| Exam Guide
(c) Here you have a cap level (e.g. the payoff has a maximum value). If the index level at
maturity exceeds Imax, the payoff is constant.
In addition to the actions in (a) above, the bank would sell S&P500 calls (same
number as long calls) with a strike price which is higher than the Index level at
starting date. In other words, the proceeds (after buying the zero-coupon bond) are
invested in bull call spreads (lower strike price = Index level at starting date) instead
of only long calls.
C
Isd
payoff at maturity
Index level
Imax
(d) In the second version with the cap level you receive money for the short calls (e.g. one
call spread is cheaper than one long call), so you can buy more call spreads (second
version) than long calls (first version). Thus the participation rate P is higher in the
second version until the index level at maturity does not exceed a certain value Ibe, as
you can see in the following graph.
payoff at maturity
Imax
version 2
Ibe
C
Isd version 1
Index level
Exam Guide
(e) Yes, it has an impact. If a lower Imax is chosen, the call spread is cheaper (you receive
more money for the short call), so you can buy more call spreads. Therefore the
participation rate is higher (but the cap level is lower). Correspondingly, you have a
lower P with a higher cap level if a higher Imax is chosen.
Question 6: Portfolio Management
(a) The more efficient the market is, the lower the IR (which is an expression of the
active manager’s skills) will be. Theory would therefore dictate that allocation to
individual active managers be decreased, and, as a result, allocation to passive
managers would increase.
(b) Allocations to individual managers would be as follows:
A: (20/2) ′ (0.20/10.0) = 0.20
B: (20/2) ′ (0.20/8.0) = 0.25
C: (20/2) ′ (0.10/5.0) = 0.20
P: 1 – (0.20 + 0.25 + 0.20) = 0.35
(c) When there is a positive correlation between excess returns, the combined tracking
error of the two will be larger than when they are mutually independent and as a
result, the IR will be smaller. This would dictate a reduction in allocations to A and
B. The allocation to C would not change because it is independent of A and B. The
reduction in allocations to A and B would therefore result in an increase in the
allocation to P.
(d) Generally speaking, the larger the amounts involved, the lower the returns from
active investments, for several reasons: there are limits to the number of stocks
providing a , high-volume trading will have a “market impact”; and costs will
otherwise rise as well. Therefore, if one increases allocations (amounts under
management) according to past IRs, there is a chance that the a will be lower than in
the past.
Question 7: Portfolio Management
The main problem as soon as the portfolio has been constructed is the potential monthly
rebalancing needed in order to realign your portfolio with the benchmark. In fact if the
50%/50% weighting is valid at the beginning of a month, there is very little chance that
this weighting scheme will still be same after one month (unless performances of SMI and
MSCI Europe are exactly the same). The index will automatically and without any cost be
realigned towards the initial weights, while the portfolio will have to bear the transaction
costs for such regular rebalancing.
There will be a negative drag on the relative performance due to transaction costs.
Furthermore, there is a danger of a high turnover when adjusting on a monthly basis if
markets tend to exhibit trend reversal performance in the long run.
On the positive side, a regular turnover can help the manager to adapt smoothly to the
continually changing structure of the benchmark.
Exam Guide
Question 8: Portfolio Management
(a) SV: 2 + (0.85 ′ 8) + (0.8 ′ –2) + (1 ′ 0.1) = 7.3%
SG: 2 + (0.95 ′ 8) + (1.3 ′ –2) + (1 ′ 0.1) = 7.1%
LV: 2 + (0.90 ′ 8) + (2 ′ –2) + (8 ′ 0.1) = 6.0%
LG: 2 + (1.10 ′ 8) + (3 ′ –2) + (10 ′ 0.1) = 5.8%
We choose the portfolio Small Value.
(b) either: 2 + (1 ′ 8) + (2.405 ′ –2) + (8.3 ′ 0.1) = 6.02% or:
7.3 ′ 5/100 + 7.1 ′ 5/100 + 6 ′ 40/100 + 5.8 ′ 50/100 = 6.02%
The market is a weighted average, thus its return is bounded by the 4 portfolios.
(c) SV: 2 + (0.85 ′ (10 – 2) = 8.8%
SG: 2 + (0.95 ′ 8) = 9.6%
LV: 2 + (0.90 ′ 8) = 9.2%
LG: 2 + (1.10 ′ 8) = 10.8%
The competitor chooses the portfolio Large Growth.
(d) where x = market beta
x1 + x 2 = 1
(x1 ′ 0.85) + (x2 ′ 1.1) = 1
so if x2 = 1 – x1 then,
(x1 ′ 0.85) + ((1 – x1) ′ 1.1) = 1
thus x1 = 0.40 and x2 = 0.60.
The other competitor puts 40% of her portfolio in Small Value and 60% in Large
Growth. |
