CIS March 2013 Exam Diet
Examination Paper 2.3:
Derivatives Valuation Analysis
Portfolio Management
Commodity Trading and Futures
Level 2
Derivative Valuation and Analysis (1 – 12)
1.
Ope holds a position in the shares of P Ltd. She believes that the market price of P
Ltd will remain at or near its current price of N35 per share for the next quarter. If
her goal is to increase the return on this investment over the next quarter, which of
the following strategies would be most appropriate?
A. Selling calls at N40
B. Buying calls at N30
C. Buying puts at N30
D. Selling puts at N45
2.
An index is currently 965 and the continuously compounded dividend yield on the
index is 2.3%. What is the no-arbitrage price on a one-year index forward contract if
the continuously compounded risk-free rate is 5%?
A. 991.4
B. 991.1
C. 987.2
D. 994.05
3.
Portfolio insurance is a term often used to describe:
A. Selling covered calls on a long underlying assets position.
B. Buying protective puts on a long underlying asset position.
C. Selling out-of-the-money puts to enhance portfolio return.
D. Selling out-of-the-money calls to insure a higher return over holding the asset
alone.
4.
Which of the following will cause the value of a put option on a stock to increase?
A. The increase in the risk-free rate.
B. The payment of a dividend.
C. An increase in the price of the underlying stock.
D. Lower volatility in the price of the underlying shares.
Use the information below to answer questions 5 and 6:
You are given the following information about a call option on the shares of Bongo plc:
Current share price
Exercise price
Risk-free rate
Standard deviation of return
on the shares
Time to expiry
N100
N95
10%
50%
3 months
Additional information:
N(d1) = 0.6664
N(d2) = 0.5714
5.
Using the Black-Scholes valuation model, what is the value of the call option on the
shares of Bongo plc?
A. N6.35
B. N10.55
C. N13.70
D. N15.63
6.
An investor who holds 5,000 shares of Bongo plc would like to eliminate the risk of
shareholding. Using delta hedging strategy, which of the following is the appropriate
action to take?
A. Sell 7,503 call options.
B. Buy 5,000 call options.
C. Sell 8,750 put options.
D. Buy 2,857 put options.
7.
The difference between a long straddle and a long strangle is that in the strangle:
A. The exercise price of the put is higher than the exercise price of the call.
B. The exercise price of the call is higher than the exercise price of the put.
C. The underlying stock price doesn’t have to move as much to end up in-themoney.
D. If the underlying stock doesn’t move, the position losses more than in the
straddle.
8.
The spot price for an asset is N90, the cost of carry is 9.8 percent, and the 1-year
futures price is N99. Based on this information, assuming efficient markets, and
using the continuous-time model, the appropriate strategy in this case is:
A. Cash and carry arbitrage.
B. Reverse cash and carry arbitrage.
C. No action because the result is a no-arbitrage when a portfolio is heavily
margined.
D. No action because the cost of carry is equal to the implied repo rate.
9.
An investor decided to buy 100 shares of ABC and simultaneously write one call on
ABC shares when the stock price hits N35. The strike price of the call is N32.50 and
the premium is N4.50. Which of the following statements would be inconsistent with
this strategy?
A. The maximum potential gain would be N450
B. The investor’s outlook suggests little price volatility for ABC shares.
C. The net cost of the portfolio would be N3,050
D. The maximum potential loss would be N3,050
10. A firm can use an interest-rate swap to hedge the risk of rising interest rates by:
A. Converting floating-rate debt into synthetic fixed-rate debt.
B. Closing a pay-fixed position.
C. Converting fixed-rate debt into synthetic floating-rate debt.
D. Closing a receive-floating position.
11. With two call options available, you decide to construct a bull-call spread. The first
option has an exercise price of N30 at a premium of N2, and the second call has an
exercise price of N40 with a premium of N0.50. If at expiration, the underlying asset
price closes at N45, what is the most that you can profit from this trade?
A. N8.00
B. N8.50
C. N10.00
D. N11.50
12. A cap on a floating rate note, from the bondholder’s perspective, is equivalent to:
A. Writing a series of puts on fixed income securities.
B. Owning a series of calls on fixed income securities.
C. Writing a series of interest rate puts.
D. Writing a series of calls on fixed income securities.
Portfolio Management (13 – 28)
13. Adding more stocks to an equity portfolio will most likely:
A. Lower unsystematic risk.
B. Increase unsystematic risk.
C. Lower systematic risk.
D. Increase systematic risk.
14. All
A.
