CHAPTER 17
EQUITY-PORTFOLIO MANAGEMENT
Passive versus Active Management
Passive Equity Portfolio Management (Long-term buy-and-hold
strategy)
Active Equity Portfolio Management (Attempts to outperform a
passive benchmark portfolio adjusted for risk)
Overview of Passive Equity Portfolio Management Strategies
Indexing Portfolio Strategy
Passive Index Portfolio
Full replication
Sampling
Quadratic optimization or programming
Overview of Active Equity Portfolio Management Strategies
Practical Difficulties of Active Management
Higher transaction costs and higher risk
Key to Success
Be consistent
Minimize trading activity
Three Strategies
Time the market
Catch the "hot" concept
Stockpicking
Global Investing
Overweight/underweight countries in portfolio
Industry rather than country approach
Sector rotation strategy
Styles (style investing)
Does Style Matter?
Timing Between Styles
Value versus Growth
266
Expectational Analysis and Value/Growth Investing
Futures and Options in Equity Portfolio Management
Modifying Portfolio Risk and Return: A Review
The Use of Futures in Asset Allocation
The Use of Derivatives in Equity Portfolios
Hedging Portfolio Inflows
Hedging Portfolio Outflows
The Standard & Poor's 500 Index Futures Contract
Determining How Many Contracts to Trade to Hedge a
Deposit or a Withdrawal
Determining How Many Contracts to Trade to Adjust
Portfolio Beta
Using Futures in Passive Equity Portfolio Management
Using Futures in Active Equity Portfolio Management
Modifying Systematic Risk
Modifying Unsystematic Risk
Modifying the Characteristics of an International Equity
Portfolio
Taxable Portfolios
Tax Efficient Investing Strategies
Ways to Diversify Concentrated Portfolios
Asset Allocation Strategies
Integrated Asset Allocation
Strategic Asset Allocation
Tactical Asset Allocation
Insured Asset Allocation
Selecting an Allocation Method
267
CHAPTER 17
Answers to Questions
1.
Passive portfolio management strategies have grown in
popularity because investors are recognizing that the
stock market is fairly efficient and that the costs of an
actively managed portfolio are substantial.
2.
Numerous studies have shown that the majority of portfolio
managers have been unable to match the risk-return
performance of stock or bond indexes.
Following an
indexing portfolio strategy, the portfolio manager builds
a portfolio that matches the performance of an index,
thereby reducing the costs of research and trading.
In an indexing strategy, the portfolio manager's evaluation is based upon how closely the portfolio tracks the
index or "tracking error," rather than a risk-return
performance evaluation.
3.
Stock-market index portfolios are probably more difficult
to construct and maintain because securities must
frequently be bought and sold in order to reflect cash
inflows and outflows, company mergers and acquisitions,
etc..
4.
Three basic techniques exist for constructing a passive
portfolio: (1) full replication of an index is where all
securities in the index are purchased proportionally to
their weight in the index; (2) in sampling the portfolio
managers purchases only a sample of the stocks in the
benchmark index; and (3) quadratic optimization or
programming techniques utilize computer programs that
analyze historical security information in order to
develop a portfolio that minimizes tracking error.
5.
There are tradeoffs between using the full replication
and the sampling method.
Fully replicating an index is
more difficult to manage and has higher trading commission
costs, when compared to the sampling method.
However,
tracking error occurs from sampling, which should not be
the case in the full replication of the index.
6.
There are a number of active management strategies discussed in the chapter including sector rotation, the use
of factor models, quantitative screens, and linear
programming methods.
268
Following a sector rotation strategy, the manager overweights certain economic sectors, industries or other
stock attributes in anticipation of an upcoming economic
period or the recognition that the shares are undervalued.
Using a factor model, portfolio managers examine the
sensitivity of stocks to various economic variables. The
managers then "tilt" the portfolios by trading those
shares most sensitive to the analyst's economic forecast.
Through the use of computer databases and quantitative
screens, portfolio managers are able to identify groups of
stocks based upon a set of characteristics.
