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.
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 (bn) and the R2. This allowed us to predict the likely result of the dependent variable (p (x)) for an out of sample period of January 2001 to December 2003.
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 (p). 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).
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:
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. p >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. p <0.3) then the growth portfolio was chosen.
Results
The coefficients that best fit this data series were slightly different from the first 6. We chose:
- The percentage change in the equity market over the previous month
- The moving average change in the equity market over the last 6 months
- 2 continuous months of growth outperformance
- VIX index
- 3 month CD rate
The changes made a big difference to the regression. The new model registered an improved R2 of 8.5%. Unfortunately, these results were not replicated out of sample and only 52% of the predicted results were correct in the forecast period, from January 2000 to December 2003
Unfortunately, during the out of sample forecast period both the S&P and the Dow experienced strong bear markets. As the bubble burst, value stocks consistently outperformed growth stocks. Thus, the model appears to have significantly underperformed the market.
Alarmingly, the variable weight portfolios did not significantly reduce volatility in earnings over the period.
Phase 3
Method
In the next iteration, we made one major adjustment to the model. We decided to sample over the whole time period from 1976 to 2003 to allow for the full range of the economic cycles. The graph below shows the growth in the S&P500 over time from January 1976 (where n=100). It shows that picking a sample of 1976 until the end of 1999 is not representative. Instead, we decided to base the regression on a randomized sample of 50% of the months over the period to develop the coefficients of the model.
Results
Our results are significantly improved using this measure. We found that in sample R2 improved to 8.5%.[9] This means that the model predicted the outperforming portfolio 62.1% of the time in sample. Out of sample, the predictability remained high with the model predicting the outperforming portfolio 58.1% of the time.
The best variables that fit this model were:
- 3 continuous months of value outperformance
- 2, 3 continuous months of growth outperformance
- Spread between the Aaa and T-bond
- PE ratio compared to 10 year moving average
This graph represents the results the performance of each of the portfolios. It is based exclusively on out of sample data.
The results show that using the full switch portfolio is optimal. It marginally underperforms the value only portfolio under standard market conditions though it significantly outperforms the value portfolio in growth periods (e.g. 1978-79, 1988-1991 and in 1999). The Sharpe ratio of this portfolio is also significantly greater than the other dynamic weight portfolios and the value portfolio.
Conclusions and implications
Implications of research
Our research suggests that it is worthwhile using a predictive model as we have outlined for asset allocation between growth and value based funds.
Practically, we envisage that such a strategy can be combined with other investment strategies, such as the long-short value and growth portfolios, to provide an incremental improvement in performance. Such an approach does require a highly disciplined approach to investing and hence may not suit all investors.
Problems with the approach
The process that we have followed takes no account of any structural shifts in the market and hence, may make future forecasting prone to error.
Further research
We suggest that a number of further avenues of research be investigated to confirm the practical nature of the approach. First, we suggest the investigation of the impact of trading costs on portfolio returns to see whether such a strategy is actually beneficial to investors. Secondly, we propose checking the veracity of such an approach by reapplying to the US market at various points in its history to examine the stability of predictive model structure (predictive variables and their coefficients) Thirdly, we propose extending to liquid overseas markets, to investigate whether this form of model in generally applicable.
Appendix A
Return in the equity market over the previous month
Average monthly return in the equity market over the last 2 months
Average monthly return in the equity market over the last 3 months
Average monthly return in the equity market over the last 4 months
Average monthly return in the equity market over the last 5 months
Average monthly return in the equity market over the last 6 months
Value has outperformed growth portfolio for 2 consistent months
Value has outperformed growth portfolio for 3 consistent months
Growth has outperformed value portfolio for 1 month
Growth has outperformed value portfolio for 2 consistent months
Growth has outperformed value portfolio for 3 consistent months
5 year cumulative return in the equity market
5 year annualized cumulative return in the equity market
12 month annual return
Risk free rate
5 year cumulative market risk premium
5 year annualized market risk premium
Equity Premium
1 year average dividend yield
1 year average dividend yield – 5 year old data
1 year average risk free rate
1 year average risk free rate – 5 year old data
Commercial Paper (average)
Commercial Paper – 5 year old data
Aaa bond yield
Aaa bond yield – 5 year old data
Baa bond yield
Baa bond yield – 5 year old data
Aaa – Tbill yield spread
30yr T-bond yield
Aaa – Tbond yield spread
Baa – Aaa yield spread
1 year debt
2 year debt
3 year debt
5 year debt
10 year debt
20 year debt
3 month debt
6 month debt
Certificate of Deposit – 1 month maturity
Certificate of Deposit – 3 month maturity
Certificate of Deposit – 6 month maturity
US long-term corporate debt
US long-term government debt
US intermediate term government debt
US 30 day government debt
CPI inflation
Average S&P price-earnings ratio
S&P price-earnings ration to 10 yr Moving average (percent)
S&P comp
Dividend
Earnings
Consumer Price Index
Real Price
Real Dividend
Real Earnings
Price to average 10-yr earnings
Change in real earnings
Change in real GDP (percent)
VIX (Implied volatility)
[1] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
[2] Lakonishok, J.; Vishny, R.W.; Shleifer, A. 1993. Contrarian Investment, Extrapolation and Risk, Working Paper No. 4360, National Bureau of Economic Research, May
[3] Fama, E.; French, K.R. 1992. The Cross-section of Expected Stock Returns, The Journal of Finance, June
[4] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_portfolios.html
[5] From January 1927 to December 1999 inclusively
[6] Nagelkerke R square; Cox & Snell R square of 1.0%
[7] http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_bench_factor.html; data based on NYSE constituents
[8] The implied volatility on the S&P 100 (OEX) option
[9] Nagelkerke R square; Cox & Snell R square of 6.3%