# The Analysis of Disposition Effect

# The Disposition Effect

In recent years, an irrational phenomenon in financial markets is grabbing the attention of behavioral economists: the disposition effect. Firstly discovered by H. Shefrin and M. Statman (1985), the disposition effect consists in the realization that investors are more likely to sell an asset when it is gaining value compared to when it is losing value. A phenomenon which is closely related to sunk costs’ bias, diminishing sensitivity, and loss aversion.

From 1985 until now, the disposition effect has been documented in US retail stock investors as well as in foreign retail investors and even among professionals and institutions. By the time, it is a well-established fact that the disposition effect is a real behavioral anomaly that strongly influences the final profits (or losses) of investors. Furthermore, being able to correctly capture these irrational behaviors timely is even more important in periods of high financial volatility as nowadays.

The `dispositionEffect` package allows to quickly evaluate the presence of disposition effect’s behaviors of an investor based solely on his transactions and the market prices of the traded assets.

# Package loading

    library(dispositionEffect)
    library(dplyr)
    library(tidyr)
    library(lubridate)
    library(skimr)
    library(ggplot2)
    library(ggridges)

# Data

The dataset `DEanalysis` is provided within the package allowing to reproduce a full analysis on the disposition effect.

    help("DEanalysis")

The disposition effect analysis is performed on two fundamental types of data frames:

- portfolio transactions, that is all the financial transactions an investor did during a specific period of time. A single transaction is made up of 6 features: the investor id, the asset id, the type of the transaction (it can be a buy or a sell), the traded quantity, the traded price, and the datetime.

- market prices, that is the prices found on the stock markets for each traded asset and each transaction datetimes.

## Portfolio Transactions

First of all, we need to extract and understand the structure of the transaction dataset.

    trx <- DEanalysis$transactions # transactions
    head(trx)
    #>   investor type asset quantity   price            datetime
    #> 1    44382    B  3NGL    15000  0.2540 2017-10-25 14:16:00
    #> 2    44382    B  3NGL     5000  0.2485 2017-10-26 17:35:00
    #> 3    44382    B  3NGL     4000  0.2400 2017-10-27 10:20:00
    #> 4    44382    B GAS3L    23000  0.1880 2017-10-27 17:06:00
    #> 5    44382    B  3NGL     5000  0.2214 2017-10-27 17:35:00
    #> 6    44382    B  3NGS      130 32.7650 2017-10-30 17:35:00

    skimr::skim(trx)

Data summary
Name | trx
Number of rows | 4917
Number of columns | 6
_______________________ |
Column type frequency: |
POSIXct | 1
character | 3
numeric | 2
________________________ |
Group variables | None

Variable type: POSIXct

skim_variable | n_missing | complete_rate | min | max | median | n_unique
--- | --- | --- | --- | --- | --- | ---
datetime | 0 | 1 | 2010-01-05 11:38:00 | 2018-12-18 13:24:00 | 2013-07-30 16:25:00 | 4766

Variable type: character

skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace
--- | --- | --- | --- | --- | --- | --- | ---
investor | 0 | 1 | 5 | 5 | 0 | 10 | 0
type | 0 | 1 | 1 | 1 | 0 | 2 | 0
asset | 0 | 1 | 1 | 6 | 0 | 337 | 0

Variable type: numeric

skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
quantity | 0 | 1 | 3081.49 | 15580.36 | 0 | 123.00 | 485.00 | 1850.00 | 652920 | ▇▁▁▁▁
price | 0 | 1 | 878.15 | 3697.85 | 0 | 1.76 | 7.47 | 25.26 | 22130 | ▇▁▁▁▁

The portfolio transaction dataset is made up of the six fundamental variables described above.
This real sample dataset contains transactions on 10 investors on 337 traded assets, from January 2010 until December 2018.

One important feature is the `type` variable. It states if a transaction is a “Buy” (B) or a “Sell” (S), and only this two values are allowed.

    unique(trx$type)
    #> [1] "B" "S"

Moreover, as expected, not all the investors are active on the whole period of analysis.