Using linear programming techniques, portfolio managers
are able to develop portfolios that maximize objectives
while satisfying linear constraints.
7.
Managers attempt to add value to their portfolio by: (1)
timing their investments in the various markets in light
of market forecasts and estimated risk premiums; (2)
shifting funds between various equity sectors, industries,
or investment styles in order to catch the next "hot"
concept; and (3) stockpicking of individual issues (buy
low, sell high).
8.
The portfolio manager could emphasize or overweight, relative to the benchmark, investments in natural resource
stocks. The portfolio manager could also purchase options
on natural resource stocks.
9.
The job of an active portfolio manager is not easy. In
order to succeed, the manager should maintain his/her
investment philosophy, "don't panic." Since the transaction costs of an actively managed portfolio typically
account for 1 to 2 percent of the portfolio assets, the
portfolio must earn 1-2 percent above the passive
benchmark just to keep even.
Therefore, it recommended
that a portfolio manager attempt to minimize the amount of
portfolio trading activity. Numerous portfolio turnovers
will result in diminishing portfolio profits due to
growing commission costs.
10.
CFA Examination Level III (1992)
10(a). The following four factors favor active management
269
1.Economic diversity. The diversity of the Otunian economy
across various sectors may offer the opportunity for
the active investor to employ top down sector rotation
strategies.
2. High transactions costs. Very high transaction costs
may
discourage trading activity
by international
investors and lead to inefficiencies that can be
exploited by active investors.
3. Capital restrictions. Restrictions on capital market
flows can lead to market inefficiencies that can be
exploited.
4. Developing economy and markets. Developing or emerging
markets
have inefficiently priced securities and
rapidly growing economies. This allows opportunities
for active managers.
The following factors favor indexation.
1. High transaction costs will lead to a bias against
active trading and more support for indexation.
2. Settlement problems. Would discourage active trading
and favor indexing.
3. Restrictions on capital flows. This can be viewed as a
factor supporting indexing because it can diminish
the appeal of active trading because it limits
repatriation of profits.
4. Financial disclosure and accounting standards. Wide
availability of reliable financial information leads
to greater market efficiency and thus supports
indexing.
10(b). Short term market inefficiencies and long term prospects
for the economy would support active management.
Indexation is supported by high transaction costs,
settlement problems and restrictions on capital flows.
A strong argument can be made for indexing or active
management.
11.
Investment style involves constructing the portfolio in
such a way as to capture one or more characteristics of
equity securities.
270
Value stocks are stocks that appear to be underpriced
because their price/book or price/earnings ratio is low or
their dividend yield is high, when compared to the rest of
the market. Growth stocks, on the other hand, are stocks
that demonstrate above-average earnings per share increase
and usually have above-average ratios of price/book and
price/earnings.
12.
Style identification is important for portfolio managers
and their clients for the following reasons: (1)
investment style communicates information to clients about
the manager's focus, area of expertise, and stock
evaluation methods; (2) determining an portfolio manager's
style is useful for measuring his/her performance relative
to a benchmark; (3) style identification allows an
investor to properly diversify his/her portfolio; and (4)
style investing allows control of the total portfolio to
be
shared
between
the
investment
managers
and
a
knowledgeable sponsor who hires investment managers.
13.
CFA Examination Level III (1994)
In essence the EMH maintains that the only risk that is
priced is systematic risk and thus it would be impossible
for investors to pick stocks that offer returns that
exceed that predicted by the CAPM. The finding that value
stocks outperform growth stocks could be viewed as a
challenge to the EMH because it implies that P/E and P/BV
can be used to predict returns. According to EMH (that is
the CAPM), it is only beta or systematic risk that can be
used to predict returns. However if you view P/E and P/BV
as proxies for risk then the EMH is not necessarily
contradicted.
14.
Studies have shown that over the long run, on average,
value stocks offer somewhat higher returns than growth
stocks. These empirical findings can be explained by:
(1) The empirical studies have focused on before-tax
returns of value and growth stocks.
Value stocks have
higher dividends and lower expected capital gains than
growth stocks.
