Thursday 2 January 2014

How To Calculate Portfolio Return?

Year 2013 has passed... Happy New Year 2014 to all.

When I try to calculate my overall portfolio return for year 2013, I face some problems.

As mentioned in previous posts in this blog, I only started to get really serious with stock market investment from June 2013, and I only started to calculate gain on monthly basis from October 2013.

Prior to June 2013, I have sold all the stocks and only left one Tambun behind. As the gain & loss of previous transactions almost break even, I'll consider July 2013 as the start of my portfolio for 2013.

However, this will not reflect the true performance of the portfolio for year 2013 as Tambun, which carries a high percentage in the portfolio, was bought and accumulated since 2012. All other stocks were bought after June 2013 though.

Another problem is, I bought and sold shares quite a number of times since the start of July 2013. How can I calculate the true return of my portfolio accurately?

For example,

Mr Y put in RM10,000 in his portfolio on the 1st of Jan 2013 and do nothing after that. In the end of the year (31 Dec 2013), his portfolio value increases to RM15,000. His portfolio return will be 50%. This is straight forward.

If Mr Y adds RM5,000 to buy another stock on 1st Dec 2013 and its share price remain the same until end of Dec 2013, what will be his overall return for year 2013?

In this case, his total investment in year 2013 will be RM15,000 (initial RM10,000 + later RM5,000), and his portfolio value in the end of Dec 2013 will be RM20,000 (value from initial RM15,000 + value from later RM5,000). Does the return of his portfolio calculated as:

Total gain in 2013 divided by total investment in 2013, ie:

[RM20,000 - RM15,000] / RM15,000 = 33.3% ??

I don't think it is a true reflection of the performance of this portfolio as the additional investment made in December does not have much time to generate return.

For the denominator of RM15,000 in this calculation, RM10,000 of it generates return for 12 months, while RM5,000 of it only generates return for 1 month. This has unfairly dragged down the overall portfolio performance from 50% to 33%.

Lets study another scenario,

Mr B bought 10,000 shares of stock Z at RM1.00 per share on 1st Jan 2013. His initial investment will be RM10,000.

He sold 2,000 shares of stock Z on 1st June 2013 at the price of RM1.50 per share, with a net gain of RM1,000 (excluding transaction cost).

In the end of Dec 2013, stock Z closes at RM2.00 per share. What will be Mr B's overall return in year 2013?

[Unrealized gain + realized gain] divided by initial capital value, ie:
[RM2 - RM1] x 8000 shares + [RM1.50 - RM1] x 2000 shares, divided by RM10,000 = 90% ??


[Unrealized gain + realized gain] divided by end capital value, ie:
[RM2 - RM1] x 8000 shares + [RM1.50 - RM1] x 2000 shares, divided by RM8,000 = 112.5% ??

This calculation seems reasonable but not quite right. Though Mr B initial investment is RM10,000 in Jan 2013, it has been reduced to RM8,000 from June 2013 onward after 2,000 shares have been sold. In other words, the share price gain from June to Dec 2013 (from RM1.50 to RM2.00) is generated from only RM8,000 capital, not RM10,000 as used in the denominator of the calculation above.

If we change the denominator to RM8,000, which is the capital remaining in the end of 2013, the same question still arises as the return from Jan to June 2013 is generated from RM10,000, not RM8,000.

In real life, most investors buy and sell shares multiple times during a year, and have a net increase or decrease from their initial capital. This makes the calculation of portfolio return even more complicated.

I try to search online to find out the way to calculate portfolio return more accurately and find one method using approximation equation. The formula is:

Ending value - 0.5(net changes)
----------------------------------------------                         -   1  x100%
Beginning value + 0.5(net changes)

Net changes can be net addition or net withdrawal from Jan 13 to Dec 13.

From the example of Mr B above, beginning value is RM10,000, ending value is RM16,000 (8,000 shares x RM2). Net changes will be net withdrawal of RM3,000, thus -3,000  (2,000 shares x RM1.50).

16,000 - 0.5(-3,000)
-----------------------------                - 1 x100%   =  105.9%
10,000 + 0.5(-3,000)

Thus, Mr B's portfolio return for year 2013 is 105.9%.

The basis of the formula is actually quite simple, average (50%) of the withdrawal is added into the beginning value and subtracted from the ending value, and vice versa.

For Mr Y's case in earlier example, his portfolio return should be:

20,000 - 0.5(5,000)
---------------------------                - 1 x 100%  =  40%
10,000 + 0.5(5,000)

This is an approximation equation and will not be 100% precise. Like statistics, the accuracy will improve if the additions and withdrawals are done evenly and the amounts are not large compared to total portfolio value.

This formula includes both realized and unrealized gain for a period of time. To include the dividend gain, I will add it into the ending value to generate my overall return for year 2013.

