According to Google Finance, at 11.20am on 22 September, PHAU shares were trading at about $172.7 each. From my HL receipt I don't know what I actually paid in terms of dollars, only in pounds and that was £111.9787 for each share. Assuming what I paid was somewhere near the $172.7 per share I think I got an exchange rate at about $1.54 to £1.
According to Google Finance, the pound ended the 22 Sept trading at around $1.535 so this looks about right (Basically I bought on a day when the pound was particularly weak against the dollar so my pounds didn't buy so much. But then the strong dollar was the reason that the gold price fell... I'm hoping the fact that the price of gold fell further than the value of the pound made it vaguely worthwhile buying point. But these are all concepts I still have to get my head around).
This evening (a balmy but apocalyptic feeling October 3) my HL account said that my PHAU investment was down 7.61% and valued the 8 shares at £838.71. Considering the buying price had been £895.8296, the fall works out at around 6.3%. The other 1.3% is the £11.95 fee.
If I wanted to sell now, it would cost me another £11.95 in fees so, in effect, I am really down 8.91% on my original investment. I do not have to take the conversion fee from pounds into dollars into account as that, I hope, can only be what the £838.71 figure is based on - the value of my dollar investment in pounds.
Although I own a dollar denominated ETF I cannot keep dollars in my pound denominated Hargreaves Lansdown account so, as far as I can tell, I have no choice in the timing of the conversion from dollar into pounds.
So my PHAU shares - denominated in dollars but valued in pounds - have fallen by 6.3% (from £895.8296 to £838.71). Over the same period the dollar denominated ETF shares has fallen from $172.7 to $162.07 - a fall of 6.15%.
The difference between the fall of 6.3% in pounds and the 6.15% in dollars should be accountable somewhere. I'd imagine it would be a combination of the exchange rate and the spread between the price I bought at (bid) and price I could sell at (offer).
If the discrepancy is due to the value of the dollar I would expect the value of the dollar to have fallen by 0.15% against the pound over this period. On 22 September I was given an exchange rate of $1.54 to £1.
According to HL the exchange rate on my ETF is $1.5459 but Google Finance has the current rate around $1.5575. Even if the later rate is the one being used to calculate the value of my PHAU shares, it does not account for the 1.15% discrepancy over the last 7 trading days.
So the difference will also have something to do with the spread between the buying and selling price of the shares. At close today, according to the London Stock Exchange, the bid price was $161 while the offer price was $164.15 - that's a 1.95% spread, more than I was expecting. (It turns out that the LSE's spread data is talking about something else - Hargreaves has more realistic looking spreads on its factsheet for PHAU) It may not have been that wide when I bought my shares, and I don't know what price I paid for my ETF shares in dollars when I originally bought them.
The fact that the price at the time on the exchange gave a mid price of $172.7 doesn't tell me what I paid for it and unfortunately this price doesn't seem to be shown on my receipt.
Another point of possible interest is that my deal was done on Plus Markets, not the LSE. I don't know if that's significant. On 23 September I bought £1000 of the BlackRock Gold and General fund too. I am still working on my investment strategy - basically I'm blowing in the wind pretty much at the moment.