(2) Value stocks have higher risk premiums, that is, lower
comfort zone for investors. Specifically, uncertain about
the future leads investors to perceive value stocks as
more riskier and less desirable.
Therefore, although an investor should probably consider
value stocks as part of any diversified portfolio, they
should also consider other investment styles in order to
properly diversify his/her portfolio.
271
15.
CFA Examination Level III (1995)
A higher P/E need not imply overvaluation because
1.It may simply reflect the fact that earnings are
expected to grow faster and the market is reflecting
this higher growth expectation.
2. It may reflect the fact that the companies operate in
different industries.
3. It may reflect the fact that the industries the
companies operate in are at different stages in the
life cycle – younger industries tend to have higher P/E
ratios.
A higher P/B need not imply overvaluation because
1.It may be because of off-balance sheet assets that are
relected in the stock price but not the book value for
Newsoft.
2. Newsoft may be using its assets efficiently. This would
justify a higher P/B.
3. Capital Corp. may have
inflate book value and
relative to Newsoft.
16.
obsolete assets that would
thus give it a lower P/B
One skill that separates a bad value-stock portfolio
manager from a good one is knowing when to buy a stock.
Buying a stock too early results in poor stock
performances as the bad or disappointing news continues.
A value manager who picks the right time to buy a stock
enjoys the benefits of good news about the firm and from a
rising stock price as others jump on the bandwagon and buy
the stock.
One skill that separates a good growth portfolio manager
from a bad one is knowing when to sell. The bad growth
manager remains optimistic about the firm for too long or
believes that any bad news will soon be replaced by good
news.
Bad growth portfolio managers hold onto their
stocks so long that previously earned returns shrink or
disappear.
17.
Completeness funds (or customized passive portfolios) are
constructed to complement active portfolios that do not
cover the entire market.
272
18.
CFA Examination Level III (1986)
18(a). A futures contract is an agreement to buy or sell an asset
at a future date, at a price fixed today. An option on
futures contract gives the buyer the right but not the
obligation to buy or sell the futures contract at a future
date at a price fixed today.
Essentially futures have symmetrical impact on portfolio
returns. That is a long position in futures increases
exposure to the asset whereas a short position reduces
exposure to the asset. Because an option can expire
without being exercised, they do not have a symmetrical
impact on returns.
18(b). Buying a put while owning the asset has the effect of
limiting downside loss, while still maintaining exposure
to upside gain (protective put). Writing a covered call
limits upside gain but does not limit downside loss.
19.
Hedge ratio is the appropriate number of futures contracts
that must be bought or sold in order to hedge a position.
Futures contracts are used in order to maintain the
desired exposure to stocks (in this case) when the
portfolio experiences a cash inflow or outflow.
20.
Equity portfolio management strategies are classified as
either passive or active. Unlike the immunization of bond
portfolios, no middle ground exists between the two
strategies.
Some have argued that an active/passive
portfolio
management
style
does
exist
for
equity
portfolios, however most people believe such styles really
reflect active management philosophies.
21.
An after tax efficient frontier is shifted down because
investors have lower returns after paying taxes. The shift
left occurs because the tax code allows capital losses to
be netted against capital gains, consequently the
variation in returns over time is reduced.
22.
If life expectancy is long then the tradeoff between tax
consequences and return potential from investing in a
diversified portfolio may make rebalancing a poorly
diversified portfolio appropriate. If life expectancy is
short then the better approach may be to simply pass the
stock to heirs on a stepped up basis.
23.
A value manager will have a lower cost basis than a growth
manager who is likely to pay a relatively higher price in
the expectation of high future returns. The value manager
will have larger capital gains taxes, and thus will need
273
to have a larger expected return advantage to earn higher
after tax returns relative to the growth manager.
24.
Taxes give rise to the following complications
1. Asset reallocations will trigger capital gains and thus
reduce wealth.
2. Periodic rebalancing of the portfolio will also trigger
taxable events.
3. Markowitz mean-variance optimization is indifferent to
the investor’s time horizon. Thus depending on life
expectancy, rebalancing may or may not be appropriate.
25.
