Derivative Valuation and Analysis (1 – 12)
1.
According to the Black Scholes option valuation formula, which of the following outcomes is likely as a result of an increase in the price volatility of an underlying asset?
A.
Only the put premium will increase while the call premium will decrease.
B.
Both the call premium and the put premium will decrease.
C.
The premium of both a call option and a put option will increase.
D.
Only the call premium will increase while the put premium will decrease.
2.
You expect the market to move sharply in the coming weeks, but you don’t know if it will rise or fall. Which option strategy would you adopt in order to benefit most from this scenario?
A.
Buy a 3-month out-of-the money call, while simultaneously selling a 3-month out-of-the-money put.
B.
Buy a 3-month out-of-the money call, while simultaneously buying a 3-month out-of-the-money put.
C.
Buy a 3-month out-of-the-money put, while simultaneously selling a 3-month out-of-the-money call.
D.
Sell a 3-month out-of-the-money call, while simultaneously selling a 3-month out-of-the money put.
3.
Which of the following statements is true with respect to futures contracts?
A.
The terms of futures contracts are structured to suit both the contracting parties.
B.
The performance of futures contracts depends on the worth of the counterparty.
C.
Futures contract is an over-the-counter product.
D.
Futures contracts can be easily closed.
4.
Which of the following is/are the example(s) of hedging?
I.
In the month of April, a farmer of wheat crop which is to be harvested in July, sells a 3-month futures contract with the expectation of fall in the price of wheat.
II.
Sayo, a producer of corn flour, buys 2-month futures contract on corn, with the expectation that the price of corn will increase due to scarcity.
III.
Mohammed buys 2-month put options on the stock of Ajaokuta Steels, with the expectation of decrease in price of the stock.
A.
I only
B.
I and II only
C.
II and IV only
D.
III and IV only
5.
Which of the following statements is (are) true with respect to interest rate caps and floors?
I.
An investor may either exercise the entire series of caplets in a cap or not exercise any of them at all.
II.
An interest rate cap is a series of interest rate options, all having the exact same strike price.
III.
An interest rate floor may be used as a hedging tool by a company that issued variable rate notes.
IV.
Constructing an interest rate collar will always be cheaper than longing either of its components individually.
A.
II, III, and IV only
B.
III only
C.
I, II, and III only
D.
II and IV only

6.
An investor is trying to decide whether to write a call or write a put on ABC shares. The investor does not currently own any share of ABC. Both options have an exercise price of N50; however, the call's premium is N4 while the put's premium is N3. What's the most that this investor can lose if she were to write a put, and what's the most that she can gain by writing a call?
A.
Loss on the put position: N3. Gain on the call position: Infinite.
B.
Loss on the put position: N47. Gain on the call position: N4.
C.
Loss on the put position: N50. Gain on the call position: N54.
D.
Loss on the put position: N47. Gain on the call position: N54.
7.
Which of the following statements is true with respect to currency swaps?
A.
The notional principal amounts are only exchanged during the initiation of the swap.
B.
Once a borrower’s Naira denominated debt has been swapped for another currency, the borrower is relieved from making any Naira interest payments.
C.
During the dates of the interest exchange between the parties, only a net payment is made from the higher interest rate party over to the lower interest rate party.
D.
At the beginning of a swap, the notional amounts are exchanged at the prevailing exchange rate at that time.
8.
A 3-month call option on a single stock has an exercise price of N35 and a quoted price of N2.45. Suppose that you sell this call option and buy the underlying stock at a price X. At expiration, if the price of the underlying stock is N31.10 and your loss is
N2.45, what is X? (Assume that the contract size is one and ignore the effect of interest rates in your calculation).
A.
N31.10
B.
N32.55
C.
N36.00
D.
N37.45
9.
Currently, the S&P500 Index is at 856.50 and the annualized risk free rate is
6.2%. If the annualized dividend on the index is N13.54, what should be the futures price on the current 6-month stock index future? (Ignore the effects of the timing of dividends).
A.
885.43
B.
859.54
C.
864.51
D.
876.28
10.
Which of the following strategies would you advise against the most if you were expecting stock prices to appreciate significantly?
A.
Writing calls without actually owning the underlying asset.
B.
Writing a put while owning the underlying asset.
C.
Longing a futures contract.
D.
Writing a put without actually owning the underlying asset.
11.
The vega of an option:
I.
Is always positive for a long call or a long put.
II.
Reaches its highest level when the option is near to being “at the money”.
III.
Reflects the sensitivity of the option price to movements in the implied volatility.
A.
I and II only
B.
I and III only
C.
II and III only
D.
I, II and III

