Keep investing on a regular basis

Just to save money is not enough, we should keep our saving growing. Here is a very simple strategy: keep investing on a regular basis. 

We will use R to test this very simply idea. Suppose that we start from 2004-05-10 and we keep investing 1000 to MDY every 20 business days. The transaction cost is 10/trade. The period is intentionally selected so that it can go through the financial crisis. 

To estimate the annualized return of this strategy, we will compare the final market value of our investment to our total investment and use the formula :
(finalValue/initialInvetment) **(1/numYears)-1

Note that this formula will provide an approximate estimation of the annualized return, because the time of investment being in the market does not cover the whole period. The test shows that we can get about 6% annualized return each year from this very simply strategy.

The R script is attached at the end of the post. The results of the strategy heavily depends on the parameters of the algorithm and the studying period.

We can improve this strategy by making it more flexible. For instance, when the market condition is not good, we can try to invest more money to the equity market, believing that the economy or the market will come back sooner or later.

------------------------------------------------------R script -------------------------------------------------------

 library(tseries)


ustart  <- "2004-05-10" # start date
uend    <- "2014-08-08" # end date

ticker  <- "mdy"
quote   <- get.hist.quote(instrument=ticker,
                          start=ustart,
                          end=uend,
                          quote=c("AdjClose"),
                          provider="yahoo",
                          compression="d")

dates <- rownames(as.data.frame(quote))
quote <- as.double(quote)

# --------------------------------------------------

ptr                                   <- 0
l                                      <- length(quote)

amount                           <- 1000
investmentPeriod            <- 20
transactionCost              <- 10
totalInvestment               <- 0
shares                             <- 0
totalInvestment_std         <- 0
shares_std                       <- 0

dateIndex                        <- array()
annualizedReturn           <- array()
annualizedReturn_std     <- array()

count                              <- 0
level_low                        <- 0.03
level_high                       <- 0.05
extra_amount                <- 250


while (ptr < l) {
 
  ptr <- ptr + 1
 
  if (ptr %% investmentPeriod == 0 ) {
    count <- count + 1
    dateIndex[count] <- ptr
    if ((annualizedReturn[ptr-1] < level_low) && (count > 6)) {
      extra_amount          <- min(500,amount * (level_low - annualizedReturn[ptr-1]) * 15)
      totalInvestment            <- totalInvestment + amount + extra_amount
      shares                          <- shares + (amount + extra_amount) /quote[ptr]
    
      totalInvestment_std     <- totalInvestment_std + amount
      shares_std                   <- shares_std + amount / quote[ptr]
    
    
      # } else if ((annualizedReturn[ptr-1] > level_high) && (count > 6)) {
      # extra_amount <- max(-200, amount * (level_high - annualizedReturn[ptr-1]) * 2)
      # totalInvestment <- totalInvestment + amount + extra_amount
      # shares <- shares + (amount + extra_amount) /quote[ptr]
      #
      # totalInvestment_std <- totalInvestment_std + amount
      # shares_std <- shares_std + amount / quote[ptr]
    
    
    } else {
    
      shares                         <- shares + amount / quote[ptr]
      totalInvestment           <- totalInvestment + amount
    
      shares_std                   <- shares_std + amount / quote[ptr]
      totalInvestment_std    <- totalInvestment_std + amount
    }
  }
 
  if ((totalInvestment == 0) || (count < 6)) {
    annualizedReturn[ptr]    <- 0
  } else {
    currentValue                    <- quote[ptr] * shares
    currentValue_std             <- quote[ptr] * shares_std
    portionOfYear                 <- count * investmentPeriod / 252
    aReturn                           <- ((currentValue - count * transactionCost)/totalInvestment) ** (1/portionOfYear) - 1
    aReturn_std                    <- ((currentValue_std -count * transactionCost)/totalInvestment_std) ** (1/portionOfYear) - 1
    annualizedReturn[ptr]          <- aReturn
    annualizedReturn_std[ptr]    <- aReturn_std
  }
}



# --------- plot ----------

plot(quote, type="l", ylab="", xlab="", xaxt="n")
uPoints <- cbind(dateIndex, quote[dateIndex])
points(uPoints, pch=17, col="blue")
par(new=TRUE)
plot(annualizedReturn, type="l", col="red", ylab="MDY",xlab="",xaxt="n", yaxt="n", ylim=c(-0.15,0.15))
lines(annualizedReturn_std, type="l", col="green", ylab="return",xlab="",xaxt="n",yaxt="n",ylim=c(-0.15,0.115))
lines(rep(level_low,l),type="l", col="lightgrey")
lines(rep(level_high,l),type="l", col="lightgrey")
legend("bottomright", legend=c("price","simple","aggressive"), col=c("black","green","red"), lty=1, cex=0.45)
y_grid <- c(-0.15,-0.1,-0.05,0,0.05,0.10,0.15)
axis(4,at=y_grid, label=y_grid)
nDates <- trunc(l / 252) * 4
cc <- trunc(l/nDates)
pos <- c(1:nDates) * cc
axis(1,at=pos, label=dates[pos],las=2)
title("Invest On a Monthly Basis")


# ---------- not important --------
annualizedReturn[l]
annualizedReturn_std[l]
(quote[l]/(mean(quote[1:15]))) ** (252 /l) - 1