CHARTERED INSTITUTE OF
STOCKBROKERS
ANSWERS
Examination Paper 2.3
Derivatives Valuation Analysis
Portfolio Management
Commodity Trading and Futures
Professional Examination
March 2013
Level 2
1
SECTION A: MULTI CHOICE QUESTIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
B
B
B
C
A
B
B
A
A
B
A
A
A
C
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
D
D
A
C
A
A
B
A
C
C
D
B
B
B
B
31
32
33
34
35
36
37
38
39
40
A
A
A
B
D
D
C
C
B
D
(40 marks)
SECTION B: SHORT ANSWER QUESTIONS
Question 2 – Derivative Valuation and Analysis
When a call is purchased, the buyer pays for both the time value and the intrinsic value
of the option. As the call gets closer and closer to expiration, it will lose its time value.
As expiration of the call, the holder collects only the intrinsic value. By selling the call
prior to expiration, the holder is able to recover some of the time value previously
purchased. For a given stock price, this increases the profit or decreases the loss;
however, the shorter the holding period, the less the stock price has to move upward.
The tradeoff in deciding whether to sell an option early is between cutting the loss of
time value and giving the stock enough time to make a substantial move.
(3 marks)
Question 3 – Portfolio Management
Time – weighted average returns are based on year-by-year rates of return:
120 + 4 -1 = 24%
2010 – 2011:
100
90 + 4
-1 = - 21.67%
120
24 – 21.67-1 = 1.17%
Arithmetic mean =
2
Geometric mean: [(1.24) x (1 – 0.2167)] 0.5 -1
2011 – 2012:
= - 1.45%
(4 marks)
2
Question 4 – Commodity Trading and Futures
I.
The most important factor is to have a strong correlation between the spot and
futures prices.
II.
It is also important that the futures contract have sufficient liquidity. If the
contract is not very liquid, then the hedger may be unable to close the position at
the appropriate time without making a significant price concession. This weakens
the effectiveness of the hedge by making the futures prices less dependent on the
spot market and the normal cost-of-carry relationship between the two markets.
III.
In addition, the contract should be correctly priced or at least priced in favor of
the hedger. For example, a short (long) hedger would not want to sell (buy) a
futures contract that was underpriced (overpriced) as this would reduced the
hedging effectiveness.
(3 marks)
SECTION C: COMPLUSORY QUESTIONS
Question 5 – Derivative Valuation and Analysis
5(a)
(i)
(ii)
(iii)
(iv)
5(b)
From put – call parity:
Call + PV (E) = put + stock
1.83 + 7.e-0.06 x 90/365 = P + 60
P = N10.80
Delta of put = 0.2734 – 1 = -0.7266
Gamma of call and put on the same stock having the same exercise price
and the same expiry are the same, i.e., 0.0279
Like gamma, the vega of call and that of put are the same, i.e, 9.9144
Straddle is a combination of long call and long put
Price
=
1.83 + 10.870
= 12.63
Profit or loss (N)
Payoff diagram
Exercise price
N70
●
Stock price (N)
3
5(c)
Let x represent the number of stock needed. The portfolio is made up as follows:
Security
Qty
Delta/unit
Total
Call
1
-0.2734*
-0.2734
Stock
x
1
x
(* short call has negative delta)
To be delta neutral:
x – 0.2734 = 0,
x = 0.2734 share
Total cost:
Long stock
Short call
= 0.2734(60)
= -1(1.83)
=
=
16.40
-1.83
14.57
(Delta of short stock = -1)
5(d)
The delta of the portfolio is -1, made up as follows:
One short call
= - 0.2734
One long put (0.2734 - 1)
= - 0.7266
Total
- 1.0000
This is necessarily true, because the delta of call is N(d1), the delta of the put is
N(d1) – 1. The delta of the portfolio is:
One short call
- N (d1)
One long put
N (d1) – 1
Total
-1
If a long share of stock is added to the portfolio, the delta will be zero because
the delta of a share is always 1.0
5(e1)
5(e2)
Long bull spread with call consists of buying the call with the lower exercise
price (call B) and selling the call with the higher exercise price (Call A)
Total cost = 11.64 – 1.83 = N9.81
The delta is deltaB – deltaA = 0.8625 – 0.2734 = 0.5891
Question 6 – Portfolio Management
