Tuesday, July 17, 2012

Internal Rate of Return

In response to my latest performance post, reader Hugh asks two questions:

1) What is "internal rate of return" and how is it calculated?

2) Why is it hard to compare your internal rate of return to that of the S&P500?

What is "internal rate of return" and how is it calculated?

The internal rate of return of a stream of cashflows (which is all an investment is in terms of its performance) is the annualized effective compound return rate.  A natural question is - well what's that?  The easiest way to think about it is to compare it to an interest rate on a bank deposit.  A bank term deposit of $10 000 may have an interest rate of 6% (let's assume after tax) for a term of 5 years.  As long as interest is paid yearly, the internal rate of return for the bank deposit is 6%, because the annualized effective compound return rate is what the bank tells you it is - 6%.

That's easy to work out.  But how do you compare that to:

  • buying $5 000 IBM shares on January 1 2011, 
  • buying $3 000 Microsoft shares on July 20 2011,
  • receiving a $28 dividend from your Microsoft shares on November 20 2011,
  • selling half of your IBM shares for $3 000 (they went up in value) on December 15 2011,
  • buying $8 000 of Oracle shares on February 10 2012,
  • after all that, finding yourself with $16093 worth of shares today (17 July 2012).
The answer is excel.  You simply make a list of dates and a list of cashflows that looks like this:

You'll see that those cashflows are events based on the bullet points above.  The internal rate of return formula in excel is simply "=xirr(values, dates)".  And you get 24% in my example.

Why is it hard to compare your internal rate of return to that of the S&P500?

The fund has data on all dividends, all purchases and sales of shares since inception.  We use that to get July 14's 7.52% internal rate of return.  But how do we compare that to an investment in the S&P500?  Do we assume that on the first day we purchased shares, the alternative was to purchase the S&P500?  But what if a month after the first purchase, we purchased some different shares?  If the S&P500 has gone up since then, our performance looks terrible if we backdate the comparator to having purchased the S&P500 at the earlier date (of first purchase).  Vice versa if the S&P500 has gone down.

The problem is knowing what to compare when you are slowly adding positions to your portfolio (as we are).  The only sound way to do it is to, at every purchase and sale, assume that you had purchased or sold the S&P500 at equal value to the actual purchase or sale.  So if the fund bought $50 000 of IBM on 20 January 2012, we assume that the alternative was to buy $50 000 of the S&P500.  If the fund sold $10 000 of MSFT, we assume that the alternative was to sell $10 000 worth of the S&P500.  This method removes any influence of "market timing" in the comparison. This seems fair, since the whole premise of the fund is that market timing (for us) is impossible, and all we can try to do is buy stocks cheaply whenever we see them.

Having set that all out, if I get hold of historical prices for the S&P500, I think I might actually be able to compare performance directly with a bit of tinkering in excel.  I might try to do that sometime this week.

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