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A First-Order Analysis of the I fund
The TSP I fund is invested in a Barclay proxy to the MSCI EAFE index. It holds many stocks in about 21 countries. It's performance, in dollar terms, is very different from that in local currency terms. An approximate analysis,below, shows the key relationship: In
percentage terms, the variation of the currency is equally as important as the stock local price variation.
PD = PL * C (Stock Price in dollars, PD, = Price in Local currency PL times Currency conversion C ,units of C are dollars per local currency)
Since there are thousands of stocks in EAFE, a summation is required:
PD = SUM(i=1:N) [PL(i) C(i)]
Take a variation on PD:
dPD = SUM(i=1:N) [dPL(i) C(i) + PL(i) dC(i)]
divide by PD to get percentages:
dPD/PD = SUM(i=1:N) [ dPL(i)*C(i)/{PL(i)*C(i)} + dC(i)*PL(i)/{PL(i)*C(i)} ]
dPD/PD = SUM(i=1:N) [ dPL(i)/PL(i) + dC(i)/C(i)]
Now dPL(i)/PL(i) is just the percentage change of the stock price in local currency , and dC(i)/C(i) is the percentage change of the currency itself. It is apparent that both terms contribute equally to the price change in dollars, in percentage terms.
Here's an example. As of March 31,2004 the country participation factors in the EAFE index were:
UK 25% Japan 24% OtherEuropean: 42% Others:9%
Approximate the EAFE by 3 terms: UK 28% (Pounds), Japan 27% (Yen), European:45% (Euro) (distributing the leftover 9% equally to these 3).
PD = Ppounds * Cpounds + Pyen * Cyen + Peuro * Ceuro
In the first quarter of 2004:
The UK return was -0.83% and the Pound gained 2.66% against the dollar:
UK: dPL(1)/PL(1) = -0.83% dC(1)/C(1)=+2.66 %
overall: dPD(1)/PD(1) = 1.83%
Japan: local return: 11.77% Yen gained 3.01% to dollar
Japan: dPL(2)/PL(2) = +11.77% dC(2)/C(2)=+3.01 %
overall: dPD(2)/PD(2) = 14.78%
Rest of Europe: 1.66% Euro lost 2.77% to the dollar:
Europe: dPL(3)/PL(3) = +1.66% dC(3)/C(3)=-2.77 % overall: dPD(3)/PD(3) = -1.11%
The EAFE in dollars, then changed
0.28 * 1.83% + 0.27 * 14.78 + 0.45* (-1.11%) = 4.00%
(The actual EAFE gain for this period was 4.34%, reflecting the approximations above).
The message is clear:When considering how much to allocate to the I-fund, look at percentage changes in the European stocks and in their currencies, and realize that they contribute equally!
A First-Order Analysis of the I fund
The TSP I fund is invested in a Barclay proxy to the MSCI EAFE index. It holds many stocks in about 21 countries. It's performance, in dollar terms, is very different from that in local currency terms. An approximate analysis,below, shows the key relationship: In
percentage terms, the variation of the currency is equally as important as the stock local price variation.
PD = PL * C (Stock Price in dollars, PD, = Price in Local currency PL times Currency conversion C ,units of C are dollars per local currency)
Since there are thousands of stocks in EAFE, a summation is required:
PD = SUM(i=1:N) [PL(i) C(i)]
Take a variation on PD:
dPD = SUM(i=1:N) [dPL(i) C(i) + PL(i) dC(i)]
divide by PD to get percentages:
dPD/PD = SUM(i=1:N) [ dPL(i)*C(i)/{PL(i)*C(i)} + dC(i)*PL(i)/{PL(i)*C(i)} ]
dPD/PD = SUM(i=1:N) [ dPL(i)/PL(i) + dC(i)/C(i)]
Now dPL(i)/PL(i) is just the percentage change of the stock price in local currency , and dC(i)/C(i) is the percentage change of the currency itself. It is apparent that both terms contribute equally to the price change in dollars, in percentage terms.
Here's an example. As of March 31,2004 the country participation factors in the EAFE index were:
UK 25% Japan 24% OtherEuropean: 42% Others:9%
Approximate the EAFE by 3 terms: UK 28% (Pounds), Japan 27% (Yen), European:45% (Euro) (distributing the leftover 9% equally to these 3).
PD = Ppounds * Cpounds + Pyen * Cyen + Peuro * Ceuro
In the first quarter of 2004:
The UK return was -0.83% and the Pound gained 2.66% against the dollar:
UK: dPL(1)/PL(1) = -0.83% dC(1)/C(1)=+2.66 %
overall: dPD(1)/PD(1) = 1.83%
Japan: local return: 11.77% Yen gained 3.01% to dollar
Japan: dPL(2)/PL(2) = +11.77% dC(2)/C(2)=+3.01 %
overall: dPD(2)/PD(2) = 14.78%
Rest of Europe: 1.66% Euro lost 2.77% to the dollar:
Europe: dPL(3)/PL(3) = +1.66% dC(3)/C(3)=-2.77 % overall: dPD(3)/PD(3) = -1.11%
The EAFE in dollars, then changed
0.28 * 1.83% + 0.27 * 14.78 + 0.45* (-1.11%) = 4.00%
(The actual EAFE gain for this period was 4.34%, reflecting the approximations above).
The message is clear:When considering how much to allocate to the I-fund, look at percentage changes in the European stocks and in their currencies, and realize that they contribute equally!