    # number of transactions of each investor over years
    trx %>%
      dplyr::mutate(year = lubridate::year(datetime)) %>%
      dplyr::count(investor, year) %>%
      dplyr::arrange(year) %>%
      tidyr::pivot_wider(names_from = year, values_from = n) %>%
      dplyr::left_join(dplyr::count(trx, investor), by = "investor")
    #> # A tibble: 10 × 11
    #>    investor `2010` `2011` `2012` `2013` `2014` `2015` `2016` `2017` `2018`     n
    #>    <chr>     <int>  <int>  <int>  <int>  <int>  <int>  <int>  <int>  <int> <int>
    #>  1 62NQ8        59     35     66     91    245     NA     NA     NA     NA   496
    #>  2 743Q1        64    190    239     NA     NA     NA     NA     NA     NA   493
    #>  3 784ZZ       164     26      9    119     45     70     27     29     11   500
    #>  4 8ZQ32       196     79     35     41     56     24     46     18      4   499
    #>  5 QZ31Q        37    389     56     NA     NA     NA     NA     NA     NA   482
    #>  6 QZ621        43    232     77    114     24     NA     NA     NA     NA   490
    #>  7 QZNZN        14    107     90     70     33     63    106     NA      7   490
    #>  8 46Z68        NA     NA     NA     NA     NA     NA    170    288     24   482
    #>  9 44382        NA     NA     NA     NA     NA     NA     NA     75    415   490
    #> 10 4Q17Z        NA     NA     NA     NA     NA     NA     NA    202    293   495

Clearly, they have similar number of transactions as a whole, but they traded on different years.

## Market Prices

The market prices dataset needs only to have three variables: asset, datetime and price.

    mkt <- DEanalysis$marketprices # market prices
    head(mkt)
    #>   asset            datetime  price
    #> 1  3BAL 2017-10-25 14:16:00 42.750
    #> 2  3BAS 2017-10-25 14:16:00 15.750
    #> 3  3BRL 2017-10-25 14:16:00 28.080
    #> 4  3BRS 2017-10-25 14:16:00 19.980
    #> 5  3CFL 2017-10-25 14:16:00 17.055
    #> 6  3CFS 2017-10-25 14:16:00 24.505

    skimr::skim(mkt)

Data summary
Name | mkt
Number of rows | 258137
Number of columns | 3
_______________________ |
Column type frequency: |
POSIXct | 1
character | 1
numeric | 1
________________________ |
Group variables | None

Variable type: POSIXct

skim_variable | n_missing | complete_rate | min | max | median | n_unique
--- | --- | --- | --- | --- | --- | ---
datetime | 0 | 1 | 2010-01-05 11:38:00 | 2018-12-18 13:24:00 | 2013-06-05 09:16:00 | 4766

Variable type: character

skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace
--- | --- | --- | --- | --- | --- | --- | ---
asset | 0 | 1 | 1 | 6 | 0 | 337 | 0

Variable type: numeric

skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
price | 0 | 1 | 162.7 | 1524.68 | 0 | 1.87 | 7 | 19.5 | 22336 | ▇▁▁▁▁

Again, not all the assets prices are available in every year because we only need the market prices for those assets for the traded datetime (i.e. the datetime of the transactions dataset).

    mkt %>%
      dplyr::mutate(year = lubridate::year(datetime)) %>%
      dplyr::count(asset, year) %>%
      dplyr::arrange(year) %>%
      tidyr::pivot_wider(names_from = year, values_from = n) %>%
      head(10)
    #> # A tibble: 10 × 10
    #>    asset `2010` `2011` `2012` `2013` `2014` `2015` `2016` `2017` `2018`
    #>    <chr>  <int>  <int>  <int>  <int>  <int>  <int>  <int>  <int>  <int>
    #>  1 A2A      267    552    218    271    321    131    129    227    271
    #>  2 ACE      159     25      9    115     45     70     27     29     11
    #>  3 ACP      159     25      9    115     45     70     27     29     11
    #>  4 ACS      159     25      9    115     45     70     27     29     11
    #>  5 AEF      210    519    154    181     78    131    129     29     18
    #>  6 AEG       56     33     64     91    243     NA     NA     NA     NA
    #>  7 AGL      327    407    425    199    332     85    148     18     11
    #>  8 AGRI      64    190    237     NA     NA     NA     NA     NA     NA
    #>  9 AIGO     193     79     35     41     56     24     46     18      4
    #> 10 AKM       56     33     64     91    243     NA     NA     NA     NA

