
price
400
500
600
Call premium
(in Naira)
115
48
15
Put
premium
(in Naira)
6
36
100
Chief Ebeano, a wealthy investor, thinks that the index volatility will decrease and
therefore decides to sell 1 put with an exercise price of N400 and to sell 1 call with an
exercise price of N600.
Question 5 (c1)
Calculate the initial investment of this strategy [named short strangle].
(2 marks)
Solution 5 (c1)
The initial revenue from the sale of the straddle is: 15 + 6 = N 21
(since he sells both put and call, he collects premium both ways)
(2 marks)
Question 5(C2)
Write down the payoff (the final value VT) of this strategy at maturity as a function of the
Index value at maturity ST. Fill the blanks below with numbers and/or algebraic symbols,
etc….
(if ST  ........................)
............................................

VT (ST )  ............................................ (if .....................  ST  ......................)
............................................
(if ST  .......................)

Solution 5(c2)
(if ST  K 1  400)
 400  ST 

VT (ST )  
0
(if K 1  400  ST  K 2  600)
 S  600
(if ST  K 2  600)
T

(3 marks)
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Payoff
ST – 400
0
– (ST – 600)
Question 5(C3)
Calculate the maximum profit and/or the maximum loss, as well as the break-even points
of this strategy. Do not consider interest on option premium.
(3 marks)
Solution 5(c3)
Maximum profit = N21
Maximum loss = ∞ (Unlimited)
Break-even points = N379 and N621
(3 marks)
BEP (Workings)
1.
- (400 - ST) + 21 = 0
- 400 - ST + 21 = 0
ST = 400 – 21 = 379
2.
- (ST - 600) + 21 = 0
- ST - 600 + 21 = 0
ST
=
621
400
600
21
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Question 6 – Portfolio Management
Question 6(a)
The stock of AB Plc has a beta of 0.96 and alpha value of 1.5%. Explain the meaning and
significance of these values to the company.
(5 marks)
Solution 6(a)
The equity beta measures the systematic risk of a company’s shares, the risk that cannot
be eliminated by diversification. It is a measure of a share’s volatility in terms of
the
market’s risk, and may be estimated by relating the covariance between the returns on
the share and the returns on the market to market variance. An equity beta of 0.95
suggests that AB Plc shares are less risky than the market as a whole which has a beta of
1. If average market returns change, for example increase by 4% the return of AB Plc’s
shares would be expected to increase to 0.95 × 4% = 3.8%.
The alpha value measures the abnormal return on a share. An alpha value of 1.5%
means that the returns on AB Plc’s shares are currently 1.5% more than would be
expected given the shares systematic risk. Alpha values are only temporary and may be
positive or negative; in theory the alpha for an individual share should tend to zero. An
alpha value of 1.5% should cause investors to buy the share to benefit from the
abnormal return, which would increase share price and cause the return to fall until the
alpha value falls to zero. In a well diversified portfolio the alpha value is expected to be
zero.
Question 6(b)
Grace and Yaro both own a portfolio of shares in listed companies. Details of the portfolio
are as follows:
Grace
Yaro
Company
A
B
C
D
E
F
No. of shares
11,000
25,000
12,000
30,000
16,000
20,000
Par value
₦1
₦1
₦0.25
₦0.10
₦0.50
₦1
The following data relate to the shares:
Company
Market price
per share
Beta
A
B
C
D
E
F
₦20.00
₦18.00
₦27.5
₦8.00
₦15.00
₦26.00
0.75
0.90
0.60
1.40
1.60
1.20
Actual return
expected for next
year
13.0%
14.6%
11.4%
17.5%
20.3%
16.6%
(Note: Risk-free rate is 7% and equity market return is 15%)
Required:
For each of portfolio, estimate the following:
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Question 6(b1)
The beta factor.
Solution 6(b1)
Grace portfolio
Company
A
B
C
(4 marks)
Total market
value
(1)
220,000
450,000
330,000
1,000,000
Beta
(2)
0.75
0.90
0.60
(1 × 2)
165,000
405,000
198,000
768,000
Beta = 768,000/1,000,000 = 0.768
Yaro Portfolio
Company
D
E
Total market
value
(1)
240,000
240,000
Beta
(2)
(1 x 2)
1.40
1.60
336,000
384,000
520,000
1,000,000
1.20
624,000
1,344,000
F
Beta = 1,344,000/1,000,000 = 1.344
Question 6(b2)
The required return.
(2 marks)
Solution 6(b2)
Using CAPM, the required return is:
R = Rf + β(Rm - Rf)
Grace
R = 7 + 0.768(15 - 7) = 13.144%
Yaro
R = 7 + 1.344(15 - 7) = 17.752%
Question 6(b3)
The alpha value.
(2 marks)
Solution 6(b3)
To compute alpha value of each portfolio, we need to compute the expected return of
each portfolio.
Grace: (
Yaro: (
220
1000
x 13) + (
450
1000
240
240
x 17.5) + (
1000
1000
330
x 14.6)+(
1000
x 20.3) + (
x 11.4) = 13.192
520
x 16.6) = 17.704
1000
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Alpha value = expected return – Required return
Grace: 13.192 – 13.144 = 0.048%
Yaro: 17.704 – 17.752 = -0.048%
Question 6(C)
Compare and comment on your results for each portfolio above, explaining which
portfolio you would wish to hold in a ‘bull’ market and which in a ‘bear’ market.
(5 marks)
Solution 6(c)
The calculations demonstrate that although Grace holds a much larger number of
shares than Yaro (66,000 as compared with 48,000) the market values of the two
portfolios are identical. All the shares held by Yaro have a beta value of less than 1.0
indicating that the systematic risk level of the portfolio is less than the average
market risk (i.e defensive share). Conversely, all the shares held by Grace have beta
values in excess of 1.0, and the portfolio consequently has a much higher level of
systematic risk than the market portfolio (i.e aggressive shares).
The implication of this is that at a time when the market as a whole is rising (i.e a
bull market), the shares in Yaro’s portfolio will rise at a lower rate than that of the
