Calculation of FX IMPACT
The android app 5.5.7 has a new feature. It provides information about GAIN/LOSS in the currency in which the instrument is priced, and FX IMPACT to show how the RETURN has been increased or decreased due to currency fluctuation. This is a great idea. I thought I would like to understand how these numbers are calculated. I now understand the meaning of GAIN/LOSS, which to me at least was not immediately obvious. Here is an example:
In this example, a client with base currency GBP has a position in Adobe stock, priced in USD, consisting of shares bought at different times, at different prices and different exchange rates. The key figures are
AD = average USD price ($440.72)
AG = average GBP price (£349.32)
CD = current USD sell price ($474.49)
FX = current GBP per USD (0.7641)
AG, AD, CD are already calculated and displayed in the app. FX is implicit. It is the displayed current investment value £274.07 divided by (shares owned * CD) ie 274.07/(0.8015517*447.49) = 0.7641.
Per share, the changes expressed as factors are therefore
RETURN_f = CD * FX/AG (in GBP terms) = (GBP proceeds if sold) /(GBP cost)
GAIN/LOSS_f = CD/AD (in USD terms) = RETURN experienced by a USD investor who is oblivious of other currencies
FX IMPACT_f = AD * FX/AG. This is what RETURN would be if CD=AD, (ie if there had been no change in USD share price, and as if client had only bought and sold USD).
Note that these factors are multiplicatively correct as they should be
RETURN_f = GAIN/LOSS_f * FX IMPACT_f
To express these as % we should subtract 1 from each and multiply by 100%. So
RETURN% = (CD * FX/AG - 1) * 100%
GAIN/LOSS% = (CD/AD - 1) * 100%
FX IMPACT% = (AD * FX/AG - 1) * 100%
To express as changes to client’s GBP wealth we multiply each of the above by AG and then by number of shares owned. Using figures in the example we get
TABLE 1
| RETURN | -5.93 | -2.12% |
| GAIN/LOSS | 4.30 | 1.54% |
| FX IMPACT | -10.07 | -3.60% |
Notice that RETURN and FX IMPACT agree with the numbers given in the app, but GAIN/LOSS does not. The app gives 1.48% for GAIN/LOSS, but the true gain for a USD investor who is unaffected by fx is CD/AD = 1.01536, i.e. a 1.54% gain as shown in Table 1.
But there is another way to do it. Suppose we keep the first and third formula as above, but force things to add up by defining
GAIN/LOSS% := RETURN% - FX IMPACT%
= (CD * FX/AG - 1) * 100% - (AD * FX/AG - 1) * 100%
=(FX * AD/AG) * (CD/AD-1) * 100%
= FX * (CD - AD) /AG * 100%
As we have seen, this is not the true GAIN/LOSS% that would be experienced by a USD investor. The value that a US investor would look at is simply (CD/AD-1)*100%. What we have above is USD gain/loss per share, converted at today’s exchange rate to GBP, and then expressed as a percentage of our average GBP cost per share.
Similarly,
GAIN/LOSS = GAIN/LOSS% * AG * #shares
expresses the gain/loss in US dollars, converted to GBP at today’s exchange rate, eg
0.7641 * (474.49 - 440.72) * 0.8015517 = 4.15 (agreeing with the figure in the app),
Incidentally, this is the same as the way that RESULT is computed on the CFD side.
So the numbers make sense, so long as we understand the correct meanings of GAIN/LOSS and GAIN/LOSS%. I had started out mistakenly thinking that these should tell us what a US investor would experience in pure USD terms, making the same stock trades and not at all dependent on what’s happening with other currencies. But now we see that these figures do in fact depend on exchange rates. If we wish to obtain a true picture of separate FX effect and USD price change effect then we need to use the multiplicative factors described earlier.
The true result for the UK investor is that the USD stock price grew 1.54% compared to the average USD purchase price, but then the USD depreciated 3.60% compared to the average price at which USD was bought when building this position. Overall now each £1 has become (1+0.0154)*(1-0.0360) = £0.9788, ie down 2.12%.