A manager of an actively managed portfolio must consider
the following factors before executing a trade
1. Securities sold at a gain will generate capital gains
taxes that will erode portfolio wealth.
2. The new security needs to have an expected return
advantage to recover the tax cost.
3. The size of the expected return advantage will depend
on the expected length of the holding period and the
cost basis.
26.
The five tax-efficient investing strategies are
1. Buy and hold, since unrealized capital gains are not
taxed.
2. Use loss harvesting by netting losses against gains.
3. Use options to convert short-term capital gains into
long-term
capital
gains
for
more
favorable
tax
treatment.
4. Use tax-lot accounting where shares with the highest
cost-basis are sold first.
5. Buy growth stocks and focus on capital appreciation
rather than income.
27.
Tax efficient ways to diversify a concentrated portfolio
are
1. Borrow against the value of shares.
2. Use a collar strategy where you purchase a put with a
strike below the current stock price and sell a call
with a strike above the current stock price.
3. Use variable prepaid forwards.
4. Completion funds. Slowly liquidate the portfolio and
invest proceeds in a diversified portfolio.
5. Charitable strategies. Donate appreciated stock.
28.
An option collar
274
Profit
Stock at expiration
29.
To convert a short-term capital gain into a long terms
gain, you can write an at-the-money or out-of-the-money
call option. The strike price becomes the maximum selling
price should the stock continue to rise but the option
premium provides some downside protection in case of a
price decline. As long as the price decline is not severe,
the combined stock option position will allow the investor
to maintain some profits for lon-term capital gains
treatment.
30.
The four asset allocation strategies are: (1) integrated
asset allocation strategy, which relies on current market
expectations; (2) strategic asset allocation strategy,
which utilizes long-run projections; (3) tactical asset
allocation
strategy,
which
assumes
that
investor's
objectives and constraints remain constant over the
planning horizon; and (4) insured asset allocation
strategy, which presumes changes in investor's objectives
and constraints as market conditions change.
275
CHAPTER 17
Answers to Problems
1.
2.
Month
----Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Sum
$50 million x 1.2 x 1.10 = 66 million
Portfolio
(Ri)
--------5.0%
-2.3
-1.8
2.2
0.4
-0.8
0.0
1.5
-0.3
-3.7
2.4
0.3
---2.9
Ri - E(Ri)
---------4.7583
-2.5417
-2.0417
1.9583
0.1583
-1.0417
-0.2417
1.2583
-0.5417
-3.9417
2.1583
0.0583
S&P 500
(Rm)
------5.2%
-3.0
-1.6
1.9
0.1
-0.5
0.2
1.6
-0.1
-4.0
2.0
0.2
---2.0
E(Ri) = 2.9/12 = .2417
Rm - E(Rm)
---------5.0333
-3.1667
-1.7667
1.7333
-0.0667
-0.6667
0.0333
1.4333
-0.2667
-4.1667
1.8333
0.0333
[Ri - E(Ri)] x
[Rm - E(Rm)]
------------23.9500
8.0488
3.6071
3.3943
-0.0106
0.6945
-0.0080
1.8035
0.1445
16.4239
3.9568
0.0019
------62.0067
E(Rm) = 2.0/12 = .1667
Vari = 60.3490/12 = 5.0291
______
SDi = \/5.0291 = 2.2426
Varm = 64.7865/12 = 5.3989
______
SDm = \/5.3989 = 2.3236
COVi,m = 62.0067/12 = 5.1672
5.1672
Ri,m = ---------------- = .9916
(2.2426)(2.3236)
5.1672
Bi = ------ = .9571
5.3989
276
R2 = (.9916)2 = .9833
alpha = E(Ri) - (Bi x E(Rm))
= .2417 - (.9571)(.1667) = .0822
With a R2 value of .9833, one can conclude that the
passive portfolio did closely track the S&P 500 benchmark.
3.
The annual geometric mean for the equity risk premium is
6.7 percent.
Trading costs of 1.5 percent is equal to
22.39% of the equity risk premium.