# Disposition Effect: Single Investor Analysis

Now, first proceed to analyze the behavior of a single investor.

    # Investor QZ621
    trx_QZ621 <- dplyr::filter(trx, investor == "QZ621") # transactions
    mkt_QZ621 <- dplyr::filter(mkt, asset %in% unique(trx_QZ621$asset)) # market prices

## Gains & Losses Calculation

Based solely on this two data frames it is possible to compute the so-called realized gains (RG), realized losses (RL), paper gains (PG), and paper losses (PL), as defined by L. Mazzucchelli et al. (2021).

To sum up the main concepts are the followings:

- Realized Gain / Loss => whenever an investor closes a position in its portfolio in gain / loss

- Paper Gain / Loss => all the open positions at the moment of the transaction, and all the partially closed positions.

The `portfolio_compute` is the core interface of the package and it is used to perform all the gains and losses computations.

    p_res <- portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621)
    head(p_res)[, -5]
    #>   investor  asset quantity    price RG_count RL_count PG_count PL_count
    #> 1    QZ621  DAX2S        0 0.000000        1        0        0        0
    #> 2    QZ621      F        0 0.000000        3        2        1        1
    #> 3    QZ621 LEVMIB      400 5.551628       32       25      223       93
    #> 4    QZ621 MINI1L        0 0.000000        0        4        5        0
    #> 5    QZ621 MINI2C        0 0.000000        0        1        0        0
    #> 6    QZ621 MINI2F        0 0.000000       10        6        0        4
    skimr::skim(p_res)

Data summary
Name | p_res
Number of rows | 26
Number of columns | 9
_______________________ |
Column type frequency: |
POSIXct | 1
character | 2
numeric | 6
________________________ |
Group variables | None

Variable type: POSIXct

skim_variable | n_missing | complete_rate | min | max | median | n_unique
--- | --- | --- | --- | --- | --- | ---
datetime | 0 | 1 | 2011-02-01 17:46:00 | 2014-09-17 17:56:00 | 2012-02-15 15:03:00 | 26

Variable type: character

skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace
--- | --- | --- | --- | --- | --- | --- | ---
investor | 0 | 1 | 5 | 5 | 0 | 1 | 0
asset | 0 | 1 | 1 | 6 | 0 | 26 | 0

Variable type: numeric

skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
quantity | 0 | 1 | -751.92 | 3926.64 | -20000 | 0 | 0 | 0.00 | 400 | ▁▁▁▁▇
price | 0 | 1 | 1284.76 | 4542.57 | 0 | 0 | 0 | 0.00 | 17780 | ▇▁▁▁▁
RG_count | 0 | 1 | 5.85 | 12.01 | 0 | 0 | 2 | 4.75 | 55 | ▇▁▁▁▁
RL_count | 0 | 1 | 4.54 | 7.02 | 0 | 1 | 2 | 4.00 | 26 | ▇▁▁▁▁
PG_count | 0 | 1 | 22.08 | 59.55 | 0 | 0 | 0 | 1.75 | 223 | ▇▁▁▁▁
PL_count | 0 | 1 | 32.46 | 95.04 | 0 | 0 | 0 | 2.75 | 423 | ▇▁▁▁▁

Hence, the result is a data frame containing:

- the final portfolio of the investor (first 5 variables)
- gains and losses results of the chosen method (all the other variables), where RG = Realized Gains, RL = Realized Losses, PG = Paper Gains, and PL = Paper Losses.

