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 term2. 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
1
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
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
2
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 period5 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.
4
5
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_portfolios.html
From January 1927 to December 1999 inclusively
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).
Cumulative portfolio returns
180
160
140
Value
Momentum
120
100
50:50
80
Dyn Weights
60
Full Switch
40
20
Ja
n0
Ap 0
r-0
0
Ju
l-0
O 0
ct
-0
Ja 0
n0
Ap 1
r-0
1
Ju
l-0
O 1
ct
-0
Ja 1
n0
Ap 2
r-0
2
Ju
l-0
O 2
ct
-0
Ja 2
n0
Ap 3
r-0
3
Ju
l-0
O 3
ct
-0
3
-
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:
Average Monthly Return
Standard Deviation
Sharpe Ratio
Value
0.47%
5.84%
5.20%
Momentum
0.54%
8.10%
4.58%
50:50
0.50%
3.15%
10.70%
Dynamic weight
0.46%
3.15%
9.32%
Full Switch
0.93%
6.50%
11.70%
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.
6
Nagelkerke R square; Cox & Snell R square of 1.0%
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)
(ii)
(iii)
(iv)
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.
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 French7) was used to represent the value portfolio. Whereas the low
book to market was used as a proxy for a growth portfolio.
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 VIX8
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.  <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
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
160
140
120
Value
100
Growth
50:50
80
Dynamic weight
Full Switch when Pr >.7
60
Full Switch
40
20
Ja
n0
Ap 0
r-0
0
Ju
l-0
O 0
ct
-0
Ja 0
n0
Ap 1
r-0
1
Ju
l-0
O 1
ct
-0
Ja 1
n0
Ap 2
r-0
2
Ju
l-0
O 2
ct
-0
Ja 2
n0
Ap 3
r-0
3
Ju
l-0
O 3
ct
-0
3
0
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.
Average Monthly Return
Standard Deviation
Sharpe Ratio
Value
1.02%
7.11%
11.95%
Growth
-0.27%
7.00%
-6.28%
50:50
0.37%
6.43%
3.20%
Dynamic
weight
0.24%
6.80%
1.16%
Full Switch
when Pr >.7
0.11%
7.06%
-0.85%
Full Switch
0.02%
7.35%
-1.95%
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.
10000
1000
100
10
Jan-03
Jan-02
Jan-01
Jan-00
Jan-99
Jan-98
Jan-97
Jan-96
Jan-95
Jan-94
Jan-93
Jan-92
Jan-91
Jan-90
Jan-89
Jan-88
Jan-87
Jan-86
Jan-85
Jan-84
Jan-83
Jan-82
Jan-81
Jan-80
Jan-79
Jan-78
Jan-77
Jan-76
1
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.
9
Nagelkerke R square; Cox & Snell R square of 6.3%
1600
1400
1200
1000
Value
Growth
50:50
Dynamic weight
Full Switch when Pr >.7
Full Switch
800
600
400
200
Feb-02
Feb-00
Feb-98
Feb-96
Feb-94
Feb-92
Feb-90
Feb-88
Feb-86
Feb-84
Feb-82
Feb-80
Feb-78
Feb-76
0
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.
Return
Standard dev
Sharpe Ratio
Rank
Value
1.4%
5.2%
19.2%
2
Growth
1.0%
6.0%
9.9%
6
50:50
1.2%
5.3%
15.0%
5
Dynamic
weight
1.3%
5.2%
17.5%
3
Full Switch
when Pr >.7
1.3%
5.2%
17.1%
4
Full Switch
1.7%
5.3%
24.1%
1
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)