B.
C.
D.
of the following measures of volatility focus on downside risk except:
The range.
Semi variance.
Value at risk.
Shortfall probability.
15. A client made the following statement when he first met the portfolio manager:
“Under no circumstance should you buy any tobacco or alcohol companies. I find
them morally repulsive and I will move my account if I ever see that you used my
money to invest in one”.
This is an example of what type of constraint?
A. Time horizon.
B. Legal/regulatory.
C. Unique needs and circumstance.
D. None of the above.
16. Which of the following statements is false?
A. The SML shows that when risk is zero, return will be the nominal risk-free rate.
B. The slope of the SML is determined by investor risk perceptions.
C. The SML shows the relationship between risk and expected return.
D. Parallel shifts in the SML reflect changes in investor risk preferences.
17. Which of the following statements regarding the efficient frontier is true?
A. Markowitz defines risk in the efficient frontier context as market or systematic
risk.
B. The efficient frontier is a linear relationship between risk and return.
C. The efficient frontier assumes borrowing and lending at the risk-free rate of
interest.
D. Stocks are combined into two-stock portfolio to identify the most efficient
portfolios from a risk-return tradeoff perspective.
18. A stock currently selling for N50 is expected to increase in price by year end to N55
and pay a N1 dividend. If it has a beta of 0.7, and expected market return of 15
percent, and a risk-free rate of 8 percent, the stock would be considered:
A. Overpriced.
B. Underpriced.
C. Properly priced.
D. Properly priced if the risk-free rate falls to 6%
19. You are the owner of a N4 million portfolio with a beta of 1.0. You would like to
insure your portfolio against a fall in the index of magnitude higher than 12%. The
index currently stands at 4200. Put options on the index are available at three strike
prices. Which strike will give you the insurance you want?
A. 3,870
B. 3,840
C. 3,696
D. None of the above.
20. The risk/return performance measure that shows a portfolio’s average excess return
(compared to the riskless assets) dividend by the standard deviation of its returns is
known as the:
A. Sharpe ratio.
B. Mean absolute deviation.
C. Information ratio.
D. Coefficient of variation.
21. Given the table below:
John’s annual stock returns
1999
2000
2001
2002
15%
22%
-6%
10%
What is the geometric mean return for John’s common stock over the four years?
A. 9.75%
B. 10.25%
C. 14.21%
D. It cannot be determined because of the negative return in 2001
22. When defining the strategic asset allocation, one should essentially take into
account:
I. The level of risk aversion decided by the client.
II. The variances and covariance between all asset classes.
III. The short term risk considerations.
A.
B.
C.
D.
I and III only.
I and II only.
II and III only.
All of the above.
23. According to the Treynor-Black portfolio optimization model, assets are allocated to
both a passively managed portfolio and to an actively managed portfolio. Which of
the following is most likely to lead to a larger allocation to the actively managed
portfolio?
A. Market inefficiencies.
B. Unsystematic risk.
C. Short sales prohibition.
D. None of the above.
24. The performance of the portfolio manager, who is not responsible for the cash flow
decision is most accurately measured over a long term using
A. Internal rate of return, because it is highly sensitive to volatile markets.
B. Money weighted return because the money actually invested is what determined
the performance.
C. Time weighted return because it considers multiple short periods without cash
flows.
D. Dietz formula because it adjusts and considers the average invested capital.
25. 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.
26. Which of the following statements is/are true with respect to investing
internationally?
I. Political risk is 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.
B.
C.
D.
I only.
II and III only.
III and IV only.
I, III and IV only.
27. Analysts forecast the stock price of company ABC to be N1,000 in a year. The riskfree rate is 5% and the market risk premium is 10%. According to the CAPM what is
the maximum price you agree to pay for this stock knowing that its beta is equal to
2?
A. N750
B. N800
C. N869.50
D. N1,000
28. You come across a fund report which provides the following data for the previous
year.
Returns
Volatility
Sharpe’s Measure
Treynor’s Measure
16%
20%
0.5
0.08
What is the beta for this fund?
A. 0.80
B. 1.25
C. 1.60
D. 2.00
Commodity Trading and Futures (29 – 40)
29. Analyze the following two statements:
I.
Commodity futures prices are observed to deviate from their theoretical prices
because of trading frictions relating to the futures contracts.
II. When futures prices exceed spot prices, this is known as contango.
Are these statements correct or incorrect?
