Topic Four: Fundamentals of a Tactical Asset Allocation (TAA) Strategy

Topic Four: Fundamentals of a Tactical Asset Allocation (TAA) Strategy

Fundamentals of a Tactical Asset Allocation (TAA) Strategy Tactical Asset Allocation has been defined in various ways, including: - Tactical Asset Allocation broadly refers to active strategies which seek to enhance performance by opportunistically shifting the asset mix of a portfolio in response to the changing patterns of reward available in the capital markets. Notably, tactical asset allocation tends to refer to disciplined processes for evaluating prospective rates of return on various asset classes and establishing an asset allocation response intended to capture higher rewards. (Arnott and Fabozzi, 1988) - A TAA manager s investment objective is to obtain better-thanbenchmark returns with (possibly) lower-than-benchmark volatility by forecasting the returns to two or more asset classes, and varying asset class exposure accordingly, in a systematic manner. (Philips, Rogers, and Capaldi, 1996) - TAA strategies are strategies which attempt to deliver a positive information ratio by systematic asset allocation shifts. (Lee, 2000) 4-1

A Simplified TAA Framework Consider an active manager who forms a portfolio consisting of two assets: - A single fund of risky assets (i.e., stocks) with return R S - A risk-free security with return RF The benchmark portfolio against which the active manager competes consists of policy investment weights of: - W for the risky asset portfolio - (1 W) for the risk-free asset At the beginning of each Period t, the TAA manager forms a portfolio with the following investment weights: - [W + View t ] for the risky assets - [1 - W - View t ] for the risk-free asset 4-2

A Simplified TAA Framework (cont.) The Period t returns to the benchmark portfolio and the active TAA portfolio are: - R pt = [W] R st + [1 W] RF - R At = [W + View t ] R st + [1 - W - View t ] RF The issue comes down to whether the manager s forecasting ability for the return potential of the risky asset portfolio compared to the cash return (i.e., View t ) can consistently produce one or both of the following results: - R At R pt = (View t )[R st RF] = Alpha > 0 σ(r At ) < σ(r pt ) From the previous condition, it must be the case that (View t ) and [R st RF] must be positively correlated - This is equivalent to saying that the TAA manager must have forecasting skill in predicting the periods when R st > RF 4-3

Designing and Implementing a TAA Program There are three major steps involved in designing and running a successful tactical asset allocation program: 1. Forecasting the asset class returns for the next investment period for the portfolio s investable universe (call this the signal ) 2. Translate the forecast signal into a specific adjustment in the asset class investment weights relative to the policy benchmark (i.e. the view ) 3. Implement and adjust the periodic view on a dynamic basis over time Of these three steps, arguably the most difficult for the manager to excel at consistently is forecasting asset class returns - Notice that in order to consistently produce a view adjustment that is positively correlated with asset class return differentials, the manager must generate a variant perception viewpoint relative to the market in general 4-4

1. Forecasting Asset Class Returns Generally speaking, TAA strategies basically involve predicting which of two asset classes (or style divisions within an asset class) will produce the highest returns in the subsequent investment period - Relative to the strategic policy investment weight, the asset class with the higher forecasted returns should be overweighted in the portfolio - The asset class with the lowest forecasted relative returns should be underweighted in the portfolio The process of forecasting returns usually involves establishing the correlation coefficient between the current level of an observable economic variable and the future level of the asset class returns 4-5

1. Forecasting Asset Class Returns (cont.) Notice that it does not matter if the correlation coefficient between the economic variable and subsequent asset returns is positive or negative as long as it is statistically meaningful - A positive correlation implies a momentum-style strategy (i.e., higher levels of the variable are connected with higher future returns in the asset class) - A negative correlation implies a reversion-style strategy (i.e., higher levels of the variable are connected with lower future returns in the asset class) Once a significant correlation is established, the next step is to determine when the economic variable reaches a significant enough level (either higher or lower than normal) to suggest a substantial displacement in the forecasted returns to the asset class - A significant change in the observable level of the economic variable that triggers a portfolio adjustment is called the signal 4-6

