Portfolio ROR

How to calculate Portfolio Rate of Return.

The annualised rate of return from holding a security between two dates D1 and D2, with a starting value V1 and ending value V2 for a year which counts Y days:

Rate of return =(((D2-D1) v (1+(V2-V1)/V1))Y) -1

Follow this step-by-step example to solve:

A share is purchased for $1,000 on January 1st and sold for $13,500 on October 1st.

Therefore (D2-D1) = 275 days

And, (V2-V1)/V1) = (13,500-10,000)/10,000 = 35.00%

So, the generalised equation reduces to = 275v(1+35.00%), or in general:

Dth_root(ROR%), where D= number of days between buy and sell and ROR is the overall rate of return.

The calculation 275th_root(1+35.00%) = 1.00109.

Use this formula in Excel:

275th_root(1+35.00%) = exp(ln(1+0.35)/275) = 1.00109

The annualised rate of return is then = (1.00109) 360 -1 = 48.02% p.a.

Use this equation in Excel to solve:

The annualised rate of return = exp(ln(1.00109)*360) -1 = 0.4802

This equation holds true for NASD rules, which count 360 days in a year.

For example, the standard discount rate for 8.0% in year 1 is 0.925926 (1/(1+0.08)1

The adjusted discount rate is 1/(1+0.08)0.5 = 0.962250.

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