I thought I understood internal rate of return, but I am
unable to explain the following results. Can anyone help?

Using the performance tools in bivio, I have obtained the
following results:
A. The Club's portfolio performance for 2012 is 23.5%.
B. For seven members whose starting values are in the $7,400
- $10,400 range, the member performance results are also in
  the 23% range.
C. However, for two members whose starting values are $770
and $990 respectively; their performance results are only
18.6% and 19.5%.
D. We use auto pay so each member was credited with
contributing the same additional capital each month.

Why does the percentage increase in portfolio value not
apply equally to all members?

1. Is the difference caused solely by the size of the
starting value?
2. Would the difference in results between members change if
the portfolio value went up significantly early in the year
and then came down versus going down early in the year and
then going up later in the year? (I am wondering if it has
to do with the fact that for the seven members, capital
added in 2012 was smaller relative to their starting value
than the other two members.)

Jack Ranby

I'd say both your suggestions "1" and "2", below, play a role in explaining
the IRR differences between members. I'd say "for the seven members,
capital added in 2012 was smaller relative to their starting value than the
other two members" is especially relevent.

-Jim Thomas

----- Original Message -----
From: "John W Ranby" <ranby@azbar.org>
To: <club_cafe@bivio.com>
Sent: Tuesday, January 15, 2013 9:14 AM
Subject: [club_cafe] Member Performance - Why Does Starting Value affect
Result?


>I thought I understood internal rate of return, but I am
> unable to explain the following results. Can anyone help?
>
> Using the performance tools in bivio, I have obtained the
> following results:
> A. The Club's portfolio performance for 2012 is 23.5%.
> B. For seven members whose starting values are in the $7,400
> - $10,400 range, the member performance results are also in
> the 23% range.
> C. However, for two members whose starting values are $770
> and $990 respectively; their performance results are only
> 18.6% and 19.5%.
> D. We use auto pay so each member was credited with
> contributing the same additional capital each month.
>
> Why does the percentage increase in portfolio value not
> apply equally to all members?
>
> 1. Is the difference caused solely by the size of the
> starting value?
> 2. Would the difference in results between members change if
> the portfolio value went up significantly early in the year
> and then came down versus going down early in the year and
> then going up later in the year? (I am wondering if it has
> to do with the fact that for the seven members, capital
> added in 2012 was smaller relative to their starting value
> than the other two members.)
>
> Jack Ranby
>

> Why does the percentage increase in portfolio value not
> apply equally to all members?

By percentage increase in portfolio value do you mean internal rate of
return? If so, IRR depends on the cash flow involved, which, for each
member, would consist of their starting value, the contribution amounts
during the period, and the ending value. Since, in the case that you have
given, the starting and ending values are different, and the cash flows are
the same, you are going to get different rates of return for those with
lesser starting values.

You can check the effect of this, by clicking on 'detail' for any member and
then saving to an excel spread sheet. Put the ending value in as a negative
figure in the Investment column, and perform an XIRR function on the dates
and investment columns.

Let me know if you have any questions about this.

Rip West

I have a similar question/situation.

We had two members, each with a 1/1/2012 starting value of 287.24.
Each paid the same dues through the year, but one paid ahead by
quarters and one paid monthly.

The monthly payment one had a final investment amount of $767.24 and
Return total of 798.83. Her annualized rate of return was 5.9%.

The one who paid ahead had a final investment amount of $767.24 and
Return total of 792.57. Her annualized rate of return was 4.6%.


On Jan 15, 2013, at 1:24 PM, rip west wrote:

> Why does the percentage increase in portfolio value not
> apply equally to all members?

By percentage increase in portfolio value do you mean internal rate of
return? If so, IRR depends on the cash flow involved, which, for each
member, would consist of their starting value, the contribution
amounts during the period, and the ending value. Since, in the case
that you have given, the starting and ending values are different, and
the cash flows are the same, you are going to get different rates of
return for those with lesser starting values.

You can check the effect of this, by clicking on 'detail' for any
member and then saving to an excel spread sheet. Put the ending value
in as a negative figure in the Investment column, and perform an XIRR
function on the dates and investment columns.

Let me know if you have any questions about this.

Rip West

Hi Rita,

Yes, IRR is dependent on cash flows and Dates. Even though both members paid
the same, in total, the fact that the payments were at different times will
affect IRR and ending value. The fact that they had different ending values
also affects IRR.

