calculate S&P 500 n month return.

w <- c()
for(i in seq(1,13,1)){
　m <- matrix(as.vector(to.monthly(SP5)[,4])[i:(i+818)],nrow=13,ncol=63)
  w <- append(
    w,m[13,] / m[1,]

  )
}


gap <- 61 # when month gap is 61.
a<-Sys.time()
w <- c()
j <- (floor(length(index(to.monthly(SP5)))/gap)-1)*gap-1
for(i in seq(1,gap,1)){
# 　m <- matrix(as.vector(to.monthly(SP5)[,4])[i:(i+j)],nrow=gap,ncol=(floor(length(index(to.monthly(SP5)))/gap)-1))
m <- matrix(as.vector(to.monthly(SP5)[,4])[i:(i+j)],nrow=gap,ncol=((j+1)/gap))
  w <- append(
    w,m[gap,] / m[1,]
  )
}

s <- as.vector(matrix(t(matrix(w,ncol=gap)),ncol=1))

length(s[s<1])
mean(s[s<1])
mean(s[s>1])
length(s[s>1])
b<-Sys.time()
b -a

# テスト用サンプル gap = 61のとき有効。
# > s[1:60]
#  [1] 2.148387 2.134727 2.115674 2.113586 2.018637 2.319389 2.439462 2.344191 2.245244 2.167947
# [11] 2.332650 2.226138 2.023084 2.079817 2.256983 2.156933 2.100372 2.240935 2.204911 2.040807
# [21] 1.949699 1.986922 1.970280 1.963399 1.852527 1.859845 1.810012 1.961407 1.987846 1.897837
# [31] 1.886220 1.806632 1.728606 1.674551 1.625877 1.505081 1.580743 1.576834 1.664689 1.764419
# [41] 1.796658 1.874068 1.906667 2.047599 2.143897 2.091687 2.119548 2.225312 2.126150 2.118929
# [51] 2.057906 2.037863 2.010277 2.001712 1.959521 1.997989 1.760446 1.815657 1.702103 1.664536
# > as.vector(to.monthly(SP5)[,4])[61:120]/as.vector(to.monthly(SP5)[,4])[1:60]
#  [1] 2.148387 2.134727 2.115674 2.113586 2.018637 2.319389 2.439462 2.344191 2.245244 2.167947
# [11] 2.332650 2.226138 2.023084 2.079817 2.256983 2.156933 2.100372 2.240935 2.204911 2.040807
# [21] 1.949699 1.986922 1.970280 1.963399 1.852527 1.859845 1.810012 1.961407 1.987846 1.897837
# [31] 1.886220 1.806632 1.728606 1.674551 1.625877 1.505081 1.580743 1.576834 1.664689 1.764419
# [41] 1.796658 1.874068 1.906667 2.047599 2.143897 2.091687 2.119548 2.225312 2.126150 2.118929
# [51] 2.057906 2.037863 2.010277 2.001712 1.959521 1.997989 1.760446 1.815657 1.702103 1.664536

# > s[101:160]
#  [1] 1.605806 1.533378 1.464929 1.518325 1.432281 1.441847 1.395389 1.358812 1.389360 1.404079
# [11] 1.424603 1.379753 1.369632 1.397127 1.374649 1.372987 1.479958 1.475313 1.448524 1.415094
# [21] 1.574537 1.557912 1.556921 1.638955 1.583736 1.477864 1.535759 1.530372 1.680867 1.731036
# [31] 1.649442 1.590604 1.503399 1.437894 1.371503 1.394273 1.294020 1.310953 1.252247 1.132658
# [41] 1.147310 1.168755 1.128015 1.122711 1.258135 1.240423 1.296909 1.440987 1.493879 1.655525
# [51] 1.627168 1.583897 1.718678 1.650743 1.509798 1.528843 1.393354 1.389952 1.354965 1.396275
# > as.vector(to.monthly(SP5)[,4])[161:220]/as.vector(to.monthly(SP5)[,4])[101:160]
#  [1] 1.605806 1.533378 1.464929 1.518325 1.432281 1.441847 1.395389 1.358812 1.389360 1.404079
# [11] 1.424603 1.379753 1.369632 1.397127 1.374649 1.372987 1.479958 1.475313 1.448524 1.415094
# [21] 1.574537 1.557912 1.556921 1.638955 1.583736 1.477864 1.535759 1.530372 1.680867 1.731036
# [31] 1.649442 1.590604 1.503399 1.437894 1.371503 1.394273 1.294020 1.310953 1.252247 1.132658
# [41] 1.147310 1.168755 1.128015 1.122711 1.258135 1.240423 1.296909 1.440987 1.493879 1.655525
# [51] 1.627168 1.583897 1.718678 1.650743 1.509798 1.528843 1.393354 1.389952 1.354965 1.396275

when gap = 61,

> length(s[s<1])
[1] 137
> mean(s[s<1])
[1] 0.8869793
> mean(s[s>1])
[1] 1.629065
> length(s[s>1])
[1] 595

when gap = 14,

> length(s[s<1])
[1] 216
> mean(s[s<1])
[1] 0.8863247
> mean(s[s>1])
[1] 1.160806
> length(s[s>1])
[1] 602
> b<-Sys.time()