4(a). 1,000,000(1.06)n = 800,000(1.08)n
ln(1.25) = (n)ln(1.08) – (n)ln(1.06)
n = 11.93 years
4(b). 1,000,000(1.06)n = 800,000(1.075)n
ln(1.25) = (n)ln(1.075) – (n)ln(1.06)
n = 15.87 years
4(c). 1,000,000(1.06)n = 800,000(1.065)n
ln(1.25) = (n)ln(1.065) – (n)ln(1.06)
n = 47.45 years
5.
You could sell a put or but a call. The effective
repurchase prices are shown below for various stock prices
Stock Price
$43
$50
$57
6.
Sell
55 –
55 –
57 –
Put
6 = $49
6 = $49
6 = $51
Buy Call
43 + 7 = $50
45 + 7 = $52
45 + 7 = $52
The value of the S&P 500 futures contract is equal to $500
times the S&P 500 index value.
$500 x 1010.50 = $505,250
$3 million
6(a). ---------- x 1.05 = 5.94 contracts
$505,250
6 contracts (rounded) would be purchased to hedge cash
277
inflow.
-$8 million
6(b). ----------- x 1.05 = -15.83 contracts
$505,250
16 contracts would be sold to hedge cash outflow.
F x $505,250
7(a). 1.15 = (.95 x 1.05) + ------------ x 1.0
$100 million
1.15 = .9975 + .0050525 F
.1525 = .0050525 F
30.18 = F
(31 contracts must be purchased)
F x $505,250
7(b). 1.30 = (.95 x 1.05) + ------------ x 1.0
$100 million
1.30 = .9975 + .0050525 F
.3025 = .0050525 F
59.87 = F
7(c).
(60 contracts must be purchased)
F x $505,250
.95 = (.95 x 1.05) + ------------ x 1.0
$100 million
.95 = .9975 + .0050525 F
-.0475 = .0050525 F
-9.40 = F
7(d).
(10 contracts must be sold)
F x $505,250
0 = (.95 x 1.05) + ------------ x 1.0
$100 million
0 = .9975 + .0050525 F
-.9975 = .0050525 F
-197.43 = F
(198 contracts must be sold)
278
8(a). One S&P 500 futures contract = $500 x 985.37 = $493,685
8(b).
F x $493,685
0 = (1.0 x 1.3) + ------------ x 1.0
$1.5 million
0 = 1.3 + .3291 F
-3.950 = F
In order to make the portfolio market neutral, it is
necessary to sell 4 (rounded) futures contracts.
8(c). If the market drop by 10 percent, S&P 500 goes from 985.37
to 886.83.
i. In futures market
Sold 4 S&P 500 contracts @ $500 x 985.37
= $1,970,740
Bought 4 S&P 500 contracts @ $500 x 886.83 = 1,773,660
--------Profit in futures
$ 197,080
ii. Unhedged stock portfolio
A 10 percent market decline equals a 13% portfolio decline
assuming a beta of 1.3.
$1,500,000 x (.10 x 1.3) = ($195,000) loss in portfolio
value
$1,500,000 - $195,000 = $1,305,000 new portfolio value
iii. Hedged portfolio
Profit in futures
= $197,080
Loss in portfolio value = ($195,000)
---------Profit
$2,080
A perfectly hedged portfolio should be market neutral,
that is, no profits or losses. In this case, a small
profit occurred due to rounding.
279
8(d). If the market rises by 10 percent, S&P 500 goes from 985.37
to 1083.91
i. In futures market
Sold 4 S&P 500 contracts @ $500 x 985.37
= $1,970,740
Bought 4 S&P 500 contracts @ $500 x 1083.91= 2,167,820
--------Loss in futures
($197,080)
ii. Unhedged stock portfolio
A 10 percent market rise equals a 13% portfolio rise
assuming a beta of 1.3.
$1,500,000 x (.10 x 1.3) = $195,000 gain in portfolio
value
$1,500,000 + $195,000 = $1,695,000 new portfolio value
iii. Hedged portfolio
Loss in futures
= ($197,080)
Gain in portfolio value = ($195,000)
---------Loss
($2,080)
A perfectly hedged portfolio should be market neutral,
that is, no profits or losses. In this case, a small
loss occurred due to rounding.
