Calculating IRR in ruby

Question

Can anyone help me with a method that calculates the IRR of a series of stock trades?

Let's say the scenario is:

$10,000 of stock #1 purchased 1/1 and sold 1/7 for $11,000 (+10%)
$20,000 of stock #2 purchased 1/1 and sold 1/20 for $21,000 (+5%)
$15,000 of stock #3 purchased on 1/5 and sold 1/18 for $14,000 (-6.7%)

This should be helpful: http://www.rubyquiz.com/quiz156.html

But I couldn't figure out how to adapt any of the solutions since they assume the period of each return is over a consistent period (1 year).

Answer 1

I finally found exactly what I was looking for: http://rubydoc.info/gems/finance/1.1.0/Finance/Cashflow

gem install finance

To solve the scenario I posted originally:

include Finance
trans = []
trans << Transaction.new( -10000, date: Time.new(2012,1,1) )
trans << Transaction.new( 11000, date: Time.new(2012,1,7) )
trans << Transaction.new( -20000, date: Time.new(2012,1,1) )
trans << Transaction.new( 21000, date: Time.new(2012,1,20) )
trans << Transaction.new( -15000, date: Time.new(2012,1,5) )
trans << Transaction.new( 14000, date: Time.new(2012,1,18) )

trans.xirr.apr.to_f.round(2)

I also found this simple method: https://gist.github.com/1364990

However, it gave me some trouble. I tried a half dozen different test cases and one of them would raise an exception that I was never able to debug. But the xirr() method in this Finance gem worked for every test case I could throw at it.

Answer 2

For an investment that has an initial value and final value, as is the case with your example data that includes purchase price, sell price and a holding period, you only need to find holding period yield.

Holding period yield is calculated by subtracting 1 from holding period return

HPY = HPR - 1
HPR = final value/initial value
HPY = 11,000/10,000 - 1 = 1.1 - 1 = 0.10 = 10%
HPY = 21,000/20,000 - 1 = 1.05 - 1 = 0.05 = 5%
HPY = 14,000/15,000 - 1 = 0.9333 - 1 = -0.0667 = -6.7%

This article explains holding period return and yield

You can also annualize the holding period return and holding period yield using following formula AHPR = HPR^(1/n) AHPY = AHPR - 1

The above formulas only apply if you have a single period return as is the case with your example stock purchase and sale.

Yet if you had multiple returns, for example, you purchased a stock A on 1/1 for 100 and it's closing price over the next week climbed and fell to 98, 103, 101, 100, 99, 104

Then you will have to look beyond what HPR and HPY for multiple returns. In this case you can calculate ARR and GRR. Try out these online calculators for arithmetic rate of return and geometric rate of return.

But then if you had a date schedule for your investments then none of these would apply. You would then have to resort to finding IRR for irregular cash flows. IRR is the internal rate of return for periodic cash flows. For irregular cash flows such as for stock trade, the term XIRR is used. XIRR is an Excel function that calculates internal rate of return for irregular cash flows. To find XIRR you would need a series of cash flows and a date schedule for the cash flows.

Finance.ThinkAndDone.com explains IRR in much more detail than the articles you cited on RubyQuiz and Wiki. The IRR article on Think & Done explains IRR calculation with Newton Raphson method and Secant method using either the NPV equation set to 0 or the profitability index equation set to 1. The site also provides online IRR and XIRR calculators