A. Both statements are correct
B. Only one statement is correct, because deviations from theoretical prices are
caused by trading frictions relating to the underlying commodity
C. Only one statement is correct, because when futures prices exceed spot prices,
this is known as backwardation.
D. Both statements are incorrect
30. When maturing futures position are replaced with new futures contact positions, the
resulting outcomes is called roll yield. This yield:
A. Cannot be positive if the future markets are in backwardation.
B. Is likely to be negative if the presence of long speculators increase, resulting in
contango.
C. Cannot be negative because the investor will realize a return equal to the riskfree rate on the portfolio collateral.
D. Information on risk-free rate is required.
31. What is the profit or loss if the underlying is 95 at expiry?
price
0
90
-10
A.
B.
C.
D.
Loss 5p
Loss 10p
Profit 5p
Profit 10p
32. Suppose that storage costs are paid continuously and are proportional to the cost of
the commodity. 3-month forward price for a bushel of corn is quoted at N398.55.
Continuously compounded annual interest rate 10%. Current spot price is
375/bushel. The implied continuously compounded annual storage costs are nearest
to:
A. 14.40%
B. 12.25%
C. 15.75%
D. 11.48%
33. Which of the following trades would you recommend to a risk-averse investor
anticipating a rise in market volatility?
A. Long straddle.
B. Short strangle.
C. Bull spread.
D. Long call.
34. A futures contract for 5,000 bushels of wheat has a forward price of N82.50 per
bushel. If at maturity the spot price is N76.50 per bushel, which of the following
statements is true? Upon maturity, the holder of the:
A. Long position will have a positive cash flow of N30,000
B. Short position will have a positive cash flow of N30,000
C. Long position will have a positive cash flow of N30,000 plus the cost of carry.
D. Short position will have a positive cash flow of N30,000 minus the cost of carry.
35. Which of these are true of covered calls?
I.
II.
III.
IV.
They are riskier than uncovered calls.
They are arbitrage trades.
They can be used to generate income.
The writer of the call option will be long the asset.
A.
B.
C.
D.
I and II only.
I and IV only.
II and III only.
III and IV only.
36. All of the following are purposes of the Commodity Futures Trading Commission
(CFTC) except:
A. Approving new contracts.
B. Approving changes to existing contracts.
C. Setting the price of a seat on the CBOT.
D. Approving the founding of new futures exchanges.
37. A firm takes a long position in one contract of corn at N270 per bushel (1 contract =
5,000 bushels). The initial margin deposited was N180,000. The maintenance margin
is N120,000. If the margin were to fall to N99,900, how much would the firm have to
deposit in order to maintain the position?
A. N0
B. N20,100
C. N80,100
D. N185,100
38. Suppose that the spot price of copper is N39 per troy ounce, the 1-year futures price
is N48 and the repo rate is 6 percent. Which futures contract arbitrage strategy
would be most appropriate?
A. Repo.
B. Reverse repo.
C. Cash and carry.
D. Reverse cash and carry.
39. With respect to a futures position, basis risk would be more of a concern if a
manager intends to:
A. Close the contract with delivery.
B. Liquidate the contract prior to maturity.
C. Liquidate the contract at maturity.
D. Liquidate the contract beyond maturity.
40. The manager of an oil refinery has entered into a 2-year, annual reset swap with a
1,000,000 barrel notional principal. (We assume the manager needs a total of
2,000,000 barrels over the two years). The manager agrees to receive the market
price per barrel in one year and in two years. He also agrees to pay the swap price of
N18,367/barrel at each settlement date. If the spot price of oil in one year is
N18,468, what is the cash flow at the first settlement to (+) or from (-) the
manager?
A. - N202,000,000
B. + N202,000,000
C. - N101,000,000
D. + N101,000,000
Total = 40 marks
Question 2 – Derivative Valuation and Analysis
Explain the advantages and disadvantages to a call buyer of closing out a position prior to
expiration rather than holding it all the way until expiration.
(3 marks)
Question 3 – Portfolio Management
XYZ stock price and dividend history are as follows:
Year
2010
2011
2012
Beginning of year
price
(N)
100
120
90
Dividend paid at
year – end
(N)
4
4
4
What is the arithmetic and geometric average time-weighted rates for an investor in the
company?
(4 marks)
Question 4 – Commodity Trading and Futures
What factors must one consider when deciding on the appropriate underlying asset for a
hedge?