9(a). One S&P 500 futures contract = $500 x 1051.73 = $525,865
9(b).
F x $525,865
0 = (1.0 x 1.1) + ------------ x 1.0
$2.3 million
0 = 1.1 + .2286 F
-4.81 = F
In order to make the portfolio market neutral, it is
necessary to sell 5 (rounded) futures contracts.
280
9(c). i. In futures market
If the market drop by 10 percent, S&P 500 goes from
1051.73 to 946.56
Sold 5 S&P 500 contracts @ $500 x 1051.73
Bought 5 S&P 500 contracts @ $500 x 946.56
Profit in futures
= $2,629,325
= 2,366,400
--------$ 262,925
ii. Unhedged stock portfolio
A 13% portfolio decline is equivalent to $299,000 loss in
portfolio value ($2,300,000 x .13 = $299,000)
$2,300,000 - $299,000 = $2,001,000 new portfolio value
iii. Hedged portfolio
Profit in futures
= $262,925
Loss in portfolio value = ($299,000)
---------Loss
($36,075)
Because of unsystematic risk the stock portfolio declined
by 13 percent, rather than the 11 percent which was
covered by the hedge (1.1 beta x .10 market decline).
9(d). i. In futures market
If the market increases by 10 percent, S&P 500 goes from
1051.73 to 1156.90
Sold 5 S&P 500 contracts @ $500 x 1051.73
= $2,629,325
Bought 5 S&P 500 contracts @ $500 x 1156.90 = $2,892,250
--------Loss in futures
($262,925)
ii. Unhedged stock portfolio
A 15% portfolio increase is equivalent to $345,000
increase in portfolio value ($2,300,000 x .15 = $345,000)
$2,300,000 + $345,000 = $2,645,000 new portfolio value
281
iii. Hedged portfolio
Loss in futures
= ($262,925)
Gain in portfolio value =
345,000
---------Gain
$82,075
Because of unsystematic risk the stock portfolio increased
by 15 percent, rather than just the 11 percent which was
covered by the hedge (1.1 beta x .10 market decline).
10.
CFA Examination Level III (1999)
The number of futures contracts required is:
N = (value of the portfolio/value of the index futures)
x beta of the portfolio
=
=
=
=
[$15,000,000 / (1,000 x 250)] x 0.88
[$15,000,000 / 250,000] x 0.88
60 x 0.88
52.8 contracts
Selling (going short) 52 or 53 contracts will hedge
$15,000,000 of equity exposure.
11.
CFA Examination Level III (2000)
11(a). Style = B – M
The performance of the representative style index can be
calculated by subtracting the broad market’s return (in
this case the S&P 500 index, M) from the specific style
index return (in this case the Russell 1000 Value index,
B). This provides a more accurate picture of how the
style (value) performed versus the broad market, and any
variance explains how a value oriented portfolio would
differ from the broad market.
11(b)
Stock Selection = P – B
The performance attributable to stock selection is
calculated by subtracting the benchmark index return (in
this case the Russell 1000 Value index, B) from the
actual portfolio return (P). This calculation provides
information on active stock selection within the
portfolio, because the portfolio is being compared to the
specific style benchmark and not to the broad market.
282
Chapter 17
Answers to Spreadsheet Exercises
1.
About 12 years
Single Stock
Value
Return
Year
1000
0.08
Value
1
1080
2
1166.4
3 1259.71
4 1360.49
5 1469.33
6 1586.87
7 1713.82
8 1850.93
9
1999
10 2158.92
11 2331.64
12 2518.17
13 2719.62
14 2937.19
Diversified Stock
Value
800
Return
0.1
Year
Value
1
880
2
968
3
1064.8
4
1171.28
5
1288.41
6
1417.25
7
1558.97
8
1714.87
9
1886.36
10
2074.99
11
2282.49
12
2510.74
13
2761.82
14
3038
283
2.
