Structure of writeup



FINANCE 499

Independent study

Towards developing a new approach for dynamic asset allocation

Ling Luo

Andrew Hobley

Fei Xu

Prof. Campbell Harvey

Fuqua School of Business,

Duke University

Introduction to study

This study was envisioned to follow on from the Global Asset Allocation class, given by Prof. Campbell Harvey in January and February 2004. One of the surprising results coming from the class is the anti-cyclical nature of long-short growth and value portfolios. The graph below, prepared by Columbine Capital, follows a similar approach and demonstrates this pattern well.

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This study attempts a way to be able to predict the points of inflection in performance between a ‘value’ portfolio and a ‘growth’ portfolio. During the initial phases of the project, we faced a number of difficulties in deriving long-short portfolios due considerable problems we encountered in deriving quality monthly data from the FactSet service. Therefore, we decided to focus our attention on the published data sets created by Kenneth French.[1]

We also broadened our study to include ‘long only’ funds. There is a significant body of research that suggests that value portfolio strategies outperform growth funds over the long term[2]. Fama & French define value as meaning companies that have low book to market values.[3] However, there are still clear examples of times, for example in the run up to 2000, when growth stocks deliver significantly higher returns.

We were hoping to build on the core Asset Allocation course by building screens that can be used to develop long-short portfolios. However, we had numerous problems in deriving reliable data from FactSet, so we opted to use data compiled by Kenneth French as part of his ongoing research.

There were 3 main phases in the development process of the predictive model. At each stage, we introduced a number of refinements and adjustments to the data we used and the approach.

Phase 1

Method

Initially, we decided to use French’s UMD (‘Up Minus Down’) portfolio as a proxy for the long-short momentum portfolio and HML (‘High Minus Low’) portfolio as a proxy for the long-short value portfolio.[4]

When the value portfolio outperformed the momentum portfolio, we set the dependent variable to be 1, otherwise a 0. We then used the binary logistical regression technique in SPSS, regressing the dependent variable against a range of 54 independent macroeconomic and market based financial variables. [See Appendix A for a full list of the independent variables]. We then offset all the financial data by 1 month, so that we are regressing historic data against current portfolio performers. We offset CPI by 2 periods due to the 2-month lag for this data.

We then developed a parsimonious list of independent variables by using a combination of techniques from stepwise regression, regression of each independent variable in turn and using a selection of predicted best fit variables. We then vetted this ‘long list’ of variables for multicollinearity problem by eliminating variables with correlation coefficients greater than 65%. This led to a shortlist of 6 independent variables:

- Credit spread between Baa and Aaa

- Credit spread between Aaa and T-Bill

- Long-term corporate debt

- CPI inflation

- Change in real earnings

- Change in GDP

We then ran a regression model, using these variables over a long time period[5] and derived the correlation coefficients ((n) and the R2. This allowed us to predict the likely result of the dependent variable (( (x)) for an out of sample period of January 2001 to December 2003.

[pic]

Results

Our initial results show that we have some success at predicting the change in performance between the 2 portfolios with an R2 of 1.3%[6].

We used a number of methods of allocating the overall portfolio based on the forecast dependent variable ((). The first method allocated 50% weight to the value portfolio and 50% to the momentum portfolio (50:50 model). The second method allocated the weight as suggested by the logit regression model (dynamic weights model). The third method suggested which of the 2 portfolio types is favored in any given month and 100% of the capital is allocated to that portfolio (full switch model).

[pic]

The basic momentum portfolio increased by 10% and the value portfolio increased by 16% in value terms over the 3-year period studied. Both our conditional weighted portfolios, significantly improved on these returns by returning 22% in the dynamic weights model and 41% for the full switch model. More importantly, the Sharpe ratios are also significantly higher:

[pic]

Columbine Capital suggest using a fixed value:growth weight of 50% as an optimal way of maximizing returns whilst minimizing volatility. Our results confirm their claim that the absolute and risk adjusted returns for this 50:50 portfolio is indeed higher than either the value or momentum portfolio.

However, our results suggest that it is possible to predict the inflection point between the value and the momentum point in a marginally more accurate way than simply adopting a fixed allocation between the 2 portfolios.

Phase 2

Method

For our first major refinement of the model, we maintained the same basic process (binary logistical regression) though we instituted a number of key changes:

i) The regression timeframe was limited to 25 years. This reduced the likelihood of structural change that could invalidate the predictive power of the underlying variables.

ii) We abandoned the approach of using UMD as the momentum portfolio, instead splitting the HML factor into its components – high book to market and low book to market. The high book to market portfolio (as defined by Kenneth French[7]) was used to represent the value portfolio. Whereas the low book to market was used as a proxy for a growth portfolio.

iii) Added a number of additional factors such as momentum in the dependent factor, the PE ratio as a percent of the 10 year moving average and VIX[8]

iv) We also introduced a 4th potential mixed portfolio based on the fixed weight and the full switch methods. When there was a high degree of confidence that the value was going to outperform momentum (i.e. ( >0.7) then 100% value weighted portfolio was selected, if there was a low degree of confidence then a mixed weight portfolio was chosen. Similarly if there is a high degree of confidence that the momentum will outperform growth (i.e. ( ................
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