1. Forecasting Asset Class Returns (cont.) Stockton and Shtekhman (2010) have summarized the categories for some of the most commonly used TAA signals 4-7

1. Forecasting Asset Class Returns (cont.) The challenge in establishing that a signal has occurred is that it is necessary to determine what represents a significant movement in the underlying economic variable - Clearly, small movements in a variable (e.g., a movement in a ratio from 3.11 to 3.14) is unlikely to represent a meaningful enough movement to suggest a reliable subsequent return change One approach commonly used in practice is to standardize (or normalize) the variable using a Z-score approach: Z - score = (Current Value - Average Value) Standard Deviation A signal is produced whenever the absolute value of a Z-score exceeds a pre-determined critical level - The Z-score can be interpreted as the number of standard deviations the current value of the variable falls away from its long-term norm 4-8

2. Implementing Forecast Signals Once a viable signal has been observed, the task for the TAA manager is to translate this signal into a portfolio adjustment - Since any tactical adjustment to the portfolio will have to be a zero-sum effect, any overweight position in one asset class will have to be offset by an equivalent underweight position in another This translation from signal to portfolio adjustment can be done on either a discrete or continuous basis. For example: - Discrete: If Z-score > Critical Level then set W t = Max W If Z-score < -(Critical Level) then set W t = Min W - Continuous: Translate Z-score from its range [-, ] into a portfolio weight range [ Min W < W t < Max W] 4-9

2. Implementing Forecast Signals (cont.) Generally speaking, whether a signal leads to a discrete or continuous portfolio adjustment comes down to a judgment on the part of the portfolio manager about how closely connected the economic variable and future asset class returns actually are - If slight movements in the economic variable are closely connected to subsequent return movements, continuous portfolio adjustments are often employed - If it takes a relatively large value in a Z-score to produce a reliable future return movement, then discrete adjustments are often used 4-10

3. Adjusting the TAA Portfolio An important question that the TAA manager must address is how often to adjust the portfolio positions - This decision is sometimes dictated by how frequently the economic variable is revised. For example, some macroeconomic variables are only updated on a quarterly basis, so it would be difficult to use that measure to update the portfolio weights more often than four times a year Although it can vary widely depending on the nature of the investment problem faced by the manager, many TAA managers will update their positions on a monthly basis - Even in a program with monthly rebalancing, there is often a provision to update the tactical positions more frequently in the event of an extreme movement in financial market conditions 4-11

3. Adjusting the TAA Portfolio (cont.) A related issue that the TAA manager must be aware of is that the choice of the critical level used to define when a signal occurs will affect the frequency of portfolio adjustments that must be made - The lower the level of Critical Level that the manager selects in discrete adjustment process, the more frequent the portfolio positions will need to be a revised in a given period - Lower levels of Critical Level might produce more frequent TAA trading signals, but the accuracy of those signals might be diminished - The hit ratio represents one way of determining how frequently a signal results in an accurate return forecast 4-12

Illustrating the TAA Process: An Example Consider two different portfolio managers who invest in three asset classes in their respective countries - Common Stocks - Fixed-Income Securities - Cash The countries and benchmark indexes for these managers are as follows: - United States (in USD): - Stocks: SPX - Bonds: SBBIG - Cash: 1-month T-bill - Chile (in CLP): - Stocks: IPSA - Bonds: LVACL - Cash: LVACLI 4-13

Example of the TAA Process (cont.) Each manager faces a strategic policy benchmark allocation scheme of: - Common Stocks: W s - Fixed-Income Securities: W b - Cash: W c = (1 W s W b ) It is assumed that the benchmark allocation is rebalanced every period to maintain these allocation weights Both managers attempt to outperform their respective benchmarks over time by following a tactical asset allocation strategy - The details of the TAA strategy are as follows: - The manager starts with the benchmark allocation weights in her portfolio - At the beginning of each return period, the manager decides to either change W s or leave it the same - The manager always alters the stock allocation by adjusting the cash allocation (i.e., any stock sales get placed in cash and any stock purchases are funded with cash). This is a stock-cash switching strategy. - The bond allocation always remains the same at W b 4-14