## Disposition Effect Computation

Once that gains and losses have been computed, it is finally possible to evaluate both the disposition effect of the investor and of each traded assets, where the disposition effect is defined as:

\[DE = \bigg(\frac{RG}{RG + PG}\bigg) - \bigg(\frac{RL}{RL + PL}\bigg)\]

The DE varies between -1 and 1. Positive DE values show the presence of disposition effect irrational behaviors, while negative values show the presence of opposite disposition effect behaviors. A value of zero show that no disposition effect exists.

You almost never want to compute the disposition effect directly via the `disposition_effect` function, but you will mostly rely on the quicker and easier `disposition_compute` interface, since it designed to handle many situations.

    de <- disposition_compute(gainslosses = p_res)
    head(de)
    #>   investor  asset    DE_count
    #> 1    QZ621  DAX2S  1.00000000
    #> 2    QZ621      F  0.08333333
    #> 3    QZ621 LEVMIB -0.08637421
    #> 4    QZ621 MINI1L -1.00000000
    #> 5    QZ621 MINI2C -1.00000000
    #> 6    QZ621 MINI2F  0.40000000

As can be seen, `disposition_compute` calculates a value of disposition effect for each asset. In order to obtain the value of disposition effect of the investor, one can simply compute an aggregate statistic, such as the mean or the median, on the assets’ values.
To do this we can simply use once again `disposition_compute` specifying the desired `aggregate_fun`.

    disposition_compute(gainslosses = p_res, aggregate_fun = mean, na.rm = TRUE)
    #>   investor   DE_count
    #> 1    QZ621 -0.2115755

Moreover, by means of the `disposition_summary` function it is also easy to summarize the disposition effect behavior of the investor, obtaining common summary statistics.

    de_stat <- disposition_summary(gainslosses = p_res)
    de_stat
    #>   investor   stat   DE_count
    #> 1    QZ621    Min -1.0000000
    #> 2    QZ621     Q1 -0.6250000
    #> 3    QZ621 Median  0.0000000
    #> 4    QZ621     Q3  0.1284957
    #> 5    QZ621   Mean -0.2115755
    #> 6    QZ621    Max  1.0000000
    #> 7    QZ621  StDev  0.5740599

# Disposition Effect: Testing Different Arguments

Until now, we limited our analysis to the default parameters of `portfolio_compute`. However, this function has many different arguments that can be used both to fine tune the analysis and to perform more advanced calculations, such as the so-called portfolio driven disposition effect and the time series disposition effect.

Hence, we focus here on the usage of five fundamental different arguments.

## Method

Let’s start by the `method` argument. It is probably the most relevant parameter the user can control since it allows to perform five different types of analysis.

If set to “none”, no gains and losses are computed but the investor’s portfolio is updated at every transaction, resulting in the actual portfolio of the investors at time T (the end of the period).

    portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621, method = "none") %>%
      head()
    #>   investor  asset quantity    price            datetime
    #> 1    QZ621  DAX2S        0 0.000000 2012-02-22 11:36:00
    #> 2    QZ621      F        0 0.000000 2012-02-08 18:30:00
    #> 3    QZ621 LEVMIB      400 5.551628 2011-07-25 15:41:00
    #> 4    QZ621 MINI1L        0 0.000000 2011-12-08 18:19:00
    #> 5    QZ621 MINI2C        0 0.000000 2011-12-16 10:54:00
    #> 6    QZ621 MINI2F        0 0.000000 2012-05-31 19:18:00

If set to one of “count”, “total”, “value”, or “duration”, gains and losses are computed for the corresponding method.

    portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621, method = "count") %>%
      head()
    #>   investor  asset quantity    price            datetime RG_count RL_count
    #> 1    QZ621  DAX2S        0 0.000000 2012-02-22 11:36:00        1        0
    #> 2    QZ621      F        0 0.000000 2012-02-08 18:30:00        3        2
    #> 3    QZ621 LEVMIB      400 5.551628 2011-07-25 15:41:00       32       25
    #> 4    QZ621 MINI1L        0 0.000000 2011-12-08 18:19:00        0        4
    #> 5    QZ621 MINI2C        0 0.000000 2011-12-16 10:54:00        0        1
    #> 6    QZ621 MINI2F        0 0.000000 2012-05-31 19:18:00       10        6
    #>   PG_count PL_count
    #> 1        0        0
    #> 2        1        1
    #> 3      223       93
    #> 4        5        0
    #> 5        0        0
    #> 6        0        4
    portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621, method = "total") %>%
      head()
    #>   investor  asset quantity    price            datetime RG_total RL_total
    #> 1    QZ621  DAX2S        0 0.000000 2012-02-22 11:36:00      500        0
    #> 2    QZ621      F        0 0.000000 2012-02-08 18:30:00     4000     3000
    #> 3    QZ621 LEVMIB      400 5.551628 2011-07-25 15:41:00    46425    35450
    #> 4    QZ621 MINI1L        0 0.000000 2011-12-08 18:19:00        0        4
    #> 5    QZ621 MINI2C        0 0.000000 2011-12-16 10:54:00        0        1
    #> 6    QZ621 MINI2F        0 0.000000 2012-05-31 19:18:00       10        6
    #>   PG_total PL_total
    #> 1        0        0
    #> 2     2000     1500
    #> 3   101640    71585
    #> 4        5        0
    #> 5        0        0
    #> 6        0        6
    portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621, method = "value") %>%
      head()
    #>   investor  asset quantity    price            datetime    RG_value
    #> 1    QZ621  DAX2S        0 0.000000 2012-02-22 11:36:00 0.006965944
    #> 2    QZ621      F        0 0.000000 2012-02-08 18:30:00 0.006973225
    #> 3    QZ621 LEVMIB      400 5.551628 2011-07-25 15:41:00 0.008168037
    #> 4    QZ621 MINI1L        0 0.000000 2011-12-08 18:19:00 0.000000000
    #> 5    QZ621 MINI2C        0 0.000000 2011-12-16 10:54:00 0.000000000
    #> 6    QZ621 MINI2F        0 0.000000 2012-05-31 19:18:00 0.004442795
    #>       RL_value    PG_value     PL_value
    #> 1  0.000000000 0.000000000  0.000000000
    #> 2 -0.001190992 0.000678242 -0.001028584
    #> 3 -0.008053899 0.583051555 -0.068406690
    #> 4 -0.005921272 0.031142275  0.000000000
    #> 5 -0.002220704 0.000000000  0.000000000
    #> 6 -0.002014476 0.000000000 -0.001533113
    portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621, method = "duration") %>%
      head()
    #>   investor  asset quantity    price            datetime RG_duration RL_duration
    #> 1    QZ621  DAX2S        0 0.000000 2012-02-22 11:36:00    28.51667     0.00000
    #> 2    QZ621      F        0 0.000000 2012-02-08 18:30:00     5.00000    13.96667
    #> 3    QZ621 LEVMIB      400 5.551628 2011-07-25 15:41:00   876.61667  2247.78333
    #> 4    QZ621 MINI1L        0 0.000000 2011-12-08 18:19:00     0.00000   492.71667
    #> 5    QZ621 MINI2C        0 0.000000 2011-12-16 10:54:00     0.00000     0.35000
    #> 6    QZ621 MINI2F        0 0.000000 2012-05-31 19:18:00    46.65000    41.38333
    #>    PG_duration PL_duration
    #> 1 0.000000e+00       0.000
    #> 2 2.666667e-01       6.750
    #> 3 1.004278e+04    1788.117
    #> 4 4.623000e+02       0.000
    #> 5 0.000000e+00       0.000
    #> 6 0.000000e+00       7.300

In particular:

- `count` computes gains and losses as simple counts
- `total` calculates gains and losses as the sum of the quantity
- `value` measures the expected percentage gains and losses based on prices
- `duration` calculates the time in hours of held gains and losses.

