BlackDog: A Dynamic Stock/Bond Allocation Strategy

Posted on September 12, 2014 by


It is well known that portfolios that blend stocks and bonds perform well because their major asset classes are anti-correlated.  There are a few major weaknesses in the way these portfolios are typically managed however.  Namely that the ratio of stocks to bonds is usually fixed, and also that they don’t always use the best representatives of their asset classes.


BlackDog is an investment strategy that leverages a macro economic model to direct allocation between equities and fixed income.  The macro model is covered in another, recent blog. The strategy is conservative because it invests long-only in large cap US stocks and liquid US fixed income instruments. In investment simulations (back tests) and live trading, the strategy significantly outperforms market benchmarks.

The BlackDog strategy was inspired by the well-known 60/40 portfolio where 60% is allocated to US large cap stocks and 40% to bonds or other fixed income. At Lucena Research we’ve discovered three ways to improve on this standard approach that adds substantial value while preserving some of the more important features of the 60/40:

  1. Dynamic allocation: Instead of a constant 60/40 allocation between equities and bonds, we adjust the ratio based on a macro economic model. This active approach reduces exposure to stocks during uncertain times, while increasing exposure during bull markets.
  1. Better fixed income instruments: The standard bond component of the 60/40 strategy is not responsive to moves in the equity markets. We replace it with a more active group of securities that provide a stronger hedge in market downturns.
  1. Better equity selection: We skew the portfolio towards lower market cap stocks and value stocks.

When these three techniques are combined, the result is a portfolio that provides superior return with low volatility and risk.

Background: The 60/40 portfolio

60/40 portfolio (green) versus the S&P 500 Total Return benchmark (purple).

60/40 portfolio (green) versus the S&P 500 Total Return benchmark (purple).

The 60% stock / 40% bond portfolio is a cornerstone of investment practice. Wealth managers often recommend this balance because:

  • It provides diversification across the most important asset classes in the US.
  • It is weighted in favor of equities, which have a strong history of outperformance.
  • It includes bond exposure to “cushion” against severe downturns.

The chart at right illustrates the performance of a 60/40 portfolio from 2005 to mid 2014. The 60/40 portfolio is charted in green, while the S&P 500 Total Return benchmark is in purple. In this portfolio we use SPY (an S&P 500 index ETF) to represent the 60% large cap equity component and AGG (an ETF that tracks Barclay’s Aggregate Bond Index) for the 40% fixed income component. The portfolio is rebalanced monthly. The strategy has lower cumulative return than the market, but still provides several important performance properties:

  • Lower volatility: 0.77% versus 1.32% for the market.
  • Reduced drawdown: 35.53% versus 55.25% for the market.
  • Higher Sharpe Ratio: 0.57 versus 0.44.

These are great performance features, but they come at the cost of lower return than the market overall. Can we improve on that while retaining these features? We think so, and we describe how below.

How to improve? Dynamic allocation

It is clear, in hindsight, that investors would have done better in 2008 if they had known to move from stocks to fixed income at the beginning of 2008. And similarly, if we could anticipate future bull markets we’d like to be able to shift assets into equities beforehand. But,

  •  How can we predict market strength or weakness?

Short-term market timing is challenging, and may not be appropriate for conservative portfolios. However, we believe that macro economic indicators have strong longer-term predictive capability, and that it makes sense to pay attention to them.  In a recent blog we showed how an ensemble of macroeconomic factors could be used to forecast market strength.  We’ll avoid going into detail on that method here, please read the other article for details.

Lucena's macro economic model for market strength.

Lucena’s macro economic model for market strength from 1988 to 2014. The top (blue) line represents the indicator, where a larger value is bullish and small values are bearish. The bottom (red) line represents the value of the S&P 500 index.

The main point is that with our BlackDog strategy we utilize the output of the macro model to dynamically adjust allocation to large cap stocks from 30% to 70% accordingly. (Overall performance of the strategy is reported in a later section.)

How to improve? Better fixed income assets

Historical performance of the S&P 500 (blue) and AGG (red, aggregate bond index fund).

Historical performance of the S&P 500 (blue) and AGG (red, aggregate bond index fund).

We addressed the challenge of asset allocation between stocks and bonds with the macro economic model discussed above. But another problem remains: Which securities are the best representatives of these asset classes?

In order to achieve optimal performance, each of the components of a portfolio should serve a role and work together with the others. Most investors simply view the bond component of their portfolios as the “safe” part that provides a fallback in case of an equity market crash. Typically, wealth advisors suggest a blend of corporate bonds, treasuries and other instruments to fill the fixed income role. The AGG ETF holds all of these types of securities and is representative of the sorts of instruments used in many 60/40 portfolios, so we used it in our baseline 60/40 portfolio.