12.
Suppose that the spot gold price is N1,103.40 per ounce. The futures price of gold expiring in one year is quoted at N1,137.00 and risk free interest rate for financing is
3% p.a. (continuously compounded). What do you do? (Ignore all the other costs).
A.
A cash and carry arbitrage.
B.
A reverse cash and carry arbitrage.
C.
Buy spot and sell futures.
D.
Nothing
Portfolio Management (13 – 28)
13.
How is the information ratio defined?
A.
The ratio of the standard deviation of the portfolio divided by the standard deviation of the benchmark.
B.
The ratio of the average return on the portfolio less the risk free rate all divided by the standard deviation of returns on the portfolio.
C.
The ratio of the average return on long positions divided by the average return on short positions.
D.
The ratio of the average return on the portfolio less the average return on the benchmark divided by the standard deviation of the returns difference between the fund and the benchmark (i.e., the standard deviation of tracking error).
14.
Ms. Samuel estimates the covariance between Stock A and Stock B to be 0.471. The variance of Stock A is estimated at 0.516, and the variance of Stock B is estimated at 0.609. Which of the following comes closest to the correlation coefficient between the stocks?
A.
0.94
B.
0.89
C.
0.84
D.
0.79
15.
Which of these does not create ‘market anomaly’?
A.
Firm size.
B.
Calendar effect.
C.
Earnings surprises.
D.
None of the above.
16.
According to portfolio insurance theory, the portfolio can be totally immunized for the systematic risk by bringing the portfolio β closer to:
A.
-1
B.
1
C.
0.5
D.
0
17.
You manage an equity fund with total assets of N100 million. 80% of the total fund assets are invested in equities (the beta of this equity portfolio against the equity market index: 1.1) and 20% are invested in cash. The equity index futures price
(one month maturity) currently trades at 4400 points (contract size: N10 per point).
What do you have to do in order to hedge your portfolio against market moves during the coming 30 days (Assume a simple risk free rate of 2.4% p.a.)?
A.
Sell 182 futures contracts.
B.
Buy 182 futures contracts.
C.
Sell 2000 futures contracts.
D.
Buy 2000 futures contract.
18.
Following the constant mix strategy, _________
A.
You buy high and sell low.
B.
You buy low and sell high.
C.
You don’t enter any transactions.
D.
None of the above answers is correct.

19.
Which of the following statements regarding human capital is true?
I.
Human capital represents the investor's capacity to generate income by working.
II.
Human capital represents the investor's accumulated savings.
A.
I only
B.
II only
C.
I and II
D.
Only one of the statements
20.
Which of the following option trades, when combined with owning the underlying asset, would constitute a portfolio "insurance" strategy?
A.
Selling a put on the underlying asset.
B.
Buying a put on the underlying asset.
C.
Selling a call on the underlying asset.
D.
Buying a call on the underlying asset.
21.
Which of the following statements is (are) true with respect to investing internationally?
I.
Political risk is not a major risk in global investing.
II.
There is usually a high degree of correlation between a nation's currency movements and the stock markets that exist within that nation.
III.
Investing in domestic multinational companies is usually very ineffective in achieving international diversification.
IV.
International bond portfolios are more susceptible to currency fluctuations than international stock portfolios.
A.
I and IV only
B.
III and IV only
C.
II and III only
D.
I only
22.
A portfolio consisting of 120 highly correlated securities most likely:
A.
Has a high beta.
B.
Can have a large portion of its movement explained by movements in the market index.
C.
Has a high return expectation.
D.
Has a high degree of unsystematic risk.
23.
Which of the following statements is least accurate with respect to the factors that contribute to portfolio risk?
A.
The weights of each of the securities in the portfolio must be computed.
B.
The expected return of all securities in the portfolio must be examined.
C.
The correlation of among all pair-wise combination of securities must be examined.
D.
The standard deviation of all individual securities must be examined.

