How to correctly compute stock daily return?

Augu

1 Thusday Open_Price Close_Price
2 Friday Open_Price Close_Price
3 Monday Open_Price Close_Price

The book formula is
Close_price_today - Close_price_yesterday
------------------------------------------------
Close_price_yesterday

But there is not trade in weekend, how do deal with daily return between (Friday and monday)?

I am new ...
Thanks a lot.

DMD

Active Member
By your formula, (Monday_Close - Friday_Close)/Friday_Close. That's correct.

There is also a nice approximation to this formula using a Taylor approximation. Basically,

[S(x+h)-S(x)]/S(x) ~= log(S(x+h)/S(x)) for small h.

Augu

By your formula, (Monday_Close - Friday_Close)/Friday_Close. That's correct.

There is also a nice approximation to this formula using a Taylor approximation. Basically,

[S(x+h)-S(x)]/S(x) ~= log(S(x+h)/S(x)) for small h.
is ok to use
today_close_price - today_open_price
------------------------------------------ to compute the daily return?
today_open_price

aaronhotchner

No, that's not the daily return. A stock will open above or below the close from the previous day, but no time has passed. The difference between the open and close in the same day isn't really relevant as a return. Always use closing prices in consecutive trading days.

Augu

No, that's not the daily return. A stock will open above or below the close from the previous day, but no time has passed. The difference between the open and close in the same day isn't really relevant as a return. Always use closing prices in consecutive trading days.
From DMB suggestion, it seems correct one is
s(x+h)
return over h = [ log ( -------------------) - 1 ]
s(x)
daily return is
return over h 1
--------------- X ----?
h 365

DMD

Active Member
I can't really make out the equations you put in your post. Using the logarithmic approximation is handy but it is an approximation and only works for small h. You would use h=1/252, since you need to omit weekends and holidays from the 365 days in the year.

Can you put your question in context? Why do you need to calculate these returns? It may make it easier to help you.

Augu

I can't really make out the equations you put in your post. Using the logarithmic approximation is handy but it is an approximation and only works for small h. You would use h=1/252, since you need to omit weekends and holidays from the 365 days in the year.

Can you put your question in context? Why do you need to calculate these returns? It may make it easier to help you.
Thanks for your return.
My confusion is
when compute return from last friday to coming monday, h = 3 day, it is a little special..
And also h = 1 days, it equal 1/ 252 or 1/365?

aaronhotchner

A trading day is a trading day. It's not like the stock market is moving over the weekend and you're not observing it: it's simply not moving. Close Friday to close Monday is still 1 day of stock movement. It just might be slightly more interesting because of the amount of information that could have been obtained over that time. However, most large movements over a particular day are due to business conditions that would only become available during a trading day anyway.

Use 252 days. There are not 365 possible days for stocks to move in a year.

Augu

A trading day is a trading day. It's not like the stock market is moving over the weekend and you're not observing it: it's simply not moving. Close Friday to close Monday is still 1 day of stock movement. It just might be slightly more interesting because of the amount of information that could have been obtained over that time. However, most large movements over a particular day are due to business conditions that would only become available during a trading day anyway.

Use 252 days. There are not 365 possible days for stocks to move in a year.
Thank you and DMD a lot for clarifying me .

physEcon

A trading day is a trading day. It's not like the stock market is moving over the weekend and you're not observing it: it's simply not moving. Close Friday to close Monday is still 1 day of stock movement. It just might be slightly more interesting because of the amount of information that could have been obtained over that time. However, most large movements over a particular day are due to business conditions that would only become available during a trading day anyway.

Use 252 days. There are not 365 possible days for stocks to move in a year.

As you alluded in your post, information revelation is the key here. Very often people get too distracted by viewing volatility as movement rather than as the discovery of information. At the end of the day, the way we define daily returns is just that - a definition. It's not as though there is some immutable physical truth. h=1/252 or h=1/365 are really just conventions. This actually leads to some interesting empirical investigations like this one.

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