Let's say I invested $1000 in a mutual fund on November 1, 2002

At the end of April of 2005, it is worth $1450.

My gain is $450 or 45% since I purchased it.

But how do I calculate how much average annual return it has been for the 30 month period. Or in other words, it's equivalent to an investment making X% a year?

What's the formula?

Thanks....

Qarl have you stopped taking your vitamins.?

total %, divided by number of months, times 12= average annual percentage

No... I guess I'm trying to figure out the equivalent compounded rate (annually)

If I take 45%/30 months x 12 = 18%

1000 x 1.18 = 1180
1180 x 1.18 = $1392.40
$1392.40 x 1.18 = $1643 which is too high

OK, you lost me. 18% x 2.5 years(30 months)= 45%

QUOTE (Qarl @ May 12 2005, 05:35 PM)

No... I guess I'm trying to figure out the equivalent compounded rate (annually) If I take 45%/30 months x 12 = 18% 1000 x 1.18 = 1180 1180 x 1.18 = $1392.40 $1392.40 x 1.18 = $1643 which is too high

you just figured what the 3 year rate would be not the 30 months

1000 * 1.18 = 1180 12 months
1180 * 1.18 = 1392.4 24 months
1392 * 1.09 = 1517 30 months

so the annual rate is just under 18 %

now you need to remember that the interest is figured on a monthy basis so it is probably closer to 16 % figured on a monthly rate of around 1.33 %. remember that you gain the interest on a monthly rate so you really cant figure it yearly except to be lazy

QUOTE (black73 @ May 12 2005, 05:03 PM)

total %, divided by number of months, times 12= average annual percentage

Close but not exactly, you forgot about compounding.

This is what I do for a living, I trade bonds.

In this case:

((1,450 / 1,000) ^ (1 / 30) -1 ) * 12

i.e. 1) you take the ratio of the end ovet the beginning, 1.45 in this case; 2) you take it to the power of 1 over the number of periods: the result is 1.01246. 3) You subtract 1, and this gives you 1.246%, which is you return per period, in this case, monthly. 4) You multiply the result by 12, and that gives you 14.95%, which is your annual return on a monthly compounding basis.

HTH

Michel Richard
914/6 2.2 E MFI

ROI calculation:

Initial Value: 1000
Value @2.5 years: 1450
Annual rate of return is 14.86% assuming interest is compounded daily.

Hang on, the calculation I made assumes there was no cashflow over the period i.e. you did not earn dividends or interest payments each month.

If that is true, and you want the result on a yearly compounding basis, the formula is:

((1,450 / 1,000) ^ (1/2.5) - 1

because 30 months is 2.5 years. The answer then is 16.02 %

To convert a yearly compounded figure into a monthly one:

((1 + 16.02 %) ^ ( 1 / 12 ) -1 ) * 12

In this case, there is no absolute reason for calculating on a daily, monthly, or yearly compounded basis, because there is only one cashflow at the end.
The reason for paying attention to compounding frequency is simply to ensure that you are looking at comparable figures if you compare to returns on another investment.

Michel

i invested $1000 is 914 parts in 2002, but they've rusted away to nothing now.
what is the average monthly rate of oxidation?

(sorry, since it's an OT thread anyway, i couldn't resist a bit of on-topic foolishness :-) ...)

QUOTE (ArtechnikA @ May 12 2005, 06:00 PM)

(sorry, since it's an OT thread anyway, i couldn't resist a bit of on-topic foolishness :-) ...)

Cool

QUOTE (michel richard @ May 12 2005, 06:56 PM)

Hang on, the calculation I made assumes there was no cashflow over the period i.e. you did not earn dividends or interest payments each month. If that is true, and you want the result on a yearly compounding basis, the formula is: ((1,450 / 1,000) ^ (1/2.5) - 1 because 30 months is 2.5 years. The answer then is 16.02 %

Michel, have you got any with that yield in USD? I'll take a few

That's what I needed... Thanks!

QUOTE (ArtechnikA @ May 12 2005, 06:00 PM)

i invested $1000 is 914 parts in 2002, but they've rusted away to nothing now. what is the average monthly rate of oxidation? (sorry, since it's an OT thread anyway, i couldn't resist a bit of on-topic foolishness :-) ...)

thats depretiation!!
Erik

QUOTE

14.95%, which is your annual return on a monthly compounding basis.

