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Discussion Starter · #1 · (Edited)
Here are the total returns from the different indexes for benchmarking your own returns..


EAFE (in USD)...........31.8%..........3.5%..................1.2%
FX loss fm USassets..<14.5>%......<2.6>%..............<3.1>%

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546 Posts
Discussion Starter · #5 ·
When the rates of income/loss are small simply adding the two sources is fine. That is the way most people treat the relationship between norminal returns, inflation and real returns. Nominal = real plus inflation.

But that is not technically correct and the error start to show with larger returns. The technical answer is to multiply the factors one by one. So presume $100 starting value. If it earned 20% you would normally multiply the $100 by (1+0.20) to get $120 at the end. Agreed?

When you layer FX on top of that (say a 21.05% loss) you multiply the $120 by (1-.2105).
$100 * (1+0.20)(1-0.2105) = $94.74
(94.74/100)-1 = 5.26% loss

You can prove this to yourself with a simple example.
At the boy you own US$100. It earns 20% and you end up with USD$120.
At the boy the FX was 0.75. At the eoy it was 0.95. That is a 21.05% loss (0.75/0.95)-1.
The Loonie value of your holding was (100/0.75=) $133.33 boy.
At the end of the year it was (120/0.95=) $126.32.
That is a 5.26% loss (=126.32/133.33-1)

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This may be showing my 'ignorance', but can you just add the two (the index + the FX change)? So for example:

1 year S&P: 26.5 + -14.5 = 12% ?

As leslie points out, it's not that simple. It would only work if exchange rate was a constant with time. For multi-year returns, you should go back and at least multiply annual RoR by average Exchange rate for that year, and then re-calculate the multi-year return. This would still only be a first approximation. With "Total Return" including value of distributions such as Dividends, you've essentially got something like a compounded rate of return. What was the value of the CDN dollar when each one of those distributions was made?

If someone can calculate the RoR of the EAFE in US dollars, why can't it be done in CDN $? (Probably because it is tracked daily in US$ ?) It might be easier to find someone who tracks the performance of the S&P/TSX in US dollars for comparison.

Leslie's example of doing a conversion at each end of the year, and calculating corresponding RoR in CDN$, might give you a more accurate year-to-year picture than trying to correct for an "average" FX for a given year would be. But the math is a bit beyond me at this stage of my life.

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Discussion Starter · #11 · (Edited)
I finally figured out where Guru was coming from with his "What was the value of the CDN dollar when each one of those distributions was made?", and "..trying to correct for an "average" FX for a given year would be".

He is making the wrong assumption that the total return is calculated as the sum of the index return plus the dividends. So in that scenario he is assuming you repatriate the dividends as earned but do not invest them.

In fact the total return is much more accurate. The dividends compound as soon as they are received by presuming to buy more shares of the company in question. So there are no dividends to repatriate. The FX rate during the year is of no relevance

I always feel such defeat when people respond to simple math with "But the math is a bit beyond me at this stage of my life". The function (1+%) is ubiquitous in investing. You need it
* to calculate a cumulative return (the start for benchmarking your long-term returns).
* to find the true real return (without inflation).
* to find the after tax return.
* to find the Internal Rate of Return IRR
* to find the Net Present Value NPV
* etc

Its derivation is simple.
1) The interest earned in a period equals the Present Value PV multiplied by the interest rate. ( PV * %)
2) The Future Value FV of the investment equals the sum of the PV plus the interest. PV + (PV * %) = FV
3) Simplify that equation by pulling out the PV on both sides of the + sign. You get: PV * (1+%) = FV
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