Example of the TAA Process (cont.) Each manager will consider using three different TAA switching signals at the beginning of every return period: - Momentum: Based on the level of current stock prices compared to past average levels - Value: Based on the normalized level of fundamental value metrics in the current period - Volatility: Based on the normalized level of stock volatility in the current period Monthly return and factor variable data was obtained for both countries for the period December 1999-June 2015 - The TAA investment period is assumed to be January 2001 June 2015, which leaves the first thirteen months of data for the purpose of estimating forecast factors 4-15

Example of the TAA Process (cont.) TAA Strategy #1: Stock Momentum - At each month t (starting in January 2001), calculate the following ratio: (Stock Index Level) t-1 / SMA t-2,t-11 where SMA is the 11-month simple moving average of past stock index levels from two months to 11 months in the past - Adjust the asset class weight in Month t as follows: (i) (ii) (iii) If S -1 /SMA > (1 + CHG) then W s * = StockMax% If (1 CHG) < S -1 /SMA < (1 + CHG) then W s * = W s (i.e., policy) If S -1 /SMA < (1 - CHG) then W s * = StockMin% - Set the following minimum and maximum levels for the stock allocation in each Month t: - StockMax% = 1 - W b - StockMin% = 0 4-16

TAA Strategy #1, Version 1: W s = 0.6, W b = 0.0, W c = 0.4 CHG = 10% 4-17

TAA Strategy #1, Version 2: W s = 0.6, W b = 0.3, W c = 0.1 CHG = 10% 4-18

TAA Strategy #1, Version 3: W s = 0.6, W b = 0.0, W c = 0.4 CHG = 7% 4-19

Example of the TAA Process (cont.) Summary Comments on Momentum TAA Strategy: - Over this particular time frame, the most basic form of the stock momentum-based TAA strategy was very effective in the U.S. market but somewhat less so in the Chilean market - Increased monthly returns in both markets - Decreased volatility and drawdown in U.S.; increase volatility and drawdown in Chile - Positive information ratios in both markets; particularly high IR in Chile - Annualized tracking errors for the momentum TAA strategy were in the 5-7% range - This is a typical level for a U.S.-based actively managed mutual fund, but may be too high for other types of institutionally managed portfolios - The results are somewhat sensitive to the conditions that are selected - The benefits of the TAA strategy are reduced somewhat when there are constraints placed on the tactical overweight position for equity - More frequent trading (i.e., a lower CHG level) leads to similar benefits but with slightly higher tracking errors 4-20

Example of the TAA Process (cont.) TAA Strategy #2: Fundamental Valuation - At each month t (starting in January 2001), calculate the following normalized value (i.e., Z-score) of a fundamental value ratio: Z t = [(Value Ratio) t-1 (Avg. Value Ratio) t-1,t-13 ]/ σ(value Ratio) t-1,t-13 where Value Ratio is defined as: U.S.: (Earnings Per Share/Price) ratio Chile: (Book/Price) ratio - Adjust the asset class weight in Month t as follows: (i) (ii) (iii) If Z > CritLevel then W s * = StockMax% If CritLevel < Z < CritLevel then W s * = W s (i.e., policy) If Z < -CritLevel then W s * = StockMin% - Set the following minimum and maximum levels for the stock allocation in each Month t: - StockMax% = 1 - W b - StockMin% = 0 4-21

TAA Strategy #2, Version 1: W s = 0.6, W b = 0.0, W c = 0.4 CritLevel = 1.5 4-22

TAA Strategy #2, Version 2: W s = 0.6, W b = 0.3, W c = 0.1 CritLevel = 1.5 4-23

TAA Strategy #2, Version 1 - REVISED: Reverse the Fundamental Signal If Z > CritLevel then W s * = StockMin% If Z < -CritLevel then W s * = StockMax% 4-24

