How to convert daily return into an annalized return of a stock price?
Message posted by Carlos (via 168.70.249.2) on July 16, 2001 at 2:20 AM (ET)

Dear sir,

I got a set of daily closing rate of a stock (p1,P2,...Pn). I covert the data into daily yield (r) by (P2-P1)/P1. Then I convert the daily yield into continous compounding yield R by In(1+r). At this point, I face a few problems.

1. When I convert continous compounding yield into annalized yield, a text book said I should multiple R by the squared root of 365 days. ie. R * (365)^0.5.. Why??? ( Investment, by Bodie, Kane, Marcus 4th - McGraw Hill Page 908)

2. During the exercise, I found only 260 trading days for the stock. Should I adjust the number of days from 365 into 260 ??

The aim of the exercise is to test the CAPM model of the stock against an risk asset such as the treasury fund bills. It makes me even more confused as people can make certain yield form treasury bills over the weekend. Then should we use 260 or 365???

Thank for your attention,

Carlos++

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: How to convert daily return into an annalized return of a stock price?
Message posted by JG (via 128.8.22.80) on July 16, 2001 at 6:38 AM (ET)

Re: How to convert daily return into an annalized return of a stock price?
Message posted by Jack Tomsky (via 208.249.113.130) on July 18, 2001 at 5:02 PM (ET)

To get Rd, we start from

Pn/P1 = [1+Rd/260]^(n-1).

This results in

Rd = 260*[(Pn/P1)^(1/(n-1))-1].

To get Rc, we start from

Pn/P1 = exp[(n-1)Rc/260].

This results in

Rc = [260/(n-1)]*ln(Pn/P1).

These equations depend only the starting and ending prices, and not the intermediate prices. They find what the equivalent rates would be (daily or continuously compounded) which would take the starting prices to the ending prices.