### Raw Data Preparation

The mutual funds listed on the Ghana Stock Exchange are used for the input instances for our experiment. For accuracy of information from our sample funds and their respective fund managers, we selected six continuous historical years that is 2010–2011, 2012–2013 and 2014–2015. The raw data was collected from the Ghana Stock Exchange database for the selected funds and then calculated to provide the input variables for the models. The following section processed the data on year by year bases for all the selected funds which data is accurate.

### Inputs Instances

This study focuses on the fund manager’s momentum strategies and herding behavior as the input variables applied in FANNC and ERBPNN. These variables are used because many factors that affect mutual fund performance such as the size of the fund and other features of the fund managers have been studied in earlier researches (Anish et al. 2018).

#### Momentum Strategies

Momentum is the best known anomaly in equities. It comes with the premise that, past winners will continue to have a strong return in future, while past losers will also continue to have a weak return in the future. For this reason, it is always the best to pick the future best performing mutual funds. Momentum investors will buy stocks or equities that were past winners and sell those stocks that were past losers (Lang et al. 2018).). Chen and Xu (2018) suggest the following equation:

$$ M=\frac{1}{T}\sum \limits_{t=1}^T\sum \limits_{s=1}^N\left({\overset{\sim }{\omega}}_{s,t}-{\overset{\sim }{w}}_{s,t-1}\right){\overset{\sim }{R}}_{s,t-k+1} $$

(1)

Where \( {\overset{\sim }{\omega}}_{s,t} \) is the portfolio weight on security s at time t,

\( {\overset{\sim }{R}}_{s,t-k+1} \) is the return of security s (s = 1, … …,N) from time t-k to time t-k + 1, with k as the lag index.

The two benchmarks that are most recent times are represented by k = 1 and k = 2. They may be the major facts that affect the momentum of the fund. The study refer M_{1} as lag-1 momentum (L1M) and M_{2} as lag-2 momentum (L2M).

Again, the study crumble the L1M into “buy” and “sell” parts. The equations are:

$$ {M}_{1\kern0.5em B}=\frac{1}{T}\sum \limits_{s=1}^T\sum \limits_{s=1}^N\sum \limits_{{\overset{\sim }{\omega}}_{s,t}>{\overset{\sim }{\omega}}_{s,t-1}}\left({\overset{\sim }{\omega}}_{s,t}-{\overset{\sim }{w}}_{s,t-1}\right)\left({\overset{\sim }{R}}_{s,t}-{\overline{R}}_s\ \right) $$

(2)

$$ {M}_{1\kern0.75em S}=\frac{1}{T}\sum \limits_{s=1}^T\sum \limits_{s=1}^N\sum \limits_{{\overset{\sim }{\omega}}_{s,t}<{\overset{\sim }{\omega}}_{s,t-1}}\left({\overset{\sim }{\omega}}_{s,t}-{\overset{\sim }{w}}_{s,t-1}\right)\left({\overset{\sim }{R}}_{s,t}-{\overline{R}}_s\ \right)\kern0.5em $$

(3)

The mean is then subtracted from the return so as to have measures that will be close to zero under no momentum investing. Closely to the lag-1 momentum measures, the ‘buy’ and ‘sell’ parts of the lag-2 momentum measure are:

$$ {M}_{2\kern0.5em B}=\frac{1}{T}\sum \limits_{s=1}^T\sum \limits_{s=1}^N\sum \limits_{{\overset{\sim }{\omega}}_{s,t}>{\overset{\sim }{\omega}}_{s,t-1}}\left({\overset{\sim }{\omega}}_{s,t}-{\overset{\sim }{w}}_{s,t-1}\right)\left({\overset{\sim }{R}}_{s,t}-{\overline{R}}_s\ \right) $$

(4)

$$ {M}_{2\kern0.75em S}=\frac{1}{T}\sum \limits_{s=1}^T\sum \limits_{s=1}^N\sum \limits_{{\overset{\sim }{\omega}}_{s,t}<{\overset{\sim }{\omega}}_{s,t-1}}\left({\overset{\sim }{\omega}}_{s,t}-{\overset{\sim }{w}}_{s,t-1}\right)\left({\overset{\sim }{R}}_{s,t}-{\overline{R}}_s\ \right) $$

(5)

