user3875610 - 18 days ago 5

R Question

I am attempting to work on portfolio optimisation problem, basically we have some product, the %portfolio and the return rate. Basically I have to optimise the overall return rate to be maximum. The problem gets tricky because there is a minimum constraint specific to product

Data:

`product share_per return_per min_share_per`

prod1 0.5 0.1 0.2

prod2 0.2 0.4 0.1

prod3 0.2 0.05 0.0

prod4 0.1 0.04 0.0

prod5 0.0 0.3 0.0

Basically we are performing the optimising on column

My hopelessly bad attempt to this was

`mat <- matrix(c(0.5, 0.2, 0.2, 0.1, 0.0))`

colnames(mat) <- c("return_per")

minmax <- function(x, a) (sum(a*x))

opt <- apply(mat, 1, function(i) {

optimize(minmax, c(0, 1), a = i[["return_per"]], maximum=T)$maximum

})

mat2 <- cbind(mat, opt)

mat2

As you can see I can neither figure out where to specify the constraint specific to a row

I know constrOptim is something i should be looking but I can't figure the constraint part.

Answer

You can try this:

```
df <- read.table(text='product share_per return_per min_share_per
prod1 0.5 0.1 0.2
prod2 0.2 0.4 0.1
prod3 0.2 0.05 0.0
prod4 0.1 0.04 0.0
prod5 0.0 0.3 0.0', header=TRUE)
ret <- df$return_per
fn <- function(sp) sum(ret*sp) # objective
Amat <- rbind(diag(nrow(df)), diag(-1,nrow(df)), rep(-1,nrow(df))) # constraints
bvec <- c(df$min_share_per, rep(-1, nrow(df)), -1) # sp_j >= min_share_per,
# sp_j <= 1 and
# sum_j sp_j <= 1
init <- c(0.5,0.2,0.2,0.05,0.01) # making sure that the initial value is in the feasible region
sol <- constrOptim(init, fn, NULL, ui = Amat, ci = bvec, control=list(fnscale=-1)) # maximize
round(sol$par, 2)
# [1] 0.2 0.8 0.0 0.0 0.0
```