# Does the Croatian Stock Market Have Seasonal Affective Disorder?

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## Abstract

**:**

## 1. Introduction

## 2. Previous Research

## 3. Methodology Description

_{t}hours from sunset to sunrise at any location at date t. The SAD measure at time t is defined via photoperiod as:

_{t}measure is observed only during the fall and winter time, as previous medical literature determined that it affects people during that time only (see Jacobsen and Marquering 2008). H

_{t}is defined from spherical trigonometry as:

_{t}is sun’s declination angle at latitude δ, ${\lambda}_{t}=0.4102\mathrm{sin}\left({\scriptscriptstyle \frac{2\pi}{365}}\left({J}_{t}-80.25\right)\right)$ and J

_{t}variable which ranges from 1 to 365 (or 366), depending upon the day of the year. The asymmetry in risk aversion around winter solstice is regarded in the literature as well. Kamstra et al. (2003) defined it as the following variable:

_{t}denotes return at time t, lagged values of return series are added to control autocorrelation, MON

_{t}is the first control variable, capturing effects of Monday (value is equal to 1 on Mondays, 0 otherwise); and the second control variable is Tax

_{t}is tax-loss selling binary variable (equal to 1 for the last day of the tax year and first four of the next, 0 othervise). The error term is denoted with ε

_{t}. The MON effects (Monday or weekend effects) are one of the most famous calendar anomalies in the literature, explained in e.g., Miller (1988), where the author states that investors gain new information on stocks over the weekend. On Mondays, investors usually try to restructure their portfolios due to new information obtained over the weekend. This makes price pressures by lowering prices on Mondays. The tax selling anomaly is explained in, e.g., Lakonishok and Smidt (1988) or Agrawal and Tandon (1994). Basically, investors sell parts of their portfolios at the end of the year in order to pay fewer taxes on capital gains due to having lower performing stocks in the portfolios. At the beginning of a new year, the investors buy back the stocks they sold at the end of the previous year. For more details on mentioned calendar anomalies please refer to Škrinjarić (2012). Finally, as previous newer research finds the effects of COVID-19 pandemics on return and volatility series (Zhang et al. 2020; Barro et al. 2020; He et al. 2020), we include the binary variable Cov

_{t}which is equal to 1 starting from 1 February 2020 to 28 April 2020.

_{t}is added in model (4):

_{SAD}should be positive and if asymmetry exists in investors’ risk aversion, value of β

_{F}should be negative. This means that more depressed and risk averse investors stay away from riskier asset in fall and winter by selling stocks and buying safer assets when days are getting shorter. However, the asymmetric effects when comparing fall and winter days should be captured in the negative value of β

_{F}, which describes changing patterns of selling more stocks as winter is coming and buying them again as winter solstice passes.

_{i,t}denotes excess return on the asset i, r

_{m,t}excess market return and $\lambda $ the price of risk. In the case of excess market return, (6) becomes:

_{t}and F

_{t}variables:

_{t}and F

_{t}variables will be checked via estimating a GARCH specification of Model (5); comparing the results of estimation of (5) for the return and excess return series; and for the asymmetric effects in variable F

_{t}via splitting SAD measure into fall and winter variables and excluding the binary variable F

_{t}from the models, as in Kamstra et al. (2003).

## 4. Empirical Results

#### 4.1. Data Description

^{−5}, whilst in the other months of the year, it is equal to value −0.0002. Since a difference exists, formal models and testing could point to the existence of SAD effects on ZSE.

#### 4.2. Initial Results

#### 4.3. Robustness Checking

_{f}and SAD

_{w}, respectively. Results are shown in Table 6, where it can be seen that the differences between fall and winter SAD effects are equal to differences in the original specification in the model (from Table 3). Moreover, SAD effects are stronger in the wintertime, as it was found in the original model in Table 3. Thus, we find the results to fairly be robust and useful in future research.

#### 4.4. Simple Investing Strategies Simulation

- (i)
- First strategy is the SAD_W, in which the investor uses the contrarian strategy where he buys the stock market index before the winter time and holds it during the winter. When spring comes, he sells the index and holds the money until the new winter season arrives.
- (ii)
- Second strategy is SAD_W+F, in which investor uses contrarian strategy again (as previous one), but adds the information about asymmetric effect of the fall time. Thus, when the variable Fall is not equal to zero, then the investor does not sell the index, as returns fall additionally. Opposite is true for Fall being equal to zero.
- (iii)
- Third strategy is SAD_F, in which the investor uses the contrarian strategy, in which he buys the index when the value of Fall is not equal to zero due to lower returns, and holds the index until it is ready to be sold (when the value of Fall is zero).
- (iv)
- Fourth strategy is simulated based on those investors who are affected by the SAD effects and do the wrong thing, sell when the returns are expected to rise, and buy when the returns are expected to fall. This is called “affected”.

_{w}variable and its effects on the return series. The COVID-19 crisis has been ignored, although strategies could have included the contrarian approach here as well. This means that those who aim to exploit inefficiencies such as the SAD effects could have exploited the effects of the pandemic on stock markets. Previous literature (Zhang et al. 2020; Barro et al. 2020; He et al. 2020) has indicated that short-term effects in return series existed. This means that the strategies aiming in exploiting all these predictable issues could have performed even better. This preliminary analysis could be a basis for more sophisticated trading strategies which could be observed in future work.

