El artículo enlaza con el plan de William Bernstein que esbozó para Business Insider , que dice:
Put equal amounts of that 15% into just three different mutual funds:
• A U.S. total stock market index fund
• An international total stock market index fund
• A U.S. total bond market index fund
Over time, the three funds will grow at different rates, so once per year
you'll adjust their amounts so that they're again equal.
That's it.
Modelando esta estrategia de inversión
Escogiendo tres fondos de Google y haciendo algunos números.
MUTF: VTSMX Vanguard Total Stock Market Index
MUTF: VGTSX Vanguard Total International Stock Index Fund Investor Shares
MUTF: VBMFX Vanguard Total Bond Market Index Fund Investor Shares
El índice bursátil internacional sólo se remonta al 29 de abril de 1996, por lo que se modeló una racha de 21 años. Basado en el 15% de un salario de 550 dólares al mes con varios aumentos anuales:
annual salary total contributions final investment
rise (%) over 21 years value after 21 years
0 20,790 43,111
1 23,007 46,734
2 25,526 50,791
En términos generales, esta inversión duplica el valor de las cotizaciones en dos décadas.
Nota: Las comisiones de reequilibrio no se incluyen en la simulación.
A continuación se muestra el código utilizado para ejecutar la simulación. Si tiene Mathematica puede probar con diferentes fondos.
funds = {"VTSMX", "VGTSX", "VBMFX"};
(* Plotting the fund indices *)
{tsm, ism, tbm} = FinancialData[#, {"April 29, 1996",
DateList[], "Month"}] & /@ funds; DateListPlot[
Transpose[{First /@ #, 100 Last /@ #/#[[1, 2]]}] & /@
{tsm, ism, tbm}, PlotLegends -> funds, PlotLabel ->
"Indices from month-end April 1996 rebased to 100"]
“`
(* Plotting the investment contributions *)
salary = 550;
investment = salary*0.15;
inflation = 2;
nmonths = Length[tsm] - 1;
ny = Quotient[nmonths, 12];
iy = Array[investment/3 (1 + inflation/100)^(# - 1) &, ny];
d = Take[Flatten[ConstantArray[#, 12] & /@ iy], 12 ny];
DateListPlot[Transpose[{Take[First /@ tsm, 12 ny], 3 d}],
PlotLabel -> Row[{"Monthly contributions with ”,
inflation, “% inflation - Total = ”,
Total[3 d]}], PlotRange -> {Automatic, {0, Automatic}},
PlotMarkers -> {Automatic, 6}, FrameLabel -> {“Time”,
Rotate[Style[“$”, 12], Pi/2]}, ImageSize -> 380]
“`
(* Calculating & plotting the investment values *)
{tsm2, ism2, tbm2} = Take[Ratios@# - 1, 12 ny] & /@
Map[Last, {tsm, ism, tbm}, {2}];
d2 = 0;
ds = {};
eachyear[yr_] := Last /@ Function[series,
AppendTo[ds, Total@Array[(d[[# + 12 (yr - 1)]] +
If[# == 1, d2/3, 0]) Apply[Times,
1 + series[[# + 12 (yr - 1) ;; 12 yr]]] &,
12]]] /@ {tsm2, ism2, tbm2}
vals = Array[(d2 = Total@eachyear[#]) &, ny];
rd = Last /@ Partition[Take[First /@ tsm, {2, 12 ny + 1}], 12];
DateListPlot[Transpose[MapThread[
{{#1, #2[[1]]}, {#1, #2[[2]]}, {#1, #2[[3]]}} &,
{rd, Partition[ds, 3]}]],
PlotMarkers -> {Automatic, 8}, PlotLabel -> Row[{
"Individual fund investment values over ", ny,
" years"}], PlotLegends -> funds, Epilog -> {Red,
Arrowheads[0.06], Arrow[{{{2007, 10, 1}, 12000},
{{2008, 10, 1}, 9000}}]}, FrameLabel -> {"Time",
Rotate[Style["$", 12], Pi/2]}, ImageSize -> 400]
Observe arriba cómo el índice de bonos (VBMFX) preserva el valor durante la caída de 2008. Esto ilustra la razón de ser de la diversificación entre diferentes tipos de fondos.
DateListPlot[Transpose[{rd, vals}],
PlotMarkers -> {Automatic, 8}, PlotLabel -> Row[{
"Total investment value over time - Final value = ",
Last[vals]}], FrameLabel -> {"Time",
Rotate[Style["$", 12], Pi/2]}, ImageSize -> 400]