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**Portfolio Analysis Revisited**

Equity-Style Investment Factor Models Asset Allocation

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**Equity-Style Portfolio Construction**

In the 1970s, James Ferrel introduced an approach to portfolio construction known as cluster analysis. A cluster is a portfolio of stocks that are highly correlated with each other, but uncorrelated with other clusters or groups. Form clusters for: Cyclical Stocks Stable Stocks Growth Stocks Energy Stocks

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**Today cluster analysis is referred to as equity-style management. **

Clusters are typically broken into two major categories: Value Stocks Growth Stocks Sub-categories are often formed within these two groups: Small Cap, Large Cap, low P/e, high P/e, etc. Managers are described by their style: value style, growth style, etc.

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**Construction of Value-Stock and Growth-Stock Portfolios**

The most common way to classify value and growth stocks is to use stock price to book value ratio – P/B. Growth: high P/B Value: Low P/B

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**Methodology Select a large sample of stocks (1000).**

Determine the sample’s total market value. Compute each stock’s P/B ratio. Rank stock from low to high by P/B. Define value stocks as all those stocks that encompass the first half of the market value (or some defined percentage). Define growth stocks as all those stocks that encompass the second half of the market value (or some percentage).

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Methodology Alternative to P/B method is to use a mutiple-index measure that provides a score. The index score is constructed so that the higher the score the greater the growth stock. For Example: This is the approach used by Salomon-S-B

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Sub-styles Within a style, portfolio managers create other groupings known as sub-styles. Examples: Within either value or growth style, one could have sub-styles based on size: Small-Size Value, Large-Size Value, Small-Size Growth, Large-Size Growth. Within either value or growth style, one could have sub-styles based on P/e, BV/MV, etc. Within growth, one could have sub-styles based on high growth, low growth, above-average growth, volatility, etc. Use factor models.

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Empirical Research Study by Leinweber, Arnolt, and Luck looked at the performance of value and growth style investments. They defined value and growth by P/B. They looked monthly returns from to 1995. They found: In the U.S. from 1975 to 1995 that $1 invested in a value-grouped portfolio would have grown to $23, while $1 invested in a growth-grouped portfolio would have grown to $14. In 45% of the months in the sample, growth stocks outperformed value; with perfect foresight, one switching from growth to value would have realized $45.

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**Other Styles S&P Mid Caps S&P Small Caps PEG Portfolios**

Reference: Handbook of Equity Style Management, Editors: Coggin, Fabozzi, and Arnoldt.

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Factor Models Portfolios constructed from multifactor/APT analysis are called factor models. Two general types: statistical, macro and fundamental. Statistical Factor Models: Based on explaining security and portfolio returns based on artificial factors created from factor analysis. Macroeconomic Factor Models: Developing portfolios based on macroeconomic factors. These models are rooted in the works of Chen, Roll, and Ross and Burnmeister and McElroy. Most are proprietary models. One published model is Salomon-Smith-Barney’s Risk Attributes Model (RAM). Fundamental Models: Use a cross-sectional approach.

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RAM Model Step 1 Stock returns are explain by a set of macroeconomc variables.

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**Variable RAM Investors’ Confidence Interest Rates Inflation Shock**

Aggregate Business Fluctuations Foreign Variables Market Factors RAM RCorp – Rgovt (LT Rate – ST Rate) Actual minus expected inflation rate (Industrial Production) (Exchange Rate) Residual Market Beta

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RAM Step 2: Run a time-series regression of the stock returns against the six macroeconomic variables. Salomon-Smith-Barney regresses the returns of 3500 stocks against the above macroeconomic factors.

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RAM Step 3: Standardize the coefficients. For each coefficient, calculate the average coefficient and average standard deviation. For example, for b1:

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**Next, for stock i measure the adjusted standardized coefficient as:**

Interpretation: If adjusted b = 0 Stock’s sensitivity to factor 1 is no different than the average. If adjusted b > 0 Above average responsiveness to factor 1. If adjusted b < 0 Below average responsiveness to factor 1.

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RAM Step 4: For each stock determine its score, Si. The score is obtained by multiplying the stock’s adjusted coefficients by an estimate of the macroeconomic factors, then summing the products. Step 5: Construct a portfolio with the highest score.

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**RAM Alternative: Monte Carlo Simulation**

Construct different portfolios based on the portfolio’s sensitivity to different economic scenarios, then select the best. Steps: Identify different economic scenarios and their probabilities. For example, a scenario in which there is an exogenous supply side increase (low inflation, high gdp growth, and low rates), one in which there is a negative exogenous demand change (low gdp, low inflation, and high interest rates), or one in which there is both. Use econometric forecasting, economic indicators, etc., and define the scenarios in terms of factors value.

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**RAM 2. Construct different portfolios with different sensitivities.**

3. For each economic scenario calculate the portfolio’s score and probability. 4. For each portfolio, calculate its expected score and standard deviation based on all scenarios. 5. Rank each portfolio, S/. 6. Select the best.

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**1. High energy prices, slow down in tech:**

Scenario Factor Prob. Portfolio 1 Score Portfolio 2 Portfolio 3 1. High energy prices, slow down in tech: Low gdp, high inflation, etc. 2. High gdp, low rates, etc ETC F1 = .02 F2 = .01 F3 = 5% F4 = 2% F5 = -1% F6 = .25 Etc. .02 .01 .05 .10 .005 10 12 15 17 20 E(S) = 10 (S) = 5 = 2 E(S) = 15 (S) = 8 = 1.875 E(S) = 12 (S) = 10 = 1.2

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**Fundamental Factor Models**

Example: BARRA Model (Barra Consulting Firm) Features: Regress 1300 stocks against 13 factors: P/e, P/B, size, ROE, etc. Construct portfolios with different sensitivities. Define portfolios with different styles: Value, growth, Value-low cap, etc.

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**Asset Allocation Strategies**

Asset allocation refers to determining the portfolio mix among different asset classes: Stocks, Bonds, Money Market Value, Growth There are two general assets allocation strategies: Passive Active

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**Passive Asset Allocation**

Set long-run objectives in terms of return and risk, then determine the equity, bond, and money mix to achieve that. Strategies of pensions, LICs, etc. Use a Markowitz strategy to determine equity, bond, and money mix. Determine mix of value and growth using a P/B approach.

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**Active Asset Allocation**

Examples: Tactical Asset Allocation (TAA) and Dynamic Asset Allocation (DAA). TAA TAA strategy is aimed at enhancing returns by changing the asset mix in response to changing market conditions or return patterns. Uses indicators. Value/Growth Stock Changing: Change or tilt portfolio from value to growth or growth to value when conditions dictate. Key is to forecast this. Use factor model to change a portfolio based on a security’s sensitivity to factors: inflation, interest rates, gdp, etc.

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**TAA Valuation approach to determine stock, bond, and money mix.**

Use Indicators as signals to change allocations. Often the indicators are risk premiums: Stock/Bill RP = RS – RTB Bond/Bill RP = RB – RTB Stock/Bond RP = RS – RB There is historical evidence to support this approach.

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**TAA Study by DuBois Time Period: 1951-1989**

Looked at historical RP of Stock/Bills and the average stock returns (S&P 500) over T-Bill returns for 1, 3, and 12 Months.

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**Dynamic Asset Allocation:**

DAA is an active strategy of changing a bond and equity mix over time and in response to stock market changes in order to achieve a certain return distribution at the end of a period. For example, at the end of five years the objetive may be to have a return on the portfolio that matches the market’s return if the market has increased, but has a certain minimum return is the market has declined. DAA is a dynamic portfolio insurance strategy.

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