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CFA L3 – Asset Allocation
CFA Level 3 - Asset Allocation
Dynamic Strategies for Asset Allocation Sharpe
1. Buy-and-Hold Strategy
Investment Strategy:
The buy-and-hold strategy maintains an exposure to equities that is linearly related to the
value of equities in general. The strategy involves buying, then holding, an initial mix
(equities/bills). No mater what happens to relative values, no rebalancing required; hence this
is sometimes termed the “do nothing” strategy.
Payoff Profile
The payoff diagram for a buy-and-hold strategy is a straight line, so the value of the portfolio
rises (falls) as equities rise (fall), with a slope equal to the equity proportion in the initial mix.
The value of the portfolio will never fall below the specified floor, and the portfolio has
unlimited upside potential.
Increasing equity prices favor a buy and hold strategy; the greater the equity proportion in
the initial mix, the better (worse) the strategy will perform when equities outperform
(underperform) bills.
Appropriateness / Risk Tolerance - The strategy is particular appropriate for an investor whose
risk tolerance above the specified floor varies with wealth, but drops to zero at or below that
floor.
Costs - After the initial portfolio transaction, transaction costs are not an issue. The strategy is tax
efficient for taxable investors.
2. Constant-Mix Strategy
Investment Strategy:
The constant-mix strategy maintains an exposure to equities that is constant percentage of
total wealth. Periodic rebalancing to return to the desired mix requires the purchase (sale)
of equities as they decline (rise) in value.
Payoff Profile
This strategy, which generates a concave payoff diagram, offers relatively little downside
protection and performs relatively poorly in up markets.
The strategy performs best in a relatively flat (but oscillating or volatile) market and
capitalizes on market reversals. The constant mix strategy performs particularly well in a
time period when equity values oscillate greatly, but end close to their beginning levels;
greater volatility around the beginning values accentuates the positive performance.
Appropriateness / Risk Tolerance - The constant-mix strategy is particularly appropriate for an
investor whose risk tolerance varies proportionately with wealth; such as investor will hold
equities at all levels of wealth. This strategy requires some rule to determine when rebalancing
takes place; typical approaches avoid transaction costs until either the value of a portion of the, or
of the entire, portfolio has changed by a given percentage.
Costs - At this point, transaction costs are incurred to rebalance. Taxes can be material for taxable
investors.
3. Constant Proportion Strategy
Investment Strategy:
The constant proportion strategy maintains an exposure to equities that is constant multiple of
a “cushion” specified by the investor. The investor sets a floor below which she/he does not
wish assets to fall, and the value of that floor is invested in some non-fluctuating asset (i.e.,
Treasury bills, money market funds). Under normal market conditions the value of the portfolio
will not fall below this specified floor. The investor then selects a multiplier to be used. The
initial commitment to equities equals the multiplier times the “cushion” (the difference
between the value of the total assets to be invested and the value of the floor)
[$ in equities = multiplier x (assets – floor)].
As equity values rise (fall), the constant-proportion strategy requires the investor to
purchase (sell) additional equities. Thus following this strategy (via the formula indicated
above) keeps equities at a constant multiple of the cushion (assets-floor) and generates a
convex payoff diagram.
Payoff Profile - The constant-proportion strategy tends to give good downside protection and
performs best in directional, especially up, markets; the strategy does poorly in flat but
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CFA L3 – Asset Allocation
oscillating markets and is especially hurt by sharp market reversals.
Appropriateness / Risk Tolerance - The strategy is particularly appropriate for an investor who
has zero tolerance for risk below the stated floor but whose risk tolerance increases quickly as
equity values move above the stated floor. This strategy requires some rule to determine when
rebalancing takes place; typical approaches avoid transaction costs until either the value of a
portion of the, or of the entire, portfolio has changed by a given percentage.
Costs - At this point, transaction costs are incurred to rebalance. Taxes can be material for taxable
investors.
Other Characteristics (guideline ans for 2002 exam):
The constant-proportion strategy is consistent with higher risk tolerance, because the strategy
calls for purchasing more equities as equities increase in value; higher risk tolerance is
reflected in the resulting increased allocation to equities over time.
The constant-proportion strategy will do well in an advancing equities market; by buying
equities as their values rise, each marginal purchase has a high payoff.
