The respective liquidity measures are defined as follows:
{
$$\mbox{effective spread}_t = 2*D_t*(\mbox{PRICE}_{t} - \frac{(\mbox{BID}_{t}+\mbox{OFR}_{t})}{2}),$$
where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)).
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered quote timestamp).
}
- rs: realized spread
{
$$\mbox{realized spread}_t = 2*D_t*(\mbox{PRICE}_{t} - \frac{(\mbox{BID}_{t+300}+\mbox{OFR}_{t+300})}{2}),$$where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)).
Note that the time indication of $\mbox{BID}$ and $\mbox{OFR}$ refers
to the registered time of the quote in seconds.
}
- value_trade: trade value
{
$$\mbox{trade value}_t = \mbox{SIZE}_{t}*\mbox{PRICE}_{t}.$$
}
- signed_value_trade: signed trade value
{
$$\mbox{signed trade value}_t = D_t * (\mbox{SIZE}_{t}*\mbox{PRICE}_{t}),$$
where $D_t$ is 1 (-1) if $trade_t$ was buy (sell)
(see Boehmer (2005), Bessembinder (2003)).
}
- di_diff: depth imbalance (as a difference)
{
$$\mbox{depth imbalace (as difference)}_t = \frac{D_t *(\mbox{OFRSIZ}_{t}-\mbox{BIDSIZ}_{t})}{(\mbox{OFRSIZ}_{t}+\mbox{BIDSIZ}_{t})},$$
where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)).
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered quote timestamp).
}
- di_div: depth imbalace (as ratio)
{
$$\mbox{depth imbalace (as ratio)}_t = (\frac{D_t *\mbox{OFRSIZ}_{t}}{\mbox{BIDSIZ}_{t}})^{D_t},$$
where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)).
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered quote timestamp).
}
- pes: proportional effective spread
{
$$\mbox{proportional effective spread}_t = \frac{\mbox{effective spread}_t}{(\mbox{OFR}_{t}+\mbox{BID}_{t})/2}$$
(Venkataraman, 2001).
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered quote timestamp).
}
- prs: proportional realized spread
{
$$\mbox{proportional realized spread}_t = \frac{\mbox{realized spread}_t}{(\mbox{OFR}_{t}+\mbox{BID}_{t})/2}$$
(Venkataraman, 2001).
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered
}
- price_impact: price impact
{
$$\mbox{price impact}_t = \frac{\mbox{effective spread}_t - \mbox{realized spread}_t}{2}$$
(see Boehmer (2005), Bessembinder (2003)).
}
- prop_price_impact: proportional price impact
{
$$\mbox{proportional price impact}_t = \frac{\frac{(\mbox{effective spread}_t - \mbox{realized spread}_t)}{2}}{\frac{\mbox{OFR}_{t}+\mbox{BID}_{t}}{2}}$$
(Venkataraman, 2001).
Note that the input of this function consists of the matched trades and
quotes, so this is where the time indication refers to (and thus not to the
registered quote timestamp).
}
- tspread: half traded spread
{
$$\mbox{half traded spread}_t = D_t*(\mbox{PRICE}_{t} - \frac{(\mbox{BID}_{t}+\mbox{OFR}_{t})}{2}),$$
where $D_t$ is 1 (-1) if $trade_t$ was buy (sell) (see Boehmer (2005), Bessembinder (2003)).
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered quote timestamp).
}
- pts: proportional half traded spread
{
$$\mbox{proportional half traded spread}_t = \frac{\mbox{half traded spread}_t}{\frac{\mbox{OFR}_{t}+\mbox{BID}_{t}}{2}}.$$
Note that the input of this function consists of the matched trades and quotes,
so this is were the time indication refers to (and thus not to the registered quote timestamp).
}
- p_return_sqr: squared log return on trade prices
{
$$\mbox{squared log return on Trade prices}_t = (\log(\mbox{PRICE}_{t})-\log(\mbox{PRICE}_{t-1}))^2.$$
}
- p_return_abs: absolute log return on trade prices
{
$$\mbox{absolute log return on Trade prices}_t = |\log(\mbox{PRICE}_{t})-\log(\mbox{PRICE}_{t-1})|.$$
}
- qs: quoted spread
{
$$\mbox{quoted spread}_t = \mbox{OFR}_{t}-\mbox{BID}_{t}$$
Note that the input of this function consists of the matched trades and
quotes, so this is where the time indication refers to (and thus not to the
registered quote timestamp).
}
- pqs: proportional quoted spread
{
$$\mbox{proportional quoted spread}_t = \frac{\mbox{quoted spread}_t}{\frac{\mbox{OFR}_{t}+\mbox{BID}_{t}}{2}}$$
(Venkataraman, 2001).
Note that the input of this function consists of the matched trades and
quotes, so this is where the time indication refers to (and thus not to the
registered quote timestamp).
}
- logqs: log quoted spread
{
$$\mbox{log quoted spread}_t = \log(\frac{\mbox{OFR}_{t}}{\mbox{BID}_{t}})$$
(Hasbrouck and Seppi, 2001).
Note that the input of this function consists of the matched trades and
quotes, so this is where the time indication refers to (and thus not to the
registered quote timestamp).
}
- logsize: log quoted size
{
$$\mbox{log quoted size}_t = \log(\mbox{OFRSIZ}_{t})-\log(\mbox{BIDSIZ}_{t})$$
(Hasbrouck and Seppi, 2001).
Note that the input of this function consists of the matched trades and
quotes, so this is where the time indication refers to (and thus not to the
registered quote timestamp).
}
- qslope: quoted slope
{
$$\mbox{quoted slope}_t = \frac{\mbox{quoted spread}_t}{\mbox{log quoted size}_t}$$
(Hasbrouck and Seppi, 2001).
}
- logqslope: log quoted slope
{
$$\mbox{log quoted slope}_t = \frac{\mbox{log quoted spread}_t}{\mbox{log quoted size}_t}.$$
}
- mq_return_sqr: midquote squared return
{
$$\mbox{midquote squared return}_t = (\log(\mbox{midquote}_{t})-\log(\mbox{midquote}_{t-1}))^2,$$
where $\mbox{midquote}_{t} = \frac{\mbox{BID}_{t} + \mbox{OFR}_{t}}{2}$.
}
- mq_return_abs: midquote absolute return
{
$$\mbox{midquote absolute return}_t = |\log(\mbox{midquote}_{t})-\log(\mbox{midquote}_{t-1})|,$$
where $\mbox{midquote}_{t} = \frac{\mbox{BID}_{t} + \mbox{OFR}_{t}}{2}$.
}
- signed_trade_size: signed trade size
{
$$\mbox{signed trade size}_t = D_t * \mbox{SIZE}_{t},$$
where $D_t$ is 1 (-1) if $trade_t$ was buy (sell).
}