Instead, when method is set to “all”, then all the four measures are computed.

    p_res_all <- portfolio_compute(portfolio_transactions = trx_QZ621, market_prices = mkt_QZ621, method = "all")
    skimr::skim(p_res_all)

Data summary
Name | p_res_all
Number of rows | 26
Number of columns | 21
_______________________ |
Column type frequency: |
POSIXct | 1
character | 2
numeric | 18
________________________ |
Group variables | None

Variable type: POSIXct

skim_variable | n_missing | complete_rate | min | max | median | n_unique
--- | --- | --- | --- | --- | --- | ---
datetime | 0 | 1 | 2011-02-01 17:46:00 | 2014-09-17 17:56:00 | 2012-02-15 15:03:00 | 26

Variable type: character

skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace
--- | --- | --- | --- | --- | --- | --- | ---
investor | 0 | 1 | 5 | 5 | 0 | 1 | 0
asset | 0 | 1 | 1 | 6 | 0 | 26 | 0

Variable type: numeric

skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
quantity | 0 | 1 | -751.92 | 3926.64 | -20000.00 | 0.00 | 0.00 | 0.00 | 400.00 | ▁▁▁▁▇
price | 0 | 1 | 1284.76 | 4542.57 | 0.00 | 0.00 | 0.00 | 0.00 | 17780.00 | ▇▁▁▁▁
RG_count | 0 | 1 | 5.85 | 12.01 | 0.00 | 0.00 | 2.00 | 4.75 | 55.00 | ▇▁▁▁▁
RL_count | 0 | 1 | 4.54 | 7.02 | 0.00 | 1.00 | 2.00 | 4.00 | 26.00 | ▇▁▁▁▁
PG_count | 0 | 1 | 22.08 | 59.55 | 0.00 | 0.00 | 0.00 | 1.75 | 223.00 | ▇▁▁▁▁
PL_count | 0 | 1 | 32.46 | 95.04 | 0.00 | 0.00 | 0.00 | 2.75 | 423.00 | ▇▁▁▁▁
RG_total | 0 | 1 | 6460.62 | 15235.96 | 0.00 | 0.00 | 5.50 | 3300.00 | 58800.00 | ▇▁▁▁▁
RL_total | 0 | 1 | 8317.46 | 15673.01 | 0.00 | 3.00 | 12.00 | 7500.00 | 60000.00 | ▇▁▁▁▁
PG_total | 0 | 1 | 19834.27 | 76428.62 | 0.00 | 0.00 | 0.00 | 107.75 | 381200.00 | ▇▁▁▁▁
PL_total | 0 | 1 | 333629.88 | 1665597.17 | 0.00 | 0.00 | 0.00 | 3225.00 | 8499500.00 | ▇▁▁▁▁
RG_value | 0 | 1 | 0.01 | 0.03 | 0.00 | 0.00 | 0.00 | 0.01 | 0.15 | ▇▁▁▁▁
RL_value | 0 | 1 | -0.01 | 0.02 | -0.08 | -0.01 | 0.00 | 0.00 | 0.00 | ▁▁▁▁▇
PG_value | 0 | 1 | 0.06 | 0.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | ▇▁▁▁▁
PL_value | 0 | 1 | -7.11 | 36.03 | -183.78 | -0.03 | 0.00 | 0.00 | 0.00 | ▁▁▁▁▇
RG_duration | 0 | 1 | 654.71 | 2607.32 | 0.00 | 0.00 | 15.64 | 42.60 | 13304.53 | ▇▁▁▁▁
RL_duration | 0 | 1 | 541.90 | 1958.29 | 0.00 | 7.64 | 21.87 | 40.02 | 9872.20 | ▇▁▁▁▁
PG_duration | 0 | 1 | 833.62 | 2384.62 | 0.00 | 0.00 | 0.00 | 24.66 | 10042.78 | ▇▁▁▁▁
PL_duration | 0 | 1 | 1120.40 | 3197.62 | 0.00 | 0.00 | 0.00 | 114.80 | 13299.93 | ▇▁▁▁▁

It is important to notice that the disposition effect is only meaningful for methods `coount` and `total`. In all the other cases the disposition difference is used instead.

    disposition_compute(gainslosses = p_res_all, aggregate_fun = mean, na.rm = TRUE)
    #>   investor   DE_count   DE_total   DE_value DD_duration
    #> 1    QZ621 -0.2115755 -0.2048348 -0.1806207    112.8141

## Allow Short

The `allow_short` argument, instead, allows for short selling transactions. If set to FALSE, short selling will not be allowed and no gains or losses will be computed when this happens.

