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On my homework problem. I have this scenario below:

  • 12/10/2010 - Long Position in a stock of 800 shares at $4.5 per share.
  • 12/10/2010 - Long Position in the same stock of 200 shares at $4.55 per share.

  • 12/31/2010 - the price of the stock is $4.60/share

  • 02/28/2011 - the price of the stock is $4.58/share
  • 03/16/2011 - the price of the stock is $4.61/share

I was asked to calculate the YTD and MTD PnL for 16/03/2011.

For YTD I did the total position(800+200) times the price difference(4.61-4.60). But, not sure whether this is right way to calculate the PnL.

1

Month to date

For the month to date (MTD), the price on Feb 28th is $4.58 and the price on March 16th is $4.61 so the return is

(4.61 - 4.58) / 4.58 = 0.00655022 = 0.655022 %

which can be written more simply as

4.61 / 4.58 - 1 = 0.00655022 = 0.655022 %

The position is 1000 shares valued at $4580 on Feb 28th, so the profit on the month to date is

$4580 * 0.00655022 = $30

Calendar year to date

For the calendar year to date (YTD), the price on Dec 31st is $4.60 and the price on Feb 28th is $4.58 so the return to Feb 28th is

4.58 / 4.60 - 1 = -0.00434783 = -0.434783 %

The return from Feb 28th to March 16th is 0.655022 % so the year to date return is

(1 - 0.00434783) * (1 + 0.00655022) - 1 = 0.00217391 = 0.217391 %

or more directly

(4.58 / 4.60) * (4.61 / 4.58) - 1 = 0.00217391 = 0.217391 %

So the 2011 YTD profit on 1000 shares valued at $4600 on Dec 31st is

$4600 * 0.00217391 = $10

Year to date starting Dec 10th

For the year to date starting Dec 10th, the starting value is

800 * $4.50 + 200 * $4.55 = $4510

and the value on Dec 31st is 1000 * $4.60 = $4600

so the return is $4600 / $4510 - 1 = 0.0199557 = 1.99557 %

The year to date profit is therefore

$4510 * ((4.6 / 4.51) * (4.58 / 4.60) * (4.61 / 4.58) - 1) = $100

Note - YTD is often understood to mean calendar year to date. To cover all the bases state both, ie "calendar YTD (2011)" and "YTD starting Dec 10th 2010".

Edit further to comment

For the calendar year to date, with 200 shares sold on Jan 10th with the share price at $4.58, the return from Dec 31st to Jan 10th is

4.58 / 4.60 - 1 = -0.00434783 = -0.434783 %

The return from Jan 10th to Feb 28th is

4.58 / 4.58 - 1 = 0

The return from Feb 28th to March 16th is

4.61 / 4.58 - 1 = 0.00655022 = 0.655022 %

The profit on 1000 shares from Dec 31st to Jan 10th is $4600 * -0.00434783 = -$20

The profit on 800 shares from Jan 10th to Feb 28th is zero.

The profit on 800 shares from Feb 28th to March 16th is

800 * $4.58 * 0.00655022 = $24

So the year to date profit is $4.

  • Amazing thank you very much Chris. Really Appreciate it . But got one last question. For all your calculation the Inital price of 800 @$4.5 and 200@$4.55 price is not used. For YTD PnL Can we use the initial price to calculate the PnL for 12/10/2010 till 12/31/2010 and add it along each month? – Mark Austin Apr 19 '17 at 12:17
  • @MarkAustin I have added it in. Usually year to date would be understood to run from Dec 31st, for comparison with other stocks. For example: google.com/search?q=year+to+date . The information prior to Dec 31st may have been thrown in to confuse you, but you can cover the bases by stating both returns and explaining the difference. – Chris Degnen Apr 19 '17 at 13:02
  • Understood. Thank you very much. On your YtD calculation. I thought it would be easier to calculate the price on March 16th minus Dec 31st . i.e. (4.61-4.6)*1000 = 10 Is this same as what you did? – Mark Austin Apr 19 '17 at 13:07
  • @MarkAustin 4.60*((4.58/4.60)*(4.61/4.58) - 1) does simplify to 4.61 - 4.60. However, in going the long way round the returns for the various periods are also calculated. The returns are often useful to know. – Chris Degnen Apr 19 '17 at 14:30
  • if i have a short position instead of long position then the signs would change right? – Mark Austin Apr 20 '17 at 17:19

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