6(a)
Overall performance
Fund 1 = 26.40% - 6.20%
= 20.20%
Fund 2 = 13.22% - 6.20%
= 7.02%
6(b) Required return
Total return: Rf + β (Rm - Rf) = 6.20 + β (15.71 – 6.20)
Return for risk = β (15.71 – 6.20)
Therefore for Fund 1=
1.351 x 9.51 = 12.85%
4
Fund 2 =
0.905 x 9.51 = 8.61%
Alternative Approach:
Return for risk = Total return minus Risk free rate
Fund 1 = 6.20 + 9.51 (1.351) = 19.05%
(6.20%)
12.85%
Fund 2 = 6.20 + 9.51 (0.905) = 14.81%
(6.20%)
8.61%
6(c1)
Selectivity1 = 20.2% - 12.85% = 7.35%
Selectivity2 = 7.20% - 8.61% = - 1.59%
6(c2)
Ratio of total risk = σI / σm
Fund 1
Fund 2
= 20.67 / 13.25
= 14.20 / 13.25
= 1.56
= 1.07
Required return, based on total risk:
Fund 1 = 6.20 + 1.56 (9.51)
= 21.04%
Fund 2
= 6.20 + 1.07 (9,.51)
= 16.38%
Diversification1
Diversification2
=
=
21.04% - 19.05%
16.38% - 14.81%
= 1.99%
= 1.57%
Net selectivity
= Selectivity – Diversification
6(c3)
Fund1 = 7.35% - 1.99%
Fund2 = -1.59% - 1.57%
= 5.36%
= - 3.16%
6(d)
Even after accounting for the added cost of incomplete diversification, fund is
performance was above the market line (best performance ), while Fund2 fall
below the line
6(e1)
5
The portfolio weight is a weighted average of the beta factors of the various
assets.
Security
Beta (β)
A
0.2
B
0.8
C
1.2
D
1.6
Risk-free
0
Portfolio beta
Weight (w) Weighted Average (β x w)
0.10
0.02
0.10
0.08
0.10
0.12
0.20
0.32
0.50
0.00
0.54
We need to determine the risk-free rate and market return. Since the investor
operates in an equilibrium market, it means all the assets are on the security
market line, i.e., required return and expected return for each security are the
same. We can use the information on ANY two of the assets to formulate the
following
SML equations:
Asset A: 7.6 =
Asset B: 12.4 =
Simplified:
7.6
=
12.4 =
(1) – 4:1.9
=
(2) – (3): 10.5
Rf + 0.2 (Rm - Rf) ……… (1)
Rf + 0.8 (Rm - Rf) ……….(2)
0.8Rf + 0.2Rm …….…… (1)
0.2Rf + 0.8Rm ……….… (2)
0.2Rf + 0.05Rm …………(3)
= 0.75Rm
Rm = 14%
Subst. Rm in (3)
1.9 = 0.2Rf + 0.05 (14)
Rf = 6%
The required return (Rp)
= 6 + 0.54 (14 – 6) = 10.32%
Rp
6(e2)
Let E = the risk-free asset
M = market portfolio
Security
A
B
C
D
E
F
Return
7.6
12.4
15.6
18.8
6.0
14.0
0.10
0.10
0.10
0.20
0.5-k
K
Weight
=
This should equal 12% i.e. 10.32 + 8K = 12
K = 0.21%
The revised portfolio weights are
A
10%
B
10%
C
10%
D
20%
E (50-21)
29%
F
21%
Question 7 – Commodity Trading and Futures
Weighted Average
0.76
1.24
1.56
3.76
3-6k
14k
10.32+8K
6
7(a)
The basis is computed as the cash price minus the futures contract:
Basis = N29,300 – 30,200 = - N900
(2 marks)
7(b)
In a normal market, the prices for the more distant contracts are higher than the
prices for the nearby contracts to the more distant contracts.
In this question, prices increase the more distant the delivery data, so the market
is normal.
(2 marks)
7(c)
Selling gold futures
Sell gold via the December futures contract. This effectively locks in a December
selling price of N302.
7(d)
There are several alternatives for eliminating price risk.
Alternative 1: Sell gold via the December futures contract. This effectively locks
in a December selling price of N302.
Alternative 2: Sell gold today in the spot market and invest the proceeds in the 6month T-bill.
Alternative 3: Sell gold today in the spot market and invest the proceeds in the 2month T-bill. At the same time, buy gold by using the August futures contract and
sell gold using the December futures contract.
The most attractive alternative is the one which allows us to meet the N10 million
liabilities while selling the least amount of gold.
(2 marks)
7(d)
Assuming negligible costs other than the time value of money, the following
relationship must hold for you to be indifferent between the alternatives.
F (0, T) = S0erT
For the December contract, the futures price at which you are indifferent between
alternative 1 and 2 is:
F (0, DEC) = 29,300e0.06 x 0.5 = N30,192
The August futures price at which you are indifferent between alternatives 1 and
3 is: F (0, AUG) = 29,300e0.05 x 2/12 = N29,545
7