Rip West

Jim:

Thank you for your thoughts. However, after further thought,
I don't think the order of the portfolio going up or down
during the year matters as the XIRR going takes into account
the value at the end of the year.

Rip:

I have used the XIRR function in Excel and do reach the same
results. However, it does not help me understand the "why?"

To try to isolate the causation, I created four hypos using
the XIRR function in Excel using the following basic
assumptions:

1. There are two members; one with a starting balance of
$100 and the second with a starting balance of $1,000.

2. The starting capital doubles in the first half of the
year and no growth occurs in the second half of the year.

3. Additional capital is only added once on July 1 of the
year.

4. Each hypo changes the relative value of the additional
capital added at mid year.

The hypos are set forth in the attached PDF because the
table format would not copy into this message.

Observations:

1. The member and club XIRR are equal and stay the same when
there is no additional capital added and when the additional
capital added is proportional. Hypos #1 & 2.

2. The XIRR changes drastically when the additional capital
added is in reverse proportion to the starting capital. I
understand part of the explanation is that in the hypo the
new capital does not increase in value during the reminder
of the year so a much larger portion of the small capital
member is idle. Hypo #3.

3. The fourth hypo most closely mirrors the normal club
experience. The small capital member actually gains in
ownership percentage during the year, but still has a lower
XIRR. The member with the larger starting balance actually
has a higher XIRR than the club as a whole. I still cannot
fully understand what are the causation of the difference in
XIRR, and these results seem counter-intuitive.

Jack Ranby

Jack,

Perhaps this will help explain why the results strike you as
counter-intuitive.

In hypothetical #4, why does member B have a higher IRR than the club as a
whole? Because, growing $1000 for 12 months and growing $10 for 6 months to
a combined result of $2010 requires a higher *constant* growth rate than
growing $1100 for 12 months and growing $20 for 6 months to a combined
result of $2220.

Perhaps running through the hypothetical #4 math for Member A will give some
insight. Member A has $100 that doubles over 6 months then $10 is added and
the combined $210 grows not at all over the next 6 months.

IRR asks "what if something entirely different happened, but produced the
same result". What if all the money grew at the same *constant* growth rate
during the time it was invested? IRR tells you what that constant growth
rate would need to be in order to produce the same result ($210 after 12
months).

So, IRR posits a variation on hypothetical #4 where $100 grows at some
*constant* annual rate (call it "r") for 12 months and $10 grows at that
same constant rate for 6 of those 12 months. Note that it makes no
difference to IRR over which 6 of those 12 months the growth is assumed to
occur! So IRR considers it the same as $110 growing for the first 6 months
then $100 growing for the second 6 months (at a constant rate). In other
words, as far as IRR is concerned, *how long* the constant growth occured it
critical but *when* the constant growth occured is irrelevant.

In this case, r = 0.9598754% is the constant growth rate needed to produce
Member A's result.

$100 after 95.9875%/yr growth for 1 year = 100 x (1+0.9598754) = $195.98754.

$10 after 95.9875%/yr growth for 183 days out of 365 (Jan 1st thru Jul 1st)
= 10 x (1+0.9598754)^(183/365) = $14.01246.

195.98754 + 14.01246 = $210.

> 3. The fourth hypo most closely mirrors the normal club
> experience. The small capital member actually gains in
> ownership percentage during the year, but still has a lower
> XIRR. The member with the larger starting balance actually
> has a higher XIRR than the club as a whole. I still cannot
> fully understand what are the causation of the difference in
> XIRR, and these results seem counter-intuitive.

> So, IRR posits a variation on hypothetical #4 where $100 grows at some
> *constant* annual rate (call it "r") for 12 months and $10 grows at that
> same constant rate for 6 of those 12 months. Note that it makes no
> difference to IRR over which 6 of those 12 months the growth is assumed to
> occur! So IRR considers it the same as $110 growing for the first 6
> months then $100 growing for the second 6 months (at a constant rate).

I should have worded that last sentence differently. I'll try again ...

So IRR considers it the same as $110 growing for the first 6 months then the
result of $100 having grown for 6 months continuing to grow for another 6
months.

-Jim Thomas

Jim:

Thank you for your efforts to help me understand this
puzzle. I believe I have finally figured it out.

Jack