24.
Which of the following statements is (are) true with respect to the factors that a manager must take into account when managing the portfolios of an investment company (or mutual fund)?
I.
Time horizons tend to be fairly long term.
II.
During periods of outperformance in the markets, the liquidity needs of a fund will increase.
III.
While the funds may not be subject to tax, the unit-holders will bear the full brunt of any taxable trades that may take place within the fund.
IV.
Just like publicly-traded stocks, mutual funds are highly regulated.
A.
I and II only
B.
I, III and IV only
C.
III and IV only
D.
I, II, III and IV
Use the information below for to answer questions 25 and 26.
You have the following information about the assets and liabilities of a pension fund:
Variable Initial value N million Expected return
Equities 10.0%
Bonds
Liabilities
60
100
5.0%
5.0%
25.
What is the pension fund’s surplus return?
A.
0%
B.
4%
C.
5%
D.
10%
26.
What is the fund’s funding ratio?
A.
50%
B.
60%
C.
83.33%
D.
120%
27.
You had bought Nesta stocks at a price of N51.9 per share, and at the same time had sold call options on Nesta with strike price N61 and maturity end of December
2011 for N4.8 per share. On a per share basis, this position can have:
A.
Maximum profit = CHF 9.1, Maximum loss = -51.9
B.
Maximum profit = CHF 13.9, Maximum loss = -47.1
C.
Maximum profit = Unlimited, Maximum loss = 4.3
D.
Maximum profit = Unlimited, Maximum loss = 9.1

28.
You have the following information about two portfolios of stocks:
Portfolio Sensitivity to factor 1
Sensitivity to factor 2
Sensitivity to factor 3
Risk premium
8% -2% 0.1%
Assuming the applicable risk-free rate is 2%, compute the expected returns of stocks
X and Y using the Arbitrage Pricing Model:
A.
2% and 2% respectively.
B.
2.65% and 14.1 respectively.
C.
4.65% and 16.1% respectively.
D.
7.3% and 5.8% respectively.
Commodity Trading and Futures (29 – 40)
29.
An inverted market is caused by:
A.
Short supply.
B.
Increased demand.
C.
Both short supply and increased demand.
D.
Neither short supply nor increased demand.
30.
Which of the following participants in futures contract trading is responsible for adding liquidity to the futures markets?
A.
Short hedgers.
B.
Long hedgers.
C.
Speculators.
D.
Clearinghouses.
31.
When the futures prices trades below the exercise prices the put option is known as being:
A.
At the money.
B.
In the money.
C.
Out of the money.
D.
On the money.
32.
A futures contract buyer can expect a discount when:
A.
Delivery of the commodity in question is not made on time.
B.
The delivery grade of the commodity is poorer than the base grade.
C.
The futures contract does not contain a provision for delivering a lower-quality commodity.
D.
No discounts are available as commodity prices are fixed by the exchange.
33.
A speculator decides to exercise the option to sell 50,000 pounds of cotton at a contract-specified price and time. What has he exercised?
A.
A put.
B.
A strangle.
C.
A call.
D.
A straddle.
34.
The difference between a speculator and a hedger is that:
A.
A speculator does not want to assume risk, while a hedger does.
B.
The hedger has a lower margin requirement than the speculator.
C.
The speculator has a lower margin requirement that the hedger.
D.
Trade margins are only available for speculators.

35.
The difference between the price of nearby futures contracts and the price of distant futures contracts in a normal market is known as:
A.
Arbitrage.
B.
Carrying charge.
C.
Discount basis.
D.
Premium basis.
36.
On September 22, a speculator decides to short two December Live Cattle futures at
N92.53. Three weeks later he goes long two December Live Cattle futures at
N91.20. What is his net profit or loss? (1 contract = 400 lbs).
A.
N532 loss.
B.
N1,064 profit.
C.
N1,064 loss.
D.
N532 profit.
37.
In order to exercise an option, which of the following must be true?
A.
The option must be exercised at a profit.
B.
The purchaser of the option must be granted an “active right” to exercise by the seller of the option.
C.
The parties involved in exercising the option must be able to meet the margin requirements of the future positions they will hold.
D.
All of the options indicated must be true.
38.
When the miller promises to deliver flour which he does not have, he is:
A.
Making a forward sale.
B.
Most likely buying the futures contracts to hedge their price.
C.
Selling the futures contracts simultaneously.
D.
Making a forward sale and most likely buying the futures contract.
39.
Which of the following contributes to the fact that the actual price of exchange traded futures sometimes does not equal their theoretical price (fair price)?
I.
Transaction costs.
II.
Market illiquidity.
III.
Restrictions to short-selling.
A.
I and II only
B.
I and III only
C.
II and III only
D.
I, II and III
40.
Storage and transport costs are unlikely to be a major influence on the futures prices of which one of the following commodities?
A.
Coffee.
B.
Crude oil.
C.
Electricity.
D.
Zinc.
Total = 40 marks