That's what my calculator tells me.

QUOTE (Howard @ May 12 2005, 06:04 PM)

because 30 months is 2.5 years. The answer then is 16.02 % [/QUOTE] Michel, have you got any with that yield in USD? I'll take a few

Only Candadian dollar bonds, plus my license is no good in California. Sorry.

However, I know of some real estate in Florida . . .

QUOTE (michel richard @ May 12 2005, 08:04 PM)

However, I know of some real estate in Florida . . .

Already bought some thru my broker. Dewey, Cheatham & Howe.

QUOTE (Howard @ May 12 2005, 06:04 PM)

QUOTE (michel richard @ May 12 2005, 06:56 PM) Hang on, the calculation I made assumes there was no cashflow over the period i.e. you did not earn dividends or interest payments each month. If that is true, and you want the result on a yearly compounding basis, the formula is: ((1,450 / 1,000) ^ (1/2.5) - 1 because 30 months is 2.5 years.  The answer then is 16.02 % Michel, have you got any with that yield in USD? I'll take a few

Russell mid cap index. 1 year to date.

20.31% return. =-)

Ok, now that you all know your return lets calculate the 12mo. downside risk. That's likely to be a shocker for some of you. (Right Michel? ) Return is just one side of the coin.

-Ben M. (fee only asset mgmt.)

OK, I'll bite. Ben, please explain calculation of downside risk ..

QUOTE (Carl @ May 13 2005, 08:54 AM)

OK, I'll bite.  Ben, please explain calculation of downside risk ..

The technical term is 'Value at Risk' (VAR). Basically it's a statistical measurement used to measure the risk of an investment losing value over a specific period of time. The three components are time, confidence level, and loss percentage. Typically you choose a time interval (day, month, year, ...), a confidence level ("I want to know with 95% confidence"), and one of three variability measurement types (historical data, variance-covariance, or Monte Carlo simulation). Typically the variance-covariance method meets my needs and is less subjective in my opinion.

For regulatory reasons I'll use a purely hypothetical example using an imaginary investment, and calculate 12-month VAR with a confidence level of 99%.

Average annual return = 10.88%
1yr standard deviation = 13.10

VAR = (ave. return)+[(-1 x standard deviations for selected % certainty)x(standard deviation)]
VAR(12mo.) = 10.88% + (-2.33 x 13.1%) = -19.64%

In other words, 12mo. losses (for this imaginary investment) can be expeted to not exceed -20% most of the time for any 365 day period. Rather than just looking at the average return and saying "I ought to make 10% over the long haul" you have to realize that over a short period - 1yr in this example - you could likely see a loss of 20% in this example. VAR calculation can be performed against a single investment or an entire portfolio.

What this does is give us an indicator of potential losses over the selected time period (in this case 12 months). This is strictly a risk-evaluation tool. It can't predict the future. It is based on past performance and variability, which is not an indicator of future returns.

What I often see when meeting with an investor for the first time is that they are exposed to a higher level of downside risk than they realize.

If that was too much or not enough info I appologize.

-Ben M.

QUOTE (airsix @ May 13 2005, 08:38 AM)

Ok, now that you all know your return lets calculate the 12mo. downside risk.

Don't worry guys, we don't have the info here to do the risk calculation.

Ben,

Your post crossed mine. I meant "we don't have the info without making assumptions"

QUOTE (michel richard @ May 13 2005, 11:25 AM)

QUOTE (airsix @ May 13 2005, 08:38 AM) Ok, now that you all know your return lets calculate the 12mo. downside risk. Don't worry guys, we don't have the info here to do the risk calculation.

I meant that in jest. They should have their financial advisor calculate it or help them do it. In my example above I used an imaginary investment as an example of the math. I restrict my comments here to acadamia because I'd like to keep my licenses until I retire. I'm all about risk management though. I want everyone to have a good understanding of their risk exposure.

-Ben M.

Ok, I surender! Your post that was crossing my post was just crossed by my other post.

-Ben M.