Having trouble getting my arms around the concept of AIRR.
Help me understand it by answering this question.

Suppose you invested 10000 in a Certificate of Deposit that
returned 5% per year, compounded daily. On that same day you
also invested 10000 in a portfolio of stocks, some of which
paid dividends that were reinvested and all of which had
fluctuations in price.

At the end 12 months the porfolio had lost 2%. The CD paid
5% as expected. The AIRR of the porfolio would certainly be
lower than the AIRR of the CD.

At the end of 18 months the value of the porfolio surged to
equal the value of CD.

The values of both assets are equal.If calculated from the
date of the initial investment, are the AIRRs also equal?

If calculated for the time period starting with the end of
12 months and extending to the end of 18 months, are the
AIRRs equal?

> At the end 12 months the porfolio had
> lost 2%. The CD paid 5% as expected.
> The AIRR of the porfolio would certainly
> be lower than the AIRR of the CD.

Correct. Both investments (the CD and the stock portfolio)
started being worth the same amount (the initial $10,000
investment) and there were no later additions or
withdrawals. Under those conditions, at any given point in
time, the investment with the lower markert value will
always be the investment with the lower AIRR.


> At the end of 18 months the value of
> the porfolio surged to equal the value
> of CD. The values of both assets are equal.
> If calculated from the date of the initial
> investment, are the AIRRs also equal?

Correct. Under the conditions stated above (a single lump
sum investment and no withdrawals), there are only two
factors entering into the AIRR calculation. The date and
amount of the initial investment and the date and amount of
the current value. Since the initial investments are the
same ($10,000), if the current values are the same the AIRRs
will be the same.


> If calculated for the time period
> starting with the end of 12 months
> and extending to the end of 18 months,
> are the AIRRs equal?

No, The AIRR of the stock portfolio is higher because its
percentage increase in value over those last 6 months was
larger.

At the end of 12 months you suggested the following values:
$10,500 CD (5% APY after 1 year);
$9,800 stock portfolio (down 2%).

At the end of 18 months both are worth the same:
$10,759 CD (5% APY after 1.5 years);
$10,759 stock portfolio (same as CD value)..

Over those 6 months the CD increased in value by 2.47% (a
little less than 1/2 of 2.5%, due to compounding). Over the
same time the stock portfolio increased in value by 9.8%.
So, the stock portfolio has the higher AIRR (20.5%) over
those six months. The CD's AIRR is *always 5% (regardless
of the time period).

It's as simple as that (higher percentage change means
higher AIRR) because there are no additions or withdrawals
of cash.

-Jim Thomas

> Over those 6 months the CD increased
> in value by 2.47% (a little less than 1/2
> of 2.5%, due to compounding).

I should have said "a little more than 1/2 of 5%".

-Jim Thomas