Question 2 – Derivative Valuation and Analysis
Derivatives are regarded as highly leveraged instruments. Illustrate this feature, using a call option. ( 3 marks )
Question 3 – Portfolio Management
3(a) What are ‘alternative assets’?. Give two examples. ( 2 marks )
3(b) List two features of alternative assets that could make them attractive to investors.
( 2 marks )
Question 4 – Commodity Trading and Futures
Give three benefits that would accrue to the Nigerian economy if the commodities and futures markets are well-developed. ( 3 marks )
Question 5 – Derivative Valuation and Analysis
One of your clients holds a well-diversified equity portfolio, fully invested in the stocks on the NSE. She expects the market to decline over the next six months and asks for your advice. Her portfolio value is currently N10, 000,000, and the NSE index has a value of
3712.61.
You suggest the use of options as an instrument for hedging. You select four European type options on the NSE index (the options are referred to as ONSE options), and collect the following data:
ONSE Call Mar 10
ONSE Call Mar 10
ONSE Put Mar 10
ONSE Put Mar 10
3800 208 days price
Option delta
N238.20 0.523 days N179.00
0.585
-0.415
-0.357
5(a) Assuming the risk-free rate of interest is 3.25% (continuously compounded), determine whether the put-call parity relationship holds for the option with strike price of 3700. ( 2 marks )
5(b) You would like to show your client how she could use the option with strike price
3700 to establish a protective put strategy to hedge her portfolio.
5(b1) How many put options should she buy or sell, if the beta of the portfolio returns with the NSE index returns is 1.2? ( 3 marks )
5(b2) What is the initial cost of this strategy? ( 2 marks )
5(c) You now have reasons to believe that the equity market will be extremely volatile over the next six months, and feel there is an equal chance of either 20% rise or fall over the period.
5(c1) Suggest two option strategies that would suit the new scenario. ( 2 marks )

5(d) The option with strike price of 3600 (in the table above) has an option delta of
-0.357. Interpret this figure. ( 3 marks )
5(c2) Choose either of the strategies suggested in 5(c1) above and give details of how it works. ( 3 marks )
Question 6 – Portfolio Management
You are managing a global equity fund denominated in USD that has so far invested only in the stocks of European countries. You have decided to add Nigerian stocks to your portfolio.
The table below shows the expected rates of return, standard deviations, and correlation coefficients (all calculated using USD as base currency) estimated for the aggregate stock market of European countries and the Nigerian stock market. The risk-free interest rate is assumed to be 3%.
Expected rate of return
(annualised %)
Risk (annualised standard deviation (%)
Correlation
European Stocks
0.3
Nigerian Stock
10 15
16 30
6(a) Outline and discuss briefly the benefits and risks of investing in emerging markets like the Nigerian stock market. ( 6 marks )
6(b)
6(b1) If you wish to increase the expected rate of return on your portfolio by 1.5%, what percentage should you allocate to Nigerian stocks? ( 2 marks )
6(b2) Assuming that Nigerian stocks are included in the portfolio as calculated in
6(b1) above, what will the standard deviation of your portfolio be? ( 3 marks )
6(b3) How does the Sharpe ratio of the portfolio calculated in 6(b1) above change compared to the case of investing only in developed countries? ( 4 points )
6(c)
6(c1) Briefly justify the use of active equities portfolio management strategies.
( 3 marks )
6(c2) Explain the concept of ‘tracking error’ in a portfolio. ( 2 marks )

Question 7 – Commodity Trading and Futures
Distinguish between the following pairs of concept in the commodities market in order to clearly bring out their differences:
7(a)
7(a1) Exchange traded vs OTC-traded products. ( 2 marks )
7(a2) Cost of carry vs Fair value of futures. ( 2 marks )
7(a3) Basis vs Convergence. ( 2 marks )
7(a4) Initial margin vs Maintenance margin. ( 2 marks )
7(a5) Reputational risk vs Default risk. ( 2 marks )
7(b) A commodities trader buys a put on Cocoa at an exercise price of 11,500 for 180.
At the same time, he sells a 11,550 put at 350 on the same commodity.
7(b1) What type of trade is this, and under what condition is it appropriate?
( 2 marks )
7(b2) Draw the payoff diagram of the trade. ( 3 marks )

1) Black and Scholes Options pricing model:
2)
2)
;
General cost of carry relationship:
3) Continuous time cost of carry relationship:
4) Determinants of Options Price:
5) Correlation/Covariance:
6) Static portfolio insurance using put option:
7) Hedging with Stock Index Futures:
8) Risk adjusted performance measures:
;