Example of the TAA Process (cont.) Summary Comments on Value TAA Strategy: - The results for the fundamental value-based TAA strategy was clearly mixed during this time frame - In the U.S. market, the reversion to the mean signal worked to the extent that returns were increased and the information ratio was positive - Hit ratios in the U.S. market were also quite high - In the Chilean market, the reversion to the mean signal actually produced lower returns than the strategic benchmark; hit ratios were well below 50% - In both countries, the value TAA strategy increased volatility and drawdown levels - Interestingly, the value TAA strategy works extremely well in the Chilean market if you follow the exact opposite signal (i.e., buy stock when in appears to be overvalued) than what works in the U.S. market - In this case, returns increase while volatility remains stable, so the annualized information ratio is significantly positive - Annualized tracking error is around 5% - As in the momentum-based TAA strategy, the outcomes for the value-based strategy are somewhat sensitive to the conditions of the switching regime that is employed 4-25

Example of the TAA Process (cont.) TAA Strategy #3: Stock Volatility - At each month t (starting in January 2001), calculate the following normalized value (i.e., Z-score) of the volatility of the stock market: Z t = [(Volatility) t-1 (Avg. Volatility) t-1,t-12 ]/ σ(volatility) t-1,t-12 where Volatility is defined as: U.S.: VIX index forward-looking forecast Chile: 30-day historical standard deviation - Adjust the asset class weight in Month t as follows: (i) (ii) (iii) If Z < -CritLevel then W s * = StockMax% If CritLevel < Z < CritLevel then W s * = W s (i.e., policy) If Z > CritLevel then W s * = StockMin% - Set the following minimum and maximum levels for the stock allocation in each Month t: - StockMax% = 1 - W b - StockMin% = 0 4-26

TAA Strategy #3, Version 1: W s = 0.6, W b = 0.0, W c = 0.4 CritLevel = 1.0 4-27

TAA Strategy #3, Version 2: W s = 0.6, W b = 0.3, W c = 0.1 CritLevel = 1.0 4-28

Example of the TAA Process (cont.) Summary Comments on Volatility TAA Strategy: - Over this time horizon, the volatility-based TAA strategy was quite successful in both the U.S. and Chilean markets - Generally, following a volatility reversal TAA strategy led to increased returns with similar levels of risk compared to the strategic benchmark - Hit rates were in the range of 50-60% and there were substantially more monthly signals in the U.S. market than in Chile - Given the similarity in the findings for the U.S. and Chile, it appears that the difference between a forward-looking measure of stock volatility (U.S.) and a historical volatility measure (Chile) may not matter that much - As with the other TAA strategies, the conditions for the switching trade do appear to affect the results - Constraints on the tactical range for the equity position reduced the information ratios in both markets, but did not diminish the overall benefit - Although not shown here, the CritLevel value selected has a substantial impact on the outcome achieved 4-29

Cost and Implementation Issues One major factor that impacts the success of any TAA strategy is the transaction costs that will be incurred by the trades involved compared the strategic benchmark portfolio - It is important to recognize that a TAA strategy will not necessarily trade more frequently or incur greater transaction costs than any other actively managed portfolio strategy - It is also important to note that the strategic benchmark (i.e., passive) alternative is likely not to be a costless portfolio either - For instance, maintaining a static 60-40 combination of stocks and bonds will require frequent rebalancing whenever the returns to the two asset classes do not move by exactly the same amount in a particular investment period Stockton and Shtekhman (2010) examined the effect of transaction costs in running a simulated TAA portfolio - Their investment period was 1975-2009 - Their benchmark was 60% U.S. Stock & 40% U.S. Bonds - They formed their monthly TAA switching signal based on a model that included signals using lagged values of the term spread, credit spread, inflation, gold prices movements, and equity returns 4-30

