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How to calculate portfolio returns

InvestorInvestor
edited December 2012 in Off-Topic
There are sometimes portfolio returns floated in this forum. If your portfolio has contributions and withdrawal the return could be very different than a simple calculation that only involves beginning and final values of the portfolio. There are several ways to do this. For example, the following paper lists a few of these schemes.

https://www.pwlcapital.com/pwl/media/pwl-media/PDF-files/Justin Bender Assets/How-to-Calculate-your-Portfolio-s-Rate-of-Return_v03linked.pdf

I personally use a simplified version of modified dietz formula where all contributions and withdrawals are assumed to have happened in the middle of the period. The simplified formula is below:


Ri = (FVi - BVi - CFi) / (BVi + 0.5 * CFi)

where:

Ri = The return of the period i (To get % return of the period multiply this number by 100)
BVi = Beginning value of the portfolio
FVi = Final value of the portfolio
CFi = Net Cash Flow for the period (additions - withdrawals)

To increase the accuracy, I calculate the returns each month and geometrically link them as follows:


Rytd = (1 + R1) * (1 + R2) * ... * (1 + Rn) - 1

If you do this for 12 months you get the 1 year return.

Example: Portfolio begins with $100,000.


Month Month End Net CF Return
------ ----------- ---------- ------
January $104,417.00 $1,000.00 3.40%
February $107,016.98 $0.00 2.49%
March $107,742.56 -$1,000.00 1.62%
April $112,786.66 $5,000.00 0.04%
May $110,002.88 $1,000.00 -3.34%
June $113,522.35 $1,000.00 2.28%
July $114,850.56 $0.00 1.17%
August $117,638.49 $1,000.00 1.55%
September $119,497.18 $0.00 1.58%
October $115,305.41 -$3,000.00 -1.01%
November $115,893.47 $0.00 0.51%
December $116,090.49 $0.00 0.17%

Final Portfolio Value = $116,090.49

Monthly Returns are calculated via above formula: For example:

R1=(104,417.00-100,000.00-1,000.00)/(100,000.00+0.5*1,000.00)=3417/100500=0.0340 => 3.40%
R2=(107,016.98-104,417.00-0.00)/(104,417.00+0.5*0.00)=2599.98/104417=0.0249 => 2.49%

Portfolio Return=(1+0.034)*(1+0.0249)*(1+.0162)*(1+0.0004)*(1-0.0334)*(1+0.0228)*(1+0.0117)*(1+0.0155)*(1+0.0158)*(1-0.0101)*(1+0.0051)*(1+0.0017)-1
Portfolio Return=0.1078 => 10.78%

If $5000 net cash flow was not taken into account portfolio would be: 16.09%. The actual return is far less.

Comments

  • mnzdedwardsmnzdedwards
    Thanks Investor. I've reproduced your table in my own Excel spreadsheet. Thanks for your great clarity and example in an area that is often overlooked by average investors - What is my true return?

    Thanks for your contributions.
    Mike_E
  • TNK
    I am using SigFig, I don't know how reliable is, but I like the overview it gives me. I hope with time it will get bigger.

    Anyone else is using it?
  • InvestorInvestor
    Reply to @mnzdedwards: You are welcome. I am glad someone found it helpful.
  • fundalarmfundalarm
    Reply to @Investor: the back of the envelope calculations would be to divide the dollar return by the initial investment and the net CF, or, in your example: (116090-105000)/105000=.1056 or 10.56% it is not technically correct, but it is a good approximation for those of us who have no time or interest to track each month and each cash flow.
  • Old_JoeOld_Joe
    edited January 2013
    Reply to @fundalarm: Thanks for the simple setup JR... you're my kind of woman! (But you already knew that...) :-)
  • InvestorInvestor
    edited January 2013
    Reply to @fundalarm:

    In this case, it was close enough. You basically transferred the 5000 to the beginning of the period.

    If you want slightly better one use my formula (which treats 5000 invested in the middle of the computation period) for overall return.

    (116090.49 - 100000.00 - 5.0000) / (100000.00 + 0.5 * 5000) = 11090.49 / 102500 = 10.82% which is closer to the linked return.

    This sort of simplifications can be used if the additions and subtractions are small relative to the size of the portfolio.
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