About 12 years
Single Stock
Value
Return
Year
CG Tax Diversified Stock
2000000
0.2Value
1600000
0.06
Return
0.08
Value
1 2120000
2 2247200
3 2382032
4 2524954
5 2676451
6 2837038
7 3007261
8 3187696
9 3378958
10 3581695
11 3796597
12 4024393
13 4265857
14 4521808
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Value
1728000
1866240
2015539
2176782
2350925
2538999
2742119
2961488
3198407
3454280
3730622
4029072
4351398
4699510
284
3.
About 16 years
Single Stock
Value
Return
Year
CG Tax Diversified Stock
2000000
0.2Value
1600000
0.06
Return
0.075
Value
1 2120000
2 2247200
3 2382032
4 2524954
5 2676451
6 2837038
7 3007261
8 3187696
9 3378958
10 3581695
11 3796597
12 4024393
13 4265857
14 4521808
15 4793116
16 5080703
17 5385546
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Value
1720000
1849000
1987675
2136751
2297007
2469282
2654479
2853565
3067582
3297651
3544974
3810847
4096661
4403910
4734204
5089269
5470964
285
4.
About 48 years
Single Stock
Value
Return
Year
CG Tax Diversified Stock
2000000
0.2Value
1600000
0.06
Return
0.065
Value
1 2120000
2 2247200
3 2382032
4 2524954
5 2676451
6 2837038
7 3007261
8 3187696
9 3378958
10 3581695
11 3796597
12 4024393
13 4265857
14 4521808
15 4793116
16 5080703
17 5385546
18 5708678
19 6051199
20 6414271
21 6799127
22 7207075
23 7639499
24 8097869
25 8583741
26 9098766
27 9644692
28 10223373
29 10836776
30 11486982
31 12176201
32 12906773
33 13681180
34 14502051
35 15372174
36 16294504
37 17272174
38 18308505
39 19407015
40 20571436
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Value
1704000
1814760
1932719
2058346
2192139
2334628
2486378
2647993
2820113
3003420
3198642
3406554
3627980
3863799
4114946
4382417
4667274
4970647
5293739
5637832
6004291
6394570
6810217
7252881
7724319
8226399
8761115
9330588
9937076
10582986
11270880
12003487
12783714
13614655
14499608
15442082
16445818
17514796
18653258
19865719
286
41
42
43
44
45
46
47
48
49
50
51
52
53
54
21805722
23114065
24500909
25970964
27529222
29180975
30931833
32787743
34755008
36840309
39050727
41393771
43877397
46510041
41
42
43
44
45
46
47
48
49
50
51
52
53
54
21156991
22532195
23996788
25556579
27217757
28986911
30871060
32877679
35014729
37290686
39714580
42296028
45045270
47973213
5.
Single Stock
Value
cost
Return 1 to 2
Return > 2
Year
CG Tax Diversified Stock
800000
0.2Value
660000
100000
-0.05
Return
0.06
0.05
Value
1 760000
2 722000
3 758100
4 796005
5 835805.3
6 877595.5
7 921475.3
8 967549.1
9 1015927
10 1066723
Year
Value
1
699600
2
741576
3 786070.6
4 833234.8
5 883228.9
6 936222.6
7
992396
8
1051940
9
1115056
10
1181959
287
6.
Single Stock
Value
cost
Return 1 to 4
Return > 4
Year
7.
CG Tax Diversified Stock
1200000
0.2Value
960000
0
0.1
Return
0.08
0.06
Value
1 1320000
2 1452000
3 1597200
4 1756920
5 1862335
6 1974075
7 2092520
8 2218071
9 2351155
10 2492225
11 2641758
12 2800264
13 2968279
14 3146376
15 3335159
16 3535268
17 3747384
18 3972227
19 4210561
20 4463195
21 4730986
22 5014846
23 5315736
24 5634680
25 5972761
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Value
1036800
1119744
1209324
1306069
1410555
1523399
1645271
1776893
1919044
2072568
2238373
2417443
2610839
2819706
3045282
3288905
3552017
3836179
4143073
4474519
4832480
5219079
5636605
6087534
6574536
Student Exercise.
288