Cost and Implementation Issues (cont.) The authors performed their analysis in three subperiods, as well as in the overall time horizon - Before expenses, the TAA strategy outperformed the benchmark over the entire period and in two of the three subperiods - Portfolio turnover rates were relatively low at around 25% They then considered the transaction cost issue by computing the breakeven cost that would be necessary to offset the value added of the TAA strategy - Annual trading costs in excess of 1.1% would have offset TAA benefits over the entire investment period 4-31

Cost and Implementation Issues (cont.) One popular way to reduce the expense of shifting a portfolio s allocation between asset classes is to make that change synthetically using derivative contracts - The most commonly employed derivatives used to make synthetic adjustments to a TAA portfolio are (1) exchange-traded futures contracts and (2) over-the-counter swap contracts The following chart demonstrates the cost advantage of using futures contracts to implement a TAA trade compared to make a physical portfolio adjustment 4-32

Global TAA Extension: Active Country Selection As TAA strategies began to include non-domestic asset classes, the term Global Tactical Asset Allocation (GTAA) started to be used more widely in practice - Notice that except for the asset classes that they might include in their investable universes, there is no practical difference between the acronyms TAA and GTAA from an analytical perspective - There is often a currency hedging overlay element to implementing a GTAA program that is not necessary in a single-currency domestic TAA program The GTAA approach can also by a global portfolio manager who is responsible for investing capital in both domestic and foreign assets - For example, a global equity manager located in Chile might be responsible for investing against a benchmark that comprises 50% of the IPSA index and 50% of the U.S. S&P 500 index In this situation, the two different countries can be treated as different sectors of the global equity market and the switching model based on forecasted return differentials that we saw earlier can be adapted accordingly - One important difference between the traditional sector model for asset class divisions located in the same country and a model that switches asset classes located in two different countries is that the latter may involve a currency translation - The need for the manager to convert the domestic currency into the foreign currency in order to invest in the foreign asset creates another source of risk since the total return to the foreign asset will be a combination of (i) the return in the foreign currency and (ii) the return to the currency translation 4-33

Active Country Selection (cont.) Consider a manager who invests in both the domestic stock index (DI) and the stock index for a foreign country (FI) - Assume also that the domestic and foreign countries have different currencies and the exchange rate (FX) between the two is expressed in terms of the number of units of the domestic currency needed to acquire one unit of the foreign currency The Period t returns to the domestic and foreign indexes, expressed in the domestic currency, are R DI t = DI DI t t-1-1 4-34

Active Country Selection (cont.) R FI adj t = (FI (FI t t-1 x FX x FX t ) ) t-1-1 = FI FI t t-1 x FX FX t t-1-1 = (1+ R FI unadj t ) x (1+ R FX t ) -1 Notice that the currency-adjusted return to the foreign index is the product of (one plus) the return to the currency-unadjusted index return and (one plus) the currency translation return - This definition assumes that the domestic manager will have to buy units of the foreign currency to invest at Period t-1 and then buy back the domestic currency at Period t The essence of the GTAA switching strategy is then as follows - If E(R DI ) > E(R FIadj ): Buy domestic index - If E(R DI ) < E(R FIadj ): Buy foreign index 4-35

Example of the Country-Based TAA Process Country TAA Strategy #1: Foreign Stock (in USD) Momentum - Consider the following conditions - Time Horizon: January 2001 June 2015; monthly rebalancing - Strategic Benchmark: 50% Chile IPSA and 50% U.S SPX (in CLP) - At each month t (starting in January 2001), calculate the following statistic: IPSA-SPX Return Differential = ChUsRD t = [(Avg Annual R chile ) t-1 - (Avg Annual R us ) t-1 ] where the average annual return is calculated as simple moving average of past 12 months of sector stock index returns through month t-1 - Adjust the asset class weight in Month t as follows: (i) If ChUsRD t > CritDiff then W* chile = ChileStockMax% (ii) If -CritDiff < ChUsRD t < CritDiff then W* chile = W chile (i.e., policy) (iii) If ChUsRD t < -CritDiff then W* chile = ChileStockMin % - Set the following minimum and maximum levels for the Chile and U.S. stock allocations in each Month t: - ChileStockMax % = 100% and ChileStockMin% = 0% - W* us = 1 - W* chile 4-36