(3 marks)
Question 5 – Derivative Valuation and Analysis
Consider Call A and Put A both with exercise price of N70 and on the same stock. They
both have maturity of 90 days. The stock price is currently N60 with volatility of 0.40 and
risk free rate is 6%.
5(a) Calculate the missing values labeled (i) to (iv) in the table below:
Call A
Put A
Price
1.83
(i)
Delta
0.2734
(ii)
Gamma
0.0279
(iii)
Theta
-8.9173
-4.7790
Vega
(iv)
9.9144
Rho
3.5985
-13.4083
(4 marks)
5(b) Consider a straddle comprising of Call A and Put A. Compute the price and draw the
payoff diagram for this straddle.
(3 marks)
5(c)
Consider Call A. As noted above, the current stock price is N60, create a deltaneutral portfolio consisting of a short position of one call and the necessary number
of shares.
(2 marks)
5(d) Consider Call A and Put A from above. Assume that you create a portfolio that is
short one call and long one put. What is the delta of this portfolio? Can you find the
delta without computing? Explain. Assume that one share is added to the short
call/long put. What is the delta of the entire portfolio?
(2 marks)
5(e) Consider Call B written on the same stock as Call A but with exercise price of N50. All
other factors are the same. The following values have been correctly computed for
Call B:
Price
N11.64
Delta
0.8625
Theta
-7.7191
Required:
5e1)
Form a long bull spread with Calls from these two instruments.
5e2) What is the price of the spread and what is the delta?
(2 marks)
(2 marks)
Question 6 – Portfolio Management
You have just completed the institute’s final examinations and you have landed a dream
job as a portfolio manager. Your first task is to assess the performance of two funds within
your company. You are provided with the following historical performance data for the two
funds, a market index and the 90-day T-bill are provided in the table below
Investment
vehicle
Fund 1
Fund 2
Market index
90-day T-bill
Average rate
of return
(%)
26.40%
13.22
15.71
6.20
Standard
deviation
(%)
20.67%
14.20
13.25
0.0
Beta
R2
1.351
0.905
0.751
0.713
.
Hint:
(i)
Overall Performance = Selectivity
+
Risk
[Ra – RFR] = [Ra – Rx(βa)] + [ Rx(βa) – RFR]
(ii)
Selectivity
Diversification
Ra - Rx(βa) = Net Selectivity + [Rx(σ(Ra)) - Rx(βa)]
Required:
6(a) Compute the Fama overall performance for both funds.
(2 marks)
6(b) What is the required return for risk for both funds?
(2 marks)
6(c) For both funds, compute the measure of:
6c1) Selectivity.
(2 marks)
6c2) Diversification.
(2 marks)
6c3) Net selectivity.
(2 marks)
6(d) Explain the meaning of the net selectivity measure and how it helps you evaluate
investor performance. Which fund had the best performance?
(2 marks)
6(e) Your next task concerns the under-listed portfolio of an investor in an equilibrium
market. Fifty percent of the portfolio is invested in risk-free asset and the balance in
the four assets below:
Asset
A
B
C
D
Expected
Return
7.6%
12.4%
15.6%
18.8%
Beta
0.2
0.8
1.2
1.6
Invested in
Asset
10%
10%
10%
20%
Required:
6e1)
Compute the current beta and expected return of the portfolio.
(4 marks)
6e2)
Assume that you want an expected return of 12% and intend to obtain it by
selling risk-free asset and using the proceeds to buy the market portfolio in
the revised portfolio.
(4 marks)
Question 7 – Commodity Trading and Futures
Today is June 30. You have an anticipated liability of N10 million due to December 31. To
fund this liability, you plan to sell part of your store of gold. You have the following data to
work with.
Delivery
month
Cash price
Aug
Dec
Settle
(N)
29,300
29,740
30,200
Risk free rate*
(%)
5%
6%
* Rates are continuously compounded.
Required:
7(a) What is the basis for the December futures contracts.
(2 marks)
7(b) Is the market normal or inverted? Explain.
(2 marks)
7(c) You decided to sell gold futures using the December futures in order to lock in the
price. Analyse how this transaction eliminates price risk.
(3 marks)
7(d) Apart from selling gold futures, what other alternatives are available for eliminating
price risk?
(4 marks)
7(e) At what August and December futures prices would you be indifferent between the
alternatives?
(4 marks)
FORMULAE
1)
Black and Scholes Options pricing model:
;
2)
2)
3)
4)
General cost of carry relationship:
Continuous time cost of carry relationship:
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:
9)
10)
Binomial Option Valuation Model:
;