We analyze the dependence of future returns on past drawdowns of the monthly time series of the S&P500 Index, from 1967 to 2012. From historical data, it appears when the drawdown increases in absolute value, future returns increase, both in mean as well as in distributional values.

2. Objective
Look forward
No more portfolios
based on past performance only

3. Weather forecast example
 How could I estimate the tomorrow raining probability using the basic
statistic?
 I count how many times rain in a year, for example 120 days, and I have the
33% of raining probability for tomorrow.
 Do you trust about this forecast?

4. Weather forecast example
 The weather - forecasting model are very thoroughly
 The forecast accuracy up to 90%
 The model is based on the conditional probability principles
𝑓 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒; 𝑤𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑; ℎ𝑢𝑚𝑖𝑑𝑖𝑡𝑦; … = 𝑤𝑒𝑎𝑡ℎ𝑒𝑟 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑖𝑛𝑔

5. Insight
Could we use the conditional probability in the financial market
to estimate the future success of an investment?
Why not !!!
There are not only performance and volatility

6. Rolling time windows
 Are there more attractive periods than others to invest in the stock market?
 Are there any periods to get better chance to have positive returns in the next three
years?
 At the time of investment, can I determine in advance the probability to achieve
positive returns?

7. Rolling time windows
We analyze the dependence between future returns and past drawdowns
 Index: S&P 500
 Period: from 1967 to 2012
 Frequency: monthly

8. S&P 500 returns Vs drawdown
3 Years Return / Risk: DD = 5%
Return
Risk

9. S&P 500 returns Vs drawdown
3 Years Return / Risk: DD = 10%
Return
Risk

10. S&P 500 returns Vs drawdown
3 Years Return / Risk: DD = 15%
Return
Risk

11. S&P 500 returns Vs drawdown
3 Years Return / Risk: DD = 20%
Return
Risk

12. S&P 500 returns Vs drawdown
3 Years Return / Risk: DD = 25%
Return
Risk

13. S&P 500 returns Vs drawdown
3 Years Return / Risk: DD = 30%
Return
Risk

14. Evidence
• When the drawdown increas in absolute value (remember the drawdown is
negative) future returns increase
• Presence of mean reversion in the index price
• It makes sense to use the drawdown effect to invest

15. Empirical Facts on the Drawdown
Accademic validation

16. S&P 500 returns
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

17. S&P 500 returns Vs volatility
S&P 500 returns (on y axis) Vs volatility (on x axis)
Uncorrelation between futures returns & past volatility
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

18. S&P 500 returns Vs drawdown
S&P 500 returns (on y axis) Vs drawdown (on x axis)
Correlation between futures returns & past drawdown
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

19. Statistics
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

20. Monte Carlo Simulation
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

21. Conclusion
• This fact could be causes by the presence of mean reversion in the index price
• The mathematical model that we use should incorporate mean reversion in
order to reproduce significally thi effect
• For more detail about the model see the appendix

22. Software implementation
• DIAMAN has developed an innovative tool to estimate in advance, in the
financial market, the probability to achieve positive return
• When the propability is between 49% - 75% means less probability to get
positive returns
• When the propability is above 75% means high probability to get positive
returns

23. Equity portfolio: 2007

24. Equity portfolio: 2009

25. Model efficiency
Increasing Ex-Ante probability  Increase Ex-Post positive returns

26. Dynamic model
The grey columns show the period of the past crisis of 2007 and 2011

27. Accademic validation
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

28. More detail…
Source: The Right Time to Enter (Tiziano Vargiolu University of Padova – July 2014 World Finance Conference Venice)

29. www.diamantech.net
www.ex-ante.it
michael.zanon@diamantech.net