I'm not sure whether this is the correct & simplest way to calculate overall portfolio return for share investment. If anyone has any recommendation or objection, please feel free to comment.


  1. Hi BD, below link is about how to calculate the return by using excel. Simple and easy.

  2. Hi BD

    I also encounter the same problem (calculating return) few months back. This is what I found from some books and the web.

    There are 2 methods: Money weighted method (basically same as calculating implied IRR) and Time weighted method.

    I personally use time weighted method.

    For instance, if I made 10% return each year for 3 years, then my total return is 33.1%. (1.10 x 1.10 x 1.10) minus 1.

    If I make 1% each year for 12 years, then my return would be 12.68% p.a. To calculate annual return, just replace 12 years to 12 months... hence we calculate monthly return and multiply them to get 1 year annual return.

    Return is calculated by (Ending Amount / Opening Amount) - 1

    Hence with cash flow movements, the monthly return can be calculated by [Ending Amount / (Adjusted opening amount)] - 1, whereby adjusted opening amount is the new amount after adjusted for the cash flow movement.

    For your Mr Y case, since he put money in December, (note that "time" matters in this calculation), it's important to know when did he make the RM5k profit. Before or after he put the new money. If money is made before the new capital comes in, the annual return would be 50% (because he did make 50% from his RM10k, while the RM5k gain nothing). If the profit comes in after the new capital, then the return is 33.33%. Imagine the Rm5k new capital comes from Mr Y's business partner (let's call him MR Z). He'd definitely ask for 1/3 sharing for any profit made after he has invested his money regardless if Mr Z money was used or not.

    1. JY, Thanks for your feedback. I need quite some time to digest it :)

      It seems like the "adjusted opening amount" does not factor in time factor.

      Actually I still think the approximation equation is more accurate at this moment. It does take in the time factor but it assumes its average.

      For example, if I have RM10,000 on 1st Jan, then invest another RM5,000 on 15th Jan, and my end value on 31st Jan is RM20,000.

      If according to the formula you mention, monthly return will be

      [20,000 / 15,000] - 1 = 33%

      Am I calculate the "adjusted opening amount" correctly?

      If using the approximation method, monthly return will be:

      [20,000 - 2,500] / [10,000 + 2,500] - 1 = 40%

      The closer the additional investment made to the middle of the month (15th Jan) & the lesser the additional amount is, the more accurate it is.

      According to approximation method, our end value in this case will not be RM20,000 if we add in further investment in the month.

      Lets say if we add in another RM30,000 on 30th Jan, and our portfolio value reach RM50,000 on 31st Jan, it is unfair to put our end value as RM50,000, or beginning value at RM45,000.

      Using the approx method, our end value in this case will be RM32,500, and beginning value RM27,500.

      Though this will not be a true reflection as the additional RM30,000 is too large an amount and it's made towards the very end of month.

      However, it is still better than not using approx method.

      Just my 2 cents.

  3. Hi BD

    I used 12 monthly "approximate return" to generate a more accurate 1 year return. Now you are zooming into detail for 1 month return. Haha If you want an accurate 1 month % return, then we'll have to use 30 days daily return to compute the 1 month return, just like how the bank did it when they calculate monthly interests considering you make deposits and withdrawals everyday.

    The theory is simple. The % return is to measure your performance relative to the profit generated. Let's put aside the months and years aside for now. Let's say you made RM5000, using capital of RM10,000. The % profit is 50%, simple. If you add additional Rm5000 capital but didn't make any trades, your return (or performance) is still 50% and profit of RM5000.

    The 50% mark is important especially in fund management industry because they cannot afford to let new investors who come in especially later of the year to pull down their one year performance in terms of %. Let's say... a unit trust has an initial capital of RM100m. They made 50% for the year or RM50m. Suddenly a tycoon decided to invest RM1b into the fund, pushing the ending fund value to RM1.150b. If we use your approximation method, the annual return would be:
    1150m - 0.5(+1000m) / 100m + 0.5(+1000m) - 1
    = 8.3%

    This will be very unfair to the fund managers because their performance is affected by the mathematical computation of deposits and withdrawals made during the year, and not by the performance in the market.

    Similarly if the fund didn't make any profit until the RM1b came in, and they made RM50m from investing only Rm100m in a stock (leaving the RM1b untouched), their return for that trade is 50% but as a portfolio the return is only 4.5%.

    1. Thanks JY, I think I get what u mean. Anyway, I wonder how do others calculate investment return.

  4. I found this formula to be simple and useful but it will include the excess cash in the portfolio returns calculation

    1. Thanks NOBY. It's ok if excess cash is included in calculation, as it can show how well we utilize our cash on hands.

      Anyway, I'll stick to my own way of calculation :)