The constant-proportion strategy would do poorly in a higher volatility environment for
equities, because the strategy would sell on weakness but buy on strength, only to experience
reversals; conversely, the strategy does much better in the face of lower volatility.
The constant-proportion strategy provides good downside protection, because the strategy
sells on weakness and reduces exposure to equities as a given floor is approached.
4. Option Based Portfolio Insurance
Investment Strategy:
The strategy requires the specification of an investment horizon.
The floor value is set at the end of the future time horizon. ]
The current floor is the PV of the end of horizon floor, discount at the risk-free rate. An
amount equivalent to the floor is invested in treasury bills (T-bills).
The cushion is the difference between the portfolio value and the current floor and is invested
in call options.
Investment rules are designed to give the same payoff as a portfolio invested in T-bills and
call options.
OBPI is Similar to CPPI in the following ways:
Both are CONVEX strategies. Recall that a convex strategy sells stocks when they are falling
and buys stocks when they are rising.
OBPI assumes investor risk tolerance is directly related to wealth levels. The floor value
denotes the level of zero risk tolerance.
However, OBPI differs from CPPI in that:
The floor value is invested in T-bills and rises at the risk-free rate over the life of the
strategy.
The cushion is invested in Call options. The result is that at the horizon date, you are either
fully invested in the stock market (your calls were in-the-money) or you are fully invested in T-
bills (your options were out-of-the-money and expired worthless).
FLASHCARD CONCEPTS
1. Buy & Hold Strategy: Do nothing. The Floor Value is the original amount that was placed in T-bills and there
is no re-balancing required.
2. Constant Mix: Here, the floor value of the portfolio is set to zero and the portfolio is rebalanced to maintain a
constant stock-to-total-asset proportion.
You sell stocks as the market rises and buy stocks as the market falls. This is a CONCAVE strategy.
Buy & Hold always beats a constant mix strategy when no market reversals occur; however, constant
mix outperforms in flat, oscillating markets.
Risk Tolerance is proportionate to wealth levels.
3. Constant Proportion Portfolio Insurance (CPPI): The floor value of the portfolio is a positive value. As the
portfolio value rises above the floor value, you invest more in stocks.
Here, you buy stock as the market rises and sell stock as the market falls. This is a CONVEX Strategy.
CPPI performs well in bull markets, but performs poorly in flat, oscillating markets
Risk tolerance falls as the portfolio approaches the floor value
4. Options-based Portfolio Insurance (OBPI): Similar to CPPI in that both are CONVEX. However, OBPI
differs in that it:
The floor value is Invested in T-bills and rises at the risk-free rate over the life of the strategy.
The cushion is invested in Call options. The result is that at the horizon date, you are either fully
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CFA L3 – Asset Allocation
invested in the stock market (your calls were in-the-money) or you are fully invested in T-bills (your
options were out-of-the-money and expired worthless).
PROBLEM SET:
1. Suppose that initially, you have $100 in stock and $35 in T-bills so that total assets are $135. Suppose
also that the stock market index at the time (t0) was 124 and at t1 it rose to 135. At t2, the stock market
had fallen back to 130. Assuming at t0, you are at your optimal Stock to Total Asset (S/TA) ratio.
CALCULATE the following:
i. Optimal S/TA - 100/135 = .7407 or 74.1%
ii. Stock Holdings at t1 under Buy & Hold -
% increase in market = (135-124)/124 = .0887or 8.87%
hence, s = 100x1.0887 = $108.87
iii. Optimal Stock Holdings (under Constant Mix) -
% decrease in market = (130 - 135)/135 = -.037 or -3.7%
hence, s = 108.87x(1-.037) = $104.84
iv. Amount of Stock to buy or sell at t1 (under a Constant Mix) -
s = $108.87 so solve the following for x:
(108.87 + x) / 143.87 = .741 →x = -2.26
v. Amount of Stock to buy or sell at t2 (under a Constant Mix) -
s = 108.87 - 2.26 = 106.61 at end of t1
The drop in the market was -3.7 so
s = (106.61)(1-.037) = 102.66 &
TA = 143.87 - (106.61 - 102.66) = 139.92
so solve for x:
(102.66 + x)/139.92 = .741 →x = 1.02
2. Identify the relative investor risk tolerance characteristics of each of the following 4 investment
strategies
Buy & Hold - The investor’s tolerance for risk is zero if the value of the investor’s asset falls below the
floor value.