market as a whole. If the market as a whole rises on average by 20%, the market
value of Yaro’s portfolio should only rise by 15.40% (0.77 x 20%) in response to the
same conditions that have caused the change in the market values. Similarly, in a
bear market, the value of Yaro’s portfolio should fall by a smaller percentage amount
than that of the market as a whole. In Grace’s portfolio, the opposite will be true and
the composition of the portfolio will tend to amplify any overall market movements.
In consequence, Grace’s portfolio would be preferable in a bull market since it should
allow full advantage to be taken of positive market movements. Yaro’s portfolio is
preferred in a bear market since this should minimize downside risk.
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Question 7 – Commodity Trading and Futures
Question 7(a)
Explain why the futures price converges to the spot price and discuss what would
happen if this convergence failed.
(4 marks)
Solution 7(a)
The explanation for convergence at expiration depends on whether the market
features
delivery or cash settlement but in each case, convergence depends on
similar arbitrage arguments. We consider each type of contract in turn. For a
contract with actual delivery, failure of convergence gives rise to an arbitrage
opportunity at delivery. The cash price can be either above or below the futures
price, if the two are not equal. If the cash price exceeds the futures price, the trader
buys the future, accepts delivery, and sells the good in the cash market for the
higher price. If the futures price exceeds the cash price, the trader buys the good on
the cash market, sells futures, and delivers the cash good in fulfillment of the
futures. To exclude both types of arbitrage simultaneously, the futures price must
equal the cash price at expiration. Minor discrepancies can exist, however. There are
due to transaction costs and the fact that the short trader owns the options
associated with initiating the delivery sequence.
For a contract with cash settlement, failure of convergence also implies arbitrage.
Just before delivery, if the futures price exceeds the cash price, a trader can sell the
futures, wait for expiration, and the futures price will be set equal to the cash price.
This gives a profit equal to the difference between the cash and futures.
Alternatively, if the cash price is above the futures price, and expiration is imminent,
the trader can buy the futures and wait for its price to be marked up to equal the
cash price. Thus, no matter whether the futures price is above or below the cash
price, a profit opportunity will be available immediately.
In short, the futures and cash price converge at expiration to exclude arbitrag failure
of convergence implies the existence of arbitrage opportunities.
Question 7(b)
It is August 10 and Agbeloba John, a farmer, is making final estimates of this year’s
coin crop. His production is turning out to be much better than expected. This causes
concern because if his production is better than expected, other farmers must be
experiencing the same situation.
The current spot price is N360 per bushel, and the September corn futures (5,000
bushels per contract) price is N403.20 per bushel. At the current spot price, John
would just break even with his anticipated 60,000 bushels. His corn will not be ready
to harvest until September.
Required:
Question 7(b1)
What can Agbeloba John do to ensure his profitability? Is this a long or a short
hedge? Why?
(4 marks)
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Solution 7(b1)
Agbeloba John can sell his anticipated wheat production in the futures market. Any
opportunity gains (losses) resulting from changing wheat prices will be offset by
losses (gains) in the futures market. This is a short hedge because Farmer Agbeloba
John is selling his production forward. The counterparty to his contract might be a
producer acquiring wheat forward for whom the transaction would be a long hedge.
Question 7(b2)
At harvest time in September, John’s concerns are realized in that the cash price has
dropped to N272 per bushel. Compute John’s net wealth change due to the drop in
corn prices, assuming he hedged his anticipated production and his final yield was
60,000 bushels.
(4 marks)
Solution 7(b2)
Date
August 10
September
Cash Market
John anticipates the production of
60,000 bushels of corn which he
wishes to sell at ₦403.20 per bushel
for a total of ₦24,192,000.
John sells 60,000 bushels in the spot
market at ₦272/bushel for a total of
₦16,320,000.
Loss on cash market = ₦24,192,000
– 16,320,000 = ₦7,872,000
Futures Market
Sell 12 5,000–bushel corn
futures contracts at ₦403.20
per bushel
At maturity, the futures price
will equal the spot price.
John buys 12 contracts at
₦272/bushel.
Futures profit:
60,000(₦403.20 - 272) =
₦7,872,000
Net Wealth change = ₦0
Question 7(b3)
Suppose John’s production turned out to be only 50,000 bushels. Compute his net
wealth change.
(4 marks)
Solution 7(b3)
Date
August 10
September
Cash Market
Futures Markets
As in (ii) above
As in (ii) above
John sells 50,000 bushels in the spot market at At maturity, the futures price
₦272/bushel for a total of ₦13,600,000:
will equal the spot price. John
Opportunity losses
buys 12 contracts at
Price Change = 60,000(272 – 403.20) = 7,872,000 ₦272/bushel.
Production variation = 10,000 × 272 = -2,720,000 Futures profit: (as above) =
Total
= -10,592,000 ₦7,872,000
Net Wealth change = ₦2,720,000
John’s net wealth change is negative because he had anticipated 60,000 bushels of
corn production was 10,000 bushels less. He could have sold those 10,000 bushels at
₦272/bushel if he had them. This results in ₦2,720,000 opportunity loss attributable
to production variation.
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