#### 4.5. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Authors (year) | Market, Data | Findings |
---|---|---|

Kamstra et al. (2003) | US, Sweden, UK, Germany, Canada, New Zealand, Japan, Australia, South Africa; 1928–2003 | Seasonal affective disorder (SAD) effects exist, greater effects when further from the equator |

Garrett et al. (2005) | US, UK, Japan, Sweden, New Zealand, and Australia; 1962–2000 | SAD effects exist |

Jacobsen and Marquering (2008) | 48 countries; 1970–2004 | SAD effects insignificant |

Kamstra et al. (2009) | Replication of Jacobsen and Marquering (2008) | SAD effects found, problems of 2008 paper found |

Dolvin et al. (2009) | US, 1998–2004 | Analysts’ forecasts are under SAD effects |

Stefanescu and Dumitriu (2011) | Romania, 2002–2011 | SAD effects found, but no control variables included |

Hammami and Abaoub (2011) | Tunis, 1998–2008 | No SAD effects, Tunis is close to the equator |

Lo and Wu (2018) | US, 1998–2004 | Pessimistic analyst forecasts when SAD effects hold |

Murgea (2016) | Romania, 2000–2014 | SAD effects found in every subsample (before, during and after 2008 crisis) |

Škrinjarić (2018) | Bosnia and Herzegovina, Bulgaria, Croatia, Czech Republic, Hungary, Poland, Serbia, Slovakia, Slovenia, Romania, and Ukraine, 2010–2018 | 6 out of 11 (Croatia included) had SAD effects, only return series observed |

Descriptive Statistics | Return | Excess Return |
---|---|---|

Mean | −4.37 × 10^{−5} | −0.009 |

Standard deviation | 0.0075 | 0.0135 |

Min | −0.1073 | −0.1076 |

Max | 0.0856 | 0.0626 |

Skewness | −1.7526 | −1.2474 |

Kurtosis | 41.477 | 6.498 |

AR(5) | 94.474 (0.000) | 69.08 (0.000) |

ARCH(5) | 934.32 (0.000) | 53.09 (0.000) |

Parameter/Diagnostics | Model (1) | Model (2) | Model (3) | Model (4) |
---|---|---|---|---|

$\widehat{\mu}$ | 9.61 × 10^{−5} (0.0002) | 9.37 × 10^{−5} (0.0002) | - | - |

${\widehat{\beta}}_{SAD}$ | 0.0003 (0.0001) ** | 0.0004 (0.0002) *** | - | - |

${\widehat{\beta}}_{MON}$ | −0.0018 (0.0004) *** | −0.002 (0.0004) ** | - | - |

${\widehat{\beta}}_{Tax}$ | 0.0017 (0.001) * | 0.0014 (0.0012) | - | |

${\widehat{\beta}}_{F}$ | −0.0003 (0.0002) * | - | - | |

${\widehat{\beta}}_{\mathrm{cov}}$ | −0.0033 (0.003) | −0.0035 (0.0032) | ||

$\widehat{\lambda}$ | - | - | 3.45 (3.57) | - |

${\widehat{\alpha}}_{0,arch}$ | - | - | 1.89 × 10^{−6} (3.89 × 10^{−7}) *** | - |

${\widehat{\alpha}}_{1,arch}$ | - | - | 0.096 (0.015) *** | - |

${\widehat{\beta}}_{1,arch}$ | - | - | 0.859 (0.021) *** | - |

${\widehat{\phi}}_{0}$ | - | - | - | −0.052 (0.025) ** |

${\widehat{\phi}}_{1}$ | - | - | - | 0.055 (0.019) *** |

${\widehat{\phi}}_{2}$ | - | - | - | −0.038 (0.024) * |

Parameter/Parameter | ${\widehat{\mathit{\beta}}}_{\mathit{S}\mathit{A}\mathit{D}}$ | ${\widehat{\mathit{\beta}}}_{\mathit{F}}$ |
---|---|---|

Original (from Table 2) | 0.0004 (0.0002) *** | −0.0003 (0.0002) * |

With GARCH specification | 0.0001 (0.001) *** | −0.0002 (0.001) ** |

Parameter/Parameter | ${\widehat{\mathit{\beta}}}_{\mathit{S}\mathit{A}\mathit{D}}$ | ${\widehat{\mathit{\beta}}}_{\mathit{F}}$ |
---|---|---|

Original (from Table 2) | 0.0004 (0.0002) *** | −0.0003 (0.0002) * |

With GARCH specification | 0.0002 (0.0011) *** | −0.0002 (0.019) ** |

Parameter/Diagnostics | Model 2 | Model 4 | ||
---|---|---|---|---|

SAD f and w | Relation to the Original Model | SAD f and w | Relation to the Original Model | |

${\widehat{\beta}}_{f}$ | 0.0002 (0.520) | Difference between estimated values as for ${\widehat{\beta}}_{SAD}$ and ${\widehat{\beta}}_{F}$ | - | - |

${\widehat{\beta}}_{w}$ | 0.0004 (0.0002) *** | - | ||

${\widehat{\phi}}_{f}$ | - | - | 0.0001 (0.631) | Difference between estimated values as for ${\widehat{\phi}}_{1}$ and ${\widehat{\phi}}_{2}$ |

${\widehat{\phi}}_{w}$ | - | 0.0005 (0.000) *** |

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**MDPI and ACS Style**

Škrinjarić, T.; Marasović, B.; Šego, B.
Does the Croatian Stock Market Have Seasonal Affective Disorder? *J. Risk Financial Manag.* **2021**, *14*, 89.
https://doi.org/10.3390/jrfm14020089

**AMA Style**

Škrinjarić T, Marasović B, Šego B.
Does the Croatian Stock Market Have Seasonal Affective Disorder? *Journal of Risk and Financial Management*. 2021; 14(2):89.
https://doi.org/10.3390/jrfm14020089

**Chicago/Turabian Style**

Škrinjarić, Tihana, Branka Marasović, and Boško Šego.
2021. "Does the Croatian Stock Market Have Seasonal Affective Disorder?" *Journal of Risk and Financial Management* 14, no. 2: 89.
https://doi.org/10.3390/jrfm14020089