Country TAA Strategy #1 (SPX in USD signal): W IPSA = 0.5, W SPX-CLP = 0.5 CritDiff = 7.00% 4-37

Example of the Country-Based TAA Process (cont.) Country TAA Strategy #2: Foreign Stock (in CLP) Momentum - Consider the following conditions - Time Horizon: January 2001 June 2015; monthly rebalancing - Strategic Benchmark: 50% Chile IPSA and 50% U.S SPX (in CLP) - At each month t (starting in January 2001), calculate the following statistic: IPSA-SPX Return Differential = ChUsRD t = [(Avg Annual R chile ) t-1 - (Avg Annual R us ) t-1 ] where the average annual return is calculated as simple moving average of past 12 months of sector stock index returns through month t-1 - Adjust the asset class weight in Month t as follows: (i) If ChUsRD t > CritDiff then W* chile = ChileStockMax% (ii) If -CritDiff < ChUsRD t < CritDiff then W* chile = W chile (i.e., policy) (iii) If ChUsRD t < -CritDiff then W* chile = ChileStockMin % - Set the following minimum and maximum levels for the Chile and U.S. stock allocations in each Month t: - ChileStockMax % = 100% and ChileStockMin% = 0% - W* us = 1 - W* chile 4-38

Country TAA Strategy #2 (SPX in CLP signal): W IPSA = 0.5, W SPX-CLP = 0.5 CritDiff = 7.00% 4-39

Example of the Country TAA Process (cont.) Summary Comments on Country TAA Strategy: - The results for the country rotation TAA strategy using a momentum approach for the IPSA-SPX return differential was quite successful at adding value relative to the 50-50 benchmark - Average returns were uniformly higher for the TAA program than the benchmark - The country TAA strategy did not appear to reduce volatility or drawdown levels substantially - However, the Sharpe ratio (i.e., risk-adjusted return) increased significantly in the TAA framework - Somewhat surprisingly, the TAA strategy appears to work equally well whether returns to the foreign stock index (i.e., the U.S. SPX in this case) are expressed in USD or adjusted into CLP equivalent - This suggests that currency returns are not the primary driver for the momentum effect on which the country TAA strategy is based - There appears to be much more frequent trading and higher tracking errors associated with the country TAA strategy than with the other switching strategies we have seen - Trade signals occur in about three out of every four months and hit ratios are around 60-65% regardless of how foreign stock returns are viewed - Annualized tracking error is around 8% 4-40

Factor-Based TAA and GTAA Models As we have seen, the art of implementing a TAA program comes down to specifying a current explanation for how asset class returns will be generated in the future. - While the simple univariate correlation models we have examined are quite instructive, many managers make use of multi-factor models in attempt to increase the accuracy and validity of their forecasts Multi-factor models are attempts to implement the spirit of the Arbitrage Pricing Theory (i.e., use multiple risk factors to estimate expected asset returns) without relying on theory to establish what those factors may be. There are two general classes of multi-factor models, depending on how the risk factors are defined: Macroeconomic-based factors (e.g., inflation, unemployment, industrial production) Security Characteristic-based factors (e.g., firm size differential, value vs. growth, price momentum) 4-41