A more active set of fixed income securities (red) provides a better hedge for equities.

A more active set of fixed income securities (red) provides a better hedge for equities.

The figure at right illustrates the comparative performance of AGG and the S&P 500. As you can see, AGG provides non-volatile increasing value over time. That’s great, but we want more. We argue that the fixed income component should provide a more active hedge for equities.

The problem with AGG and other, similar fixed income securities is that they are not reactive: In other words, when the market drops significantly, these standard instruments don’t respond by increasing in value to offset the loss.

In our BlackDog strategy we use more active fixed income securities (see figure below right). Notice that our new instrument (red) is strongly anti-correlated with equities (blue). Even so, both groups of securities increase in value over time.

At first it might seem that combining these two somewhat volatile components in to a portfolio could lead to a more volatility or risk. But it’s just the opposite, with frequent rebalancing these sorts of securities provide the recipe for a great portfolio: A basket of assets whose volatilities cancel each other’s out while simultaneously increasing in value over the long run. This is a cornerstone of Modern Portfolio Theory.

BlackDog performance in backtesting

Our overall strategy then is to utilize the macro economic model to set an allocation of 30% to 70% large cap stocks with the remainder allocated to fixed income securities. We carefully select high quality securities for both the large cap side and the fixed income side so they are responsive to one another.

BlackDog performance (green) in backtesting versus the S&P 500 benchmark (purple).

BlackDog performance (green) in backtesting versus the S&P 500 benchmark (purple).

In the table below we list some of the key performance criteria of our benchmark, the 60/40 and our strategy, BlackDog. BlackDog provides 50% higher cumulative return than the market at less than ½ the volatility and about 1/3 the drawdown. Turnover averages about 5% per month.

In the figure on the next page below we provide a backtest of BlackDog from the beginning of 2005 to May 2014. In our backtesting (market simulation) we initialize a portfolio with $100M in cash. We then allow the strategy to allocate between large cap stocks and fixed income and rebalance monthly. The simulation is intitiated in January 2005 and continues through late April 2014. The simulation includes commissions and market impact simulation of 5bps for each trade. We do not use leverage.


Return Sharpe Volatility Drawdown


93.16% 0.44 1.32% -55.25%
60/40 78.70% 0.58 0.77% -35.53%
BlackDog 140.72% 1.00 0.63% -17.20%

Note that due to the anticipatory shift from equities to fixed income, BlackDog avoids significant downturn in 2008. Similarly, it shifts back into stocks in 2009, then benefits from the strong bull market since that time.

BlackDog outperforms the market in terms of total return at lower volatility and lower drawdown. The strategy provides consistent, low volatility returns.

Performance of BlackDog (orange) in forward testing from April 2, 2014 to September 11, 2014.  The benchmark (purple) is the ETF SPY.

Performance of BlackDog (orange) in forward testing from April 2, 2014 to September 11, 2014. The benchmark (purple) is the ETF SPY.

Performance in live trading and forward testing

BlackDog has been traded live since April 2, 2014 (see chart at right). Its performance in live trading since that time is similar to our simulated results in terms of performance versus the market. Specifically: Volatility is substantially lower than that of the S&P 500 (37 bps versus 57 bps per day), Sharpe Ratio is 2.83 versus 1.83 for the market, and cumulative return is 1.29% over that of the market.


The primary risks for BlackDog are stock market risk (how with the S&P 500 perform?) and interest rate risk. Of these, interest rate risk is probably the more important because we believe that when interest rates increase, the overall market and fixed income will be impacted negatively.

Please read a separate article about interest rate risk here.

Disclosures and Disclaimers

Disclaimer: This information has been prepared by Lucena Research Inc. and is intended for informational purposes only. This information should not be construed as investment, legal and/or tax advice. Additionally, this content is not intended as an offer to sell or a solicitation of any investment product or service.

Please note: Lucena is a technology company and not a certified investment advisor. Do not take the opinions expressed explicitly or implicitly in this communication as investment advice. The opinions expressed are of the author and are based on statistical forecasting based on historical data analysis. Past performance does not guarantee future success. In addition, the assumptions and the historical data based on which an opinion is made could be faulty. All results and analyses expressed are hypothetical and are NOT guaranteed. All Trading involves substantial risk. Leverage Trading has large potential reward but also large potential risk. Never trade with money you cannot afford to lose. If you are neither a registered nor a certified investment professional this information is not intended for you. Please consult a registered or a certified investment advisor before risking any capital.