# Portfolio Optimization using R and Plotly

**R – Modern Data**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

In this post we’ll focus on showcasing Plotly’s **WebGL** capabilities by charting financial portfolios using an R package called **PortfolioAnalytics**. The package is a generic portfolo optimization framework developed by folks at the **University of Washington** and *Brian Peterson* (of the PerformanceAnalytics fame).

You can see the vignette here

Let’s pull in some data first.

library(PortfolioAnalytics) library(quantmod) library(PerformanceAnalytics) library(zoo) library(plotly) # Get data getSymbols(c("MSFT", "SBUX", "IBM", "AAPL", "^GSPC", "AMZN")) # Assign to dataframe # Get adjusted prices prices.data <- merge.zoo(MSFT[,6], SBUX[,6], IBM[,6], AAPL[,6], GSPC[,6], AMZN[,6]) # Calculate returns returns.data <- CalculateReturns(prices.data) returns.data <- na.omit(returns.data) # Set names colnames(returns.data) <- c("MSFT", "SBUX", "IBM", "AAPL", "^GSPC", "AMZN") # Save mean return vector and sample covariance matrix meanReturns <- colMeans(returns.data) covMat <- cov(returns.data)

Now that we have some data, let’s get started by creating a portfolio specification. This can be done by using `portfolio.spec()`

# Start with the names of the assets port <- portfolio.spec(assets = c("MSFT", "SBUX", "IBM", "AAPL", "^GSPC", "AMZN"))

Now for some constraints. Let’s use the following:

- Box constraints
- Leverage (weight sum)

# Box port <- add.constraint(port, type = "box", min = 0.05, max = 0.8) # Leverage port <- add.constraint(portfolio = port, type = "full_investment")

Let’s use the built-in **random** solver. This essentially creates a set of feasible portfolios that satisfy all the constraints we have specified. For a full list of supported constraints see here

# Generate random portfolios rportfolios <- random_portfolios(port, permutations = 500000, rp_method = "sample")

Now let’s add some objectives and optimize. For simplicity’s sake let’s do some mean-variance optimization.

# Get minimum variance portfolio minvar.port <- add.objective(port, type = "risk", name = "var") # Optimize minvar.opt <- optimize.portfolio(returns.data, minvar.port, optimize_method = "random", rp = rportfolios) # Generate maximum return portfolio maxret.port <- add.objective(port, type = "return", name = "mean") # Optimize maxret.opt <- optimize.portfolio(returns.data, maxret.port, optimize_method = "random", rp = rportfolios) # Generate vector of returns minret <- 0.06/100 maxret <- maxret.opt$weights %*% meanReturns vec <- seq(minret, maxret, length.out = 100)

Now that we have the minimum variance as well as the maximum return portfolios, we can build out the efficient frontier. Let’s add a weight concentration objective as well to ensure we don’t get highly concentrated portfolios.

**Note:**

`random_portfolios()`

ignores any*diversification*constraints. Hence, we didn’t add it previously.- Using the
**random**solver for each portfolio in the loop below would be very compute intensive. We’ll use the**ROI**(R Optmization Infrastructure) solver instead.

eff.frontier <- data.frame(Risk = rep(NA, length(vec)), Return = rep(NA, length(vec)), SharpeRatio = rep(NA, length(vec))) frontier.weights <- mat.or.vec(nr = length(vec), nc = ncol(returns.data)) colnames(frontier.weights) <- colnames(returns.data) for(i in 1:length(vec)){ eff.port <- add.constraint(port, type = "return", name = "mean", return_target = vec[i]) eff.port <- add.objective(eff.port, type = "risk", name = "var") # eff.port <- add.objective(eff.port, type = "weight_concentration", name = "HHI", # conc_aversion = 0.001) eff.port <- optimize.portfolio(returns.data, eff.port, optimize_method = "ROI") eff.frontier$Risk[i] <- sqrt(t(eff.port$weights) %*% covMat %*% eff.port$weights) eff.frontier$Return[i] <- eff.port$weights %*% meanReturns eff.frontier$Sharperatio[i] <- eff.port$Return[i] / eff.port$Risk[i] frontier.weights[i,] = eff.port$weights print(paste(round(i/length(vec) * 100, 0), "% done...")) }

Now lets plot !

feasible.sd <- apply(rportfolios, 1, function(x){ return(sqrt(matrix(x, nrow = 1) %*% covMat %*% matrix(x, ncol = 1))) }) feasible.means <- apply(rportfolios, 1, function(x){ return(x %*% meanReturns) }) feasible.sr <- feasible.means / feasible.sd p <- plot_ly(x = feasible.sd, y = feasible.means, color = feasible.sr, mode = "markers", type = "scattergl", showlegend = F, marker = list(size = 3, opacity = 0.5, colorbar = list(title = "Sharpe Ratio"))) %>% add_trace(data = eff.frontier, x = Risk, y = Return, mode = "markers", type = "scattergl", showlegend = F, marker = list(color = "#F7C873", size = 5)) %>% layout(title = "Random Portfolios with Plotly", yaxis = list(title = "Mean Returns", tickformat = ".2%"), xaxis = list(title = "Standard Deviation", tickformat = ".2%"), plot_bgcolor = "#434343", paper_bgcolor = "#F8F8F8", annotations = list( list(x = 0.4, y = 0.75, ax = -30, ay = -30, text = "Efficient frontier", font = list(color = "#F6E7C1", size = 15), arrowcolor = "white") ))

The chart above is plotting **42,749** data points ! Also, you’ll notice that since the portfolios on the frontier(beige dots) have an added weight concentration objective, thefrontier seems sub optimal. Below is a comparison.

Let’s also plot the weights to check how diversified our optimal portfolios are. We’ll use a barchart for this.

frontier.weights.melt <- reshape2::melt(frontier.weights) q <- plot_ly(frontier.weights.melt, x = Var1, y = value, group = Var2, type = "bar") %>% layout(title = "Portfolio weights across frontier", barmode = "stack", xaxis = list(title = "Index"), yaxis = list(title = "Weights(%)", tickformat = ".0%"))

**leave a comment**for the author, please follow the link and comment on their blog:

**R – Modern Data**.

R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.