Macroeconomic-Based TAA Factor Models (cont.) Burmeister, Roll, and Ross (1994) analyzed the predictive ability of a model based on a different set of macroeconomic factors. Specifically, they define the following five risk exposures (1) confidence risk, based on unanticipated changes in the willingness of investors to take on investment risk; (2) time horizon risk, which is the unanticipated changes in investors desired time to receive payouts; (3) inflation risk, based on a combination of the unexpected components of short-term and long-term inflation rates; (4) business cycle risk, which represents unanticipated changes in the level of overall business activity; and (5) market-timing risk, defined as the part of the Standard & Poor s 500 total return that is not explained by the otherfour macroeconomic factors. The chart on the next page shows beta estimates to these risk factors for a particular stock (Reebok International Ltd.) versus the S&P 500 index and for a portfolio of small-cap firms versus a portfolio of large-cap firms. Also included in these graphs is the security s or portfolio s exposure to the BIRR composite risk index, which is designed to indicate which position has the most overall systematic risk. - These comparisons highlight how a multifactor model can help investors distinguish the nature of the risk they are assuming when they hold with a particular position. - For instance, notice that Reebok has greater exposures to all sources of risk than the S&P 500, with the incremental difference in the business cycle exposure being particularly dramatic. Additionally, smaller firms are more exposed to business cycle and confidence risk than larger firms but less exposed to horizon risk. 4-42

Macroeconomic-Based TAA Factor Models (cont.) 4-43

The Fama-French Risk Factor Models The most popular multi-factor model currently used in practice was first suggested by economists Eugene Fama and Ken French. Their model starts with the single market portfolio-based risk factor of the CAPM and supplements it with two additional risk influences known to affect security prices: A firm size factor A book-to-market factor Specifically, the Fama-French three-factor model for estimating expected excess returns takes the following form: (R it RFR t ) = α i + b i1 (R mt RFR t ) + b i2 SMB t + b i3 HML t + e it where, in addition to the excess return on a stock market portfolio, two other risk factors are defined: SMB (i.e., Small Minus Big ) is the return to a portfolio of small capitalization stocks less the return to a portfolio of large capitalization stocks HML (i.e., High Minus Low ) is the return to a portfolio of stocks with high ratios of book-to-market values (i.e., value stocks) less the return to a portfolio of low bookto-market value (i.e., growth ) stocks 4-44

The Fama-French Risk Factor Models (cont.) Mark Carhart has suggested an extension of the Fama-French threefactor model. Specifically, he argues that a fourth risk factor should be added to account for the momentum in past security prices. That is, the three-factor model should be embellished with: A return momentum factor Specifically, the Fama-French four-factor model for estimating expected excess returns takes the following form: (R it RFR t ) = α i + b i1 (R mt RFR t ) + b i2 SMB t + b i3 HML t + b i4 MOM t + e it where, in addition to the excess return on a stock market portfolio and the size and book-to-market risk factors, we have: MOM (i.e., momentum) is the return to a portfolio of stocks with the highest returns over the past year less the return to a portfolio of stocks with the lowest past returns 4-45

Incorporating Tactical Views in the Black-Litterman Model Another advantage of the BL Optimization model we saw earlier is that it provides a way for the user to incorporate his own views about asset class expected returns into the estimation of the efficient frontier. Said differently, if you do not agree with the implied returns, the BL model allows you to make tactical adjustments to the inputs and still achieve well-diversified portfolios that reflect your view. Two components of a tactical view: - Asset Class Performance - Absolute (e.g., Asset Class #1 will have a return of X%) - Relative (e.g., Asset Class #1 will outperform Asset Class #2 by Y%) - User Confidence Level - 0% to 100%, indicating certainty of return view (See the article A Step-by-Step Guide to the Black-Litterman Model by T. Idzorek of Zephyr Associates for more details on the computational process involved with incorporating user-specified tactical views) 4-46

BL Mean-Variance Optimization Example (cont.) Suppose we adjust the inputs in the process to include two tactical views: - US Equity will outperform Global Equity by 50 basis points (70% confidence) - Emerging Market Equity will outperform US Equity by 250 basis points (50% confidence) 3-47

BL Mean-Variance Optimization Example (cont.) The new optimal allocations reflect these tactical views, but in an interesting way (i.e., more U.S. Equity but no Global Equity): 3-48

BL Mean-Variance Optimization Example (cont.) This leads to the following new efficient frontier: 3-49