## Time Threshold

The `time_threshold` argument is a fundamental fine tuning parameter. It essentially controls the minimum time distance necessary to compute gains and losses.
By default it is set to “0 mins”, implying that gains and losses are always computed.
However, this may not be desirable since investor’s behaviors are not expected to change with very high frequencies.
Hence, for instance, setting it to “60 mins” states that gains and losses are calculated only if 60 minutes are passed from the last transaction.

    portfolio_compute(
      portfolio_transactions = trx_QZ621,
      market_prices = mkt_QZ621,
      time_threshold = "60 mins"
    )

This parameter is very important also because it allows to somewhat filters human operations from machines operations, without actually removing them from the analysis.

Different units may be specified.

## Exact Market Prices

The argument `exact_market_prices` is set to TRUE by default, since it is expected that the user provides market prices of each traded asset for each transaction datetime.
However, when this is not the case, one may want to set it to FALSE to allow for non exact market prices. It essentially means that the nearest price in time is used.

    portfolio_compute(
      portfolio_transactions = trx_QZ621,
      market_prices = mkt_QZ621,
      exact_market_prices = FALSE
    )

Note, however, that with `exact_market_prices` set to FALSE, unreliable results may be obtained when transactions occur with low frequency, since the market prices used as reference for the calculation may be outdated.

## Interactivity

The `verbose` and `progress` arguments may be useful for interactive use and for very long calculations on large portfolios of transactions.

    portfolio_compute(
      portfolio_transactions = trx_QZ621,
      market_prices = mkt_QZ621,
      verbose = c(1, 1),
      progress = TRUE
    )

## Other Arguments

See Portfolio Driven Disposition Effect and Time Series Disposition Effect for a guide on the usage of other, more advanced, arguments.

# Disposition Effect: Multiple Investors Analysis

Although the analysis of disposition effect can be performed simply on a single investor, the real advantages of this analysis derive from the capacity to study and understand the behaviors of many different investors that actively operate on the financial markets.

Hence, to fully grasp the power of `dispositionEffect` package, we can proceed to jointly analyze all the 10 investors’ transactions that are available into the `DEanalysis` dataset.

Furthermore, if you are interested in computing the disposition effect on large datasets, please see Disposition Effect in Parallel to understand how the benefits of parallel computing can be exploited within this framework.

    # list of transactions separated by investor
    trx_list <- trx %>%
      dplyr::group_by(investor) %>%
      dplyr::group_split()

## Gains & Losses Calculation

This time to calculate gains and losses for each investor’s portfolio we can simply `map` `portfolio_compute` on the list of transactions, specifying all the other necessary arguments as usual.

    p_res_full <- purrr::map(trx_list, portfolio_compute, market_prices = mkt)

## Disposition Effect Computation

The same procedure can be used to quickly compute the disposition effect on each resulting portfolio.

    de <- purrr::map(p_res_full, disposition_compute) %>%
      dplyr::bind_rows()
    skimr::skim(de)

Data summary
Name | de
Number of rows | 576
Number of columns | 3
_______________________ |
Column type frequency: |
character | 2
numeric | 1
________________________ |
Group variables | None

Variable type: character

skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace
--- | --- | --- | --- | --- | --- | --- | ---
investor | 0 | 1 | 5 | 5 | 0 | 10 | 0
asset | 0 | 1 | 1 | 6 | 0 | 337 | 0

Variable type: numeric

skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
DE_count | 1 | 1 | 0.06 | 0.59 | -1 | -0.29 | 0.01 | 0.5 | 1 | ▃▃▇▅▅