Constant Mix - Investor’s risk tolerance remains constant regardless of the wealth level. They will hold
stocks at all levels of wealth.
Constant Proportion Portfolio Insurance (CPPI) - Investor risk tolerance is similar to that of the buy &
hold. Investor risk tolerance drops to zero when total assets drop below the floor value.
Option-based Portfolio Insurance (OBPI) - Similar to CPPI & Buy & Hold in that the floor value denotes
the level of zero risk tolerance.
3. Compare & Contrast Constant Proportion Portfolio Insurance (CPPI) with Options-based Portfolio
Insurance (OBPI).
Comparisons: Both CPPI & OBPI are CONVEX portfolio strategies that essentially sell stock as the stock
market falls. Both methodologies rely on a predetermined floor value that denotes the investors zero risk
tolerance level.
Contrasts: Under CPPI, the ‘cushion’ is invested directly into stocks whereas under OBPI, the cushion is
invested in call options on the underlying market. Also, under OBPI, the floor value is determined as of the
chosen horizon date. At the horizon, the portfolio will be either entirely stock or T-bills.
4. You expect the stock market to be relatively volatile over the next year. You also expect that the
annual holding period return will be roughly zero. Recommend and Justify a Portfolio investment
strategy given your forecast.
Of the 4 strategies outlined in this reading, the constant mix strategy will perform the best. Although the constant
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CFA L3 – Asset Allocation
mix strategy will under-perform in a steady bull or bear market, constant mix strategies outperform in an
oscillating environment because you are always buying more shares whenever the market falls. Hence, each up
movement will have a slightly higher level of capital gains
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CFA L3 – Asset Allocation
Asset Allocation Maginn & Tuttle
FLASHCARD CONCEPTS
The asset allocation decision is the most important determinant of portfolio performance. 95% of the
variance of mutual fund returns can be attributed to asset allocation.
Investment management can be broken down into a 3-stage process
(a) Asset Allocation
(b) Manager Selection
(c) Security Selection
You should remember the formulas for expected asset & portfolio returns. These are the most probable
calculations on the Level III Test
Make sure you remember all Level I & II material on efficient frontiers and MPT. Calculations usually aren’t
required, but a solid description is. The correlation between assets and asset classes is the key to MPT
Investor preferences are quantified through indifference curves. You always want to invest on the highest
possible indifference curve (max. utility).
Tactical Asset Allocation - Take advantage of perceived inefficiencies in relative securities prices. This is a
contrarian investment strategy. Tactical allocation typically takes a short run view. Risk tolerance is assumed
to be a constant.
Strategic Asset Allocation - longer-term, policy level decision. The strategic asset mix is that allocation
that would prevail under ‘normal’ market conditions. Strategic allocation can also be though of as a constant
mix strategy.
Individual v. Society or Average Risk Tolerance -
If your individual risk tolerance moves in tandem with changes in the average risk tolerance of all
investors, then a buy-and-hold strategy is best
If your risk tolerance is more sensitive than average to changes in wealth, then Portfolio Insurance
(CPPI) is optimal
If your risk tolerance is constant relative to the average, then tactical allocation should be used
PROBLEM SET:
1. List 3 features of investor indifference curves
An investor is indifferent between any 2 portfolios that lie on the same indifference curve
Investors want to be on the highest possible indifference curve
Indifference curves do not intersect
Less risk averse individuals have flatter indifference curves
The y-intercept is called the certainty equivalent rate of return
2. Discuss the similarities and differences between strategic & tactical asset allocation strategies
Strategic Asset Allocation is a constant mix strategy whereas tactical asset allocation changes its exposure
to certain market sectors depending upon changing capital market expectations.
Long-run capital market expectations are used in strategic management whereas short-term projections are
used in tactical management. Tactical management attempts to take advantage of perceived market
inefficiencies.
Investor risk tolerance remains constant, independent of investor wealth for both methods.
Both Tactical & Strategic strategies can be though of as ‘contrarian’ in nature. The Tactical strategy is
contrarian because as prices rise, expected returns fall ant the strategic approach is contrarian because as
prices rise, the portfolio weight associated with an asset class needs to be reduced. Thus, both approaches
sell in rising markets and buy in falling markets.
