Since 1950 the 4th quarter was positive 77% of the time for the Dow Jones, and 87% of the time on election years. Will it work this year or not? If you're waiting for an answer, please stop reading. I have none. This article is about a long-term vision of seasonal patterns.

It has been proven (here) that simple seasonal strategies on ETFs may have returned 20% to 33% a year for 10 years. The idea is to invest in a stock index ETF from the 1st of March to the 30th of April, then from the 1st of October to the 31st of December; and put the money in a bond ETF (NYSEARCA:TLT) the rest of the year. The chosen index has a great influence not only on the return, but also on the risk. This article shares some ideas about evaluating the risk, then choosing a lower risk seasonal strategy, and finally using it to hedge a dynamic ETF portfolio.

## Evaluating the Risk of a Strategy

More and more investors are using simulations on the past (or "backtests") to make investment decisions. Unfortunately they often make two mistakes: they assume that a simulation has a predictive power and they focus on the return. Indeed, the main interest of a simulation is in evaluating the risk of a strategy. It can be assessed on two levels:

1- The history of drawdowns. The most obvious indicators are the maximum drawdown depth (maximum relative loss in %) and the maximum drawdown length (maximum duration in loss): the lower, the better.

2- The probabilistic robustness of the "game." Kelly's formula is a good indicator for this purpose: the higher, the better.

Two other significant data may be calculated from the drawdown:

-The **recovery effort**, which is the gain necessary to make up for a loss. If the drawdown is x, the formula is f(x) =x/(1-x) .

For example, when a portfolio has a 30% drawdown, it needs a 43% gain to recover: 0.30/(1-0.30)= 0.4286. When it has a 50% drawdown, it needs a 100% gain: 0.5/0.5= 1. I consider the recovery effort as the **drawdown cost**.

-The **marginal recovery effort**, which is the additional gain necessary to make up for an additional loss. The formula is: df(x)/dx = 1/(1-x)^{2}.

For example, when a portfolio has a 30% drawdown, an additional 1% loss needs a 2% additional gain to recover: 1/(1-0.30)^{2}= 2.04. When an additional 1% loss occurs at a 50% drawdown, it needs a 4% additional gain to recover: 1/(1-0.50)^{2}= 4. I consider it as the **drawdown marginal cost**. It is an indicator of the risk if the drawdown goes beyond its maximum historical value.

## Application to three seasonal strategies

As written in the introduction, the generic strategy is investing in stock index ETFs in March, April, then from October to the end of the year; and in TLT the rest of the time. Let's compare three variants: the first with DIA (SPDR Dow Jones Industrial Average) as stock index ETF, the second with EWG (iShares MSCI Germany Index), and the third with an equally and daily rebalanced mix of both.

The following table shows the results of a 10-year simulation from 10/1/2002 to 10/1/2012 (precision of data: 2 digits). It also shows the buy-and-hold performance for each ETF, and gold as a reference. Dividends are included and reinvested when there are.

Seasonal strategy (+div.) | Average Return (CAGR in %) | DD max depth (%) | DD cost (%) | DD Marginal cost | DD max length (weeks) | Kelly (%) |

DIA / TLT | 21 | 31 | 45 | 2.1 | 64 | 11 |

EWG / TLT | 32 | 39 | 64 | 2.7 | 53 | 12 |

EWG+DIA / TLT | 27 | 34 | 52 | 2.3 | 55 | 12 |

Buy and hold +div. | ||||||

DIA | 8.2 | 52 | 108 | 4.3 | 179 | 5 |

EWG | 12 | 64 | 178 | 7.7 | 242* | 5 |

TLT | 8 | 27 | 37 | 1.9 | 134 | 6 |

Gold | 18 | 31 | 45 | 2.1 | 76 | 8 |

*still running |

The DIA/TLT seasonal strategy was "better than gold" for the decade, with a higher return and a similar max drawdown. Looking at the "buy-and-hold" returns for DIA and TLT, it is obvious that the performance really comes from a seasonal pattern and not from an outstanding behavior of bonds or DJ stocks.

The seasonal strategy gives the best return with EWG, but DIA and the mix show a significantly lower drawdown cost. For the purpose of the next step, I want to lower the drawdown cost and keep the average return above 25% a year. So my choice is the mixed version.

## Using a seasonal strategy as an hedge

The next idea is to add it into an existing dynamic ETF portfolio and to observe the consequences on the simulated return and risk. The dynamic portfolio rules, which rely on a systematic tactical asset allocation, are out of scope here. The aim is just to show the influence of adding the seasonal strategy into the portfolio. The chosen ratio is a constant: for three parts invested in the dynamic portfolio, two parts are invested in the seasonal strategy. Other money management rules may be used.

The following 10-year simulations (10/1/2002 to 10/1/2012) are performed with a weekly rebalancing and a 0.5% rate for slippage plus commission fees.

Dynamic portfolio:

3 parts Dynamic portfolio + 2 parts seasonal strategy (DIA+EWG / TLT):

*(click to enlarge)*

The visual feeling of a smoother curve is quantified in the following table:

Strategy | CAGR (%) | DD max depth (%) | DD cost (%) | DD Marginal cost | DD max length (weeks) | Kelly (%) |

Dynamic Portfolio | 33.9 | 24 | 31 | 1.7 | 44 | 26 |

Portfolio+seasonal | 30.9 | 13 | 15 | 1.3 | 42 | 31 |

The version with the added seasonal strategy divides by two the drawdown cost and maximizes the probabilistic robustness, for a small decrease in average return.

## Conclusion

Investors can take advantage of the seasonal patterns in different assets: global indexes, sectors, individual stocks, precious metals, commodities, and even currencies. It is possible to implement pure seasonal strategies with an average return above 20% a year for 10 years. It is also possible to use seasonal patterns to improve existing strategies. This article shows, as an example, how adding a seasonal strategy in a dynamic portfolio may lower the risk for a small cost in average return.

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**Disclosure: **I am long DIA, EWG. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.