As it is shown, `de` is a data frame containing disposition effect results (variable `DE_count`) on the 10 investors for all their 337 traded assets.
Also the average disposition effects of the investors can be easily obtained,

    de_mean <- purrr::map(p_res_full, disposition_compute, aggregate_fun = mean, na.rm = TRUE) %>%
      dplyr::bind_rows() %>%
      dplyr::arrange(dplyr::desc(DE_count))
    de_mean
    #>    investor      DE_count
    #> 1     46Z68  0.6705760963
    #> 2     8ZQ32  0.5318072092
    #> 3     62NQ8  0.5049538124
    #> 4     44382  0.4917751394
    #> 5     743Q1  0.0005595955
    #> 6     QZNZN -0.0089654513
    #> 7     4Q17Z -0.1678092462
    #> 8     QZ621 -0.2115754843
    #> 9     QZ31Q -0.2149247491
    #> 10    784ZZ -0.2611998354

and the disposition effect summary statistics.

    de_stat <- purrr::map(p_res_full, disposition_summary) %>%
      dplyr::bind_rows()
    head(de_stat, 7)
    #>   investor   stat   DE_count
    #> 1    44382    Min -0.3333333
    #> 2    44382     Q1  0.3141026
    #> 3    44382 Median  0.5000000
    #> 4    44382     Q3  0.6500000
    #> 5    44382   Mean  0.4917751
    #> 6    44382    Max  1.0000000
    #> 7    44382  StDev  0.3506436

It is clearer now that some investors display irrational behaviors while other don’t.

## Visual Analysis

The graphical inspection of disposition effect results allows to easily understand what is going on and to spot possible interesting behaviors.

One may want to investigate the overall distribution, or the distributions of every statistics obtained.

    ggplot(de, aes(x = DE_count)) +
        geom_histogram(aes(y = ..density..), color = "darkblue", fill = "yellow") +
      geom_density(aes(y = ..density..), color = "darkblue", fill = "yellow", alpha = 0.4) +
        scale_x_continuous(limits = c(-1, 1)) +
        theme(
            panel.background = element_rect(fill = "grey92"),
            plot.background = element_rect(fill = "grey85", colour = NA),
            plot.title = element_text(size = 20),
            legend.position = "none"
        ) +
        labs(title = "Disposition Effect Distribution", x = "Disposition Effect", y = "Frequency")

    ggplot(de_stat, aes(x = DE_count, y = stat, fill = stat)) +
        geom_density_ridges() +
      scale_fill_viridis_d() +
        scale_x_continuous(limits = c(-1, 1)) +
        theme(
            panel.background = element_rect(fill = "grey92"),
            plot.background = element_rect(fill = "grey85", colour = NA),
            plot.title = element_text(size = 20),
            legend.position = "none"
        ) +
        labs(
            title = "Disposition Effect Statistics' Distributions",
            x = "Disposition Effect", y = ""
        )

Or deeper, one can also analyze investors’ behaviors on some specific assets to understand whether there exists on the market assets that are more subject to irrationality.

    top5_assets <- trx %>%
      dplyr::count(asset) %>%
      dplyr::arrange(dplyr::desc(n)) %>%
      dplyr::slice(1:6) %>%
      dplyr::pull(asset)

    dplyr::filter(de, asset %in% top5_assets) %>%
      ggplot(aes(x = asset, y = DE_count, fill = asset)) +
        # geom_half_boxplot(center = TRUE, width = 0.8, nudge = 0.02) +
        # geom_half_violin(side = "r", nudge = 0.02, alpha = 0.8) +
        geom_boxplot() +
        geom_jitter(color = "grey40") +
      scale_fill_viridis_d() +
        theme(
            panel.background = element_rect(fill = "grey92"),
            plot.background = element_rect(fill = "grey85", colour = NA),
            plot.title = element_text(size = 20),
            legend.position = "none"
        ) +
        labs(title = "Volatility & Disposition Effect", x = "", y = "Disposition Effect")

For more tutorials on disposition effect visit dispositionEffect.