3. For Each of the Four main asset allocation strategies, Comment on their relative level of performance
in a market environment that is characterized by rapidly changing market conditions
Integrated Asset Allocation - Like all asset allocation techniques, IAA involves a feedback loop where
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CFA L3 – Asset Allocation
current capital market conditions are fed back into the optimizer to recomputed the optimal asset allocation.
If market conditions are changing rapidly, then transaction costs may outweigh the benefits of continual
rebalancing.
Strategic Asset Allocation - In a constant mix strategy, the portfolio needs to be rebalanced periodically to
maintain the constant proportions. The performance of a constant mix strategy depends on the behavior of
the market and the decision rule regarding when the portfolio is to be rebalanced. For example, if the stock
market rises rapidly and the fund is to be rebalanced annually, the fund’s asset allocation will be severely
out of alignment (the stocks will be weighted too heavily in the portfolio). Note that there is a definite tradeoff
cost between the number of rebalancing points and transactions costs.
Tactical Asset Allocation - Since tactical asset management is designed to take advantage of perceived
inefficiencies in the asset markets, tactical allocation is better equipped to deal with rapidly changing market
conditions. The performance of a tactical system in a rapidly changing market environment depends on the
ability of the asset manager to correctly take advantage of perceived market inefficiencies.
Insured Asset Allocation - (portfolio insurance) depends on the ability to quickly move into and out of risky
assets if the market conditions move in adverse directions. The October 1987 crash showed that portfolio
insurance strategies are subject to failure when the market swings wildly in short periods of time.
Strategy Assumption about Risk Tolerance Assumption about Capital Market Expectations
Integrated Changes with Wealth Changing
Strategic Constant Constant
Tactical Constant Changing
Insured Changes with Wealth Constant
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CFA L3 – Asset Allocation
Monitoring & Rebalancing the Portfolio
FLASHCARD CONCEPTS
Costs of NOT trading include (a) Holding an over-priced asset, (b) holding an inefficient portfolio and (c)
holding a portfolio that does not meet client needs.
Costs of Trading are (a) commissions, (b) market impact, and (c) lost client confidence from excessive
trading.
Perold & Sharpe’s constant mix asset allocation strategy is the same as the DISCIPLINED Rebalancing
Strategy employed in this chapter. On average, a constant mix beats a drifting mix (i.e., a buy & hold
comprised of both stocks & bonds).
Disciplined rebalancing also typically beats a momentum strategy. Recall from Perold that CPPI is a type of
momentum strategy that buys as the market rises and sells as the market falls. Bottom line: a 60/40
constant mix strategy may be superior to other rebalancing strategies.
A Tactical Asset allocation strategy that employed futures contracts (in a simulation) outperformed the
constant mix strategy. Using futures reduced transactions costs considerably.
Key Point: Transactions costs are not simply composed of brokerage fees and these costs must be
considered when developing a portfolio rebalancing strategy.
PROBLEM SET:
1. List three costs of portfolio rebalancing. Also list three costs of not rebalancing a portfolio
Costs of Portfolio Rebalancing:
Commissions
Potential Impact on Market Prices
Lost Client Confidence if he perceives excessive trading
Costs of Not Rebalancing:
Holding an over-priced asset
Holding an inefficient portfolio
Holding a portfolio that no longer fits the clients’ needs
2. List & Describe 4 factors that may force an individual to rebalance his portfolio
Change in Wealth: Theoretically, an increase in wealth brings an increased tolerance for risk. However, in
practice, the result may be the opposite.
Changing Time Horizons: Usually, as the time horizon shortens, the investment mix becomes more
conservative.
Changing Liquidity Requirements
Tax Circumstances
Laws & Regs.
Unique Circumstances & Preferences
3. Compare the simulated investment performance of a ‘disciplined rebalancing strategy’ with a tactical
asset allocation strategy.
Simulated results for TACTICAL rebalancing significantly outperformed a disciplined rebalancing strategy.
4. Compare the simulated investment performance of market timing rebalancing strategies (e.g.,
momentum) relative to a disciplined rebalancing strategy.
Disciplined rebalancing also beat a Momentum based rebalancing strategy. The momentum based strategy
shifted funds into stocks when the stock market was moving up relative to bonds and into bonds when bonds
were going up relative to stocks Market-timing strategies tend to perform poorly relative to a disciplined
rebalancing strategy.
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