#### Herding Behaviour

Herding behaviour is a trade situation where mutual funds managers buy and sell the same stocks in the same period. Recently institutional herding behaviour attracts some interests in academics as well as in professionals (Yan et al. 2017). The three measurements of herding behaviour are: unsigned herding measure (UHM) presented by Lakonishok, Shleifer et al. (1992), which measures the average tendency of all managers to take a decision on whether to buy or to sell a particular stock at the same time. It is mathematically presented as:

$$ {UHM}_{st}=\left|{P}_{s,t}-{\overline{P}}_t\right|-\kern0.75em E\left|{P}_{s,t}-{\overline{P}}_t\right| $$

(6)

Where *P*_{s,t} equals the proportion of the mutual funds that purchase stocks during quarter _{t}, and \( \overline{p} \)_{t}, the expected value of *P*_{s,t} is the mean of *P*_{s,t} over all stocks during quarter *t*. UHM has it challenges and among which is that, it cannot most often differentiate a manager’s herding between selling and buying the stocks. The second herding measure was introduce and propose by Grinblatt, Sheridan and Wemers (1995) and they named it signed herding measure (SHM) which provides an indication of whether a fund is “following the crowd” or “going against the crowd” for a particular stock during the specified period. SHM is presented mathematically as:

$$ {SHM}_{st}={I}_{st}\times {UHM}_{s,t}-E\left[{I}_{st}\times {UHM}_{s,t}\right] $$

(7)

Where *I*_{st} is an indicator for ‘buy’ or ‘sell’ herding. *I*_{st} is defined as follows:

*I*_{st} = 0 If \( \left|{P}_{s,t}-{\overline{P}}_t\right|<\kern0.75em E\left|{P}_{s,t}-{\overline{P}}_{t.}\right| \)

*I*_{st} = 0 If \( \left|{P}_{s,t}-{\overline{P}}_t\right|>\kern0.75em E\left|{P}_{s,t}-{\overline{P}}_t\right| \)

and the mutual fund is a buyer of stock s during quarter *t,* or

If \( -\left({P}_{s,t}-{\overline{P}}_t\right)>\kern0.75em E\left|{P}_{s,t}-{\overline{P}}_t\right|\kern1em \) and the fund is a seller of stock *s*.

*I*_{st} = − 1 If \( {P}_{s,t}-{\overline{P}}_t<\kern0.75em E\left|{P}_{s,t}-{\overline{P}}_t\right|\kern.5em \) and the mutual fund is a seller of stock s during quarter *t,* Or If \( -\left({P}_{s,t}-{\overline{P}}_t\right)>\kern0.75em E\left|{P}_{s,t}-{\overline{P}}_t\right|\ \mathrm{a}\mathrm{nd}\ \mathrm{the}\ \mathrm{fund}\ \mathrm{is}\ \mathrm{a}\ \mathrm{buyer}. \)

SHM _{s,t}, is set to be zero if fewer than 10 funds trade stock _{s} during time t. If the number of funds trading stock _{s} is small, no meaningful way can indicate whether the fund is herding or not. Finally, the herding measure of a mutual fund (FHM) is then calculated by substituting the signed herding measure in place of the stock return in eq. (1).

$$ FHM=\frac{1}{T}\sum \limits_{s=1}^T\sum \limits_{s=1}^n\left({\overset{\sim }{\omega}}_{s,t}-{\overset{\sim }{w}}_{s,t-1}\right)\kern0.5em {SHM}_{s,t} $$

(8)

\( where\kern.4em {\overset{\sim }{\omega}}_{s,t} \) is the proportion of the funds trading stock _{s} during quarter t.

### Output Instances

Two sets of output cases were used as performance evaluation models to identify the classification capability and the predictive power of FANNC. The first instance used the Sharpe Index to calculate the output for the same period in where the momentum and herding measures are resolute. This is denoted as the “classification case”. The last instance used the Sharpe Index to calculate the output for the next month right after the period for momentum and herding measures. It is named the “prediction case”. The output instances are calculated as follows:

Classification Sharpe Index

$$ Sharpe\ Index=\frac{{\overline{Q}}_S-{\overline{Q}}_f}{\sigma_s} $$

(9)

Predictive Sharpe Index

$$ Sharpe\ Index=\frac{Q_s^{+}-{\overline{Q}}_f}{\sigma_s} $$

(10)

Where:

\( {\overline{Q}}_S \): The average monthly return for fund _{S} in the calculation period.

\( {Q}_s^{+} \): The return of fund _{S} for the month after the calculation period.

\( {\overline{Q}}_f \): The average monthly risk-free rate represented by the 1-year CD rate of commercial bank.

*σ*_{s}: The standard deviation of the return of the fund _{S} over the calculation period.