# quantport

The package quantport provides routines to perform portfolio optimization based on quadratic and sequential programming. With Sharpe Ratio maximization problem (tangency portfolio), the lower boundary and upper boundary for any single asset, as well as other constraints could be implemented using Sequential Programming.

The main advantage of this package is easy-to-use and simplicity. The package is based purely on functional programming. You do not need to create object like S3 or S4 to run portfolio optimization. The result from optimization will be stored in dataframe or list only. The mean vector and the covariance matrix could be used from daily, monthly or quarterly data. The package could be used in complement with your master studies in portfolio optimization or courses such as CFA, FRM, etc.

# Plan for development

In the near future, we will add further functionalities including Differential Evolutionary Optimization (DE) and Canonical Black-Litterman model.

# Installation

There are several packages required: quadprog, DEoptim, NlcOptim, ggplot2 and tidyverse. We plan to submit this package to CRAN in the near future. At the mean time, the package could be downloaded via github using devtools:

devtools::install_github("thanhuwe8/quantport")


# Usage

## Data and necessary calculation

This is a basic example which shows you how to solve the portfolio optimization problem. We have the data in the form of data.frame with 10 assets monthly return as below:

data(dataset1)


| Date | FPT | GAS | GMD | VCB | VNM | REE | MSN | VIC | HPG | SSI | | :--------- | ----------: | ----------: | ----------: | ----------: | --------: | --------: | ----------: | ----------: | ----------: | ----------: | | 2013-02-28 | -0.0771388 | 0.0292289 | 0.1640979 | -0.0149015 | 0.0198857 | 0.0117005 | -0.0587924 | 0.0077519 | -0.0280561 | -0.0270979 | | 2013-03-29 | 0.0212766 | 0.1631420 | 0.3123053 | -0.0091842 | 0.1262491 | 0.0053971 | 0.1071028 | -0.0524038 | 0.0742268 | -0.0332435 | | 2013-04-26 | -0.0156250 | -0.0093506 | -0.2403561 | -0.1434024 | 0.0688163 | 0.0107362 | -0.1209585 | -0.0233384 | 0.0575816 | -0.0223048 |

Then we calculate 2 required inputs for portfolio optimization as follows:

data_test <- dataset1[,-1]
mean_vec <- apply(data_test, MARGIN=2, mean)
cov_mat <- cov(data_test)
kable(mean_vec)


| | x | | --- | --------: | | FPT | 0.0175349 | | GAS | 0.0205154 | | GMD | 0.0171414 | | VCB | 0.0184696 | | VNM | 0.0184208 | | REE | 0.0157175 | | MSN | 0.0040312 | | VIC | 0.0257915 | | HPG | 0.0292043 | | SSI | 0.0160022 |

kable(cov_mat)


| | FPT | GAS | GMD | VCB | VNM | REE | MSN | VIC | HPG | SSI | | --- | --------: | --------: | --------: | --------: | --------: | --------: | --------: | --------: | --------: | --------: | | FPT | 0.0042614 | 0.0033102 | 0.0021415 | 0.0024455 | 0.0020232 | 0.0034155 | 0.0022578 | 0.0020202 | 0.0027855 | 0.0034875 | | GAS | 0.0033102 | 0.0116427 | 0.0025431 | 0.0035473 | 0.0022243 | 0.0027905 | 0.0044717 | 0.0024626 | 0.0048307 | 0.0032298 | | GMD | 0.0021415 | 0.0025431 | 0.0088099 | 0.0026539 | 0.0018935 | 0.0031162 | 0.0026985 | 0.0011345 | 0.0024260 | 0.0020834 | | VCB | 0.0024455 | 0.0035473 | 0.0026539 | 0.0069645 | 0.0019444 | 0.0026043 | 0.0032404 | 0.0028170 | 0.0029619 | 0.0032546 | | VNM | 0.0020232 | 0.0022243 | 0.0018935 | 0.0019444 | 0.0054617 | 0.0020543 | 0.0018221 | 0.0011131 | 0.0017396 | 0.0018961 | | REE | 0.0034155 | 0.0027905 | 0.0031162 | 0.0026043 | 0.0020543 | 0.0064170 | 0.0020180 | 0.0018594 | 0.0027920 | 0.0038513 | | MSN | 0.0022578 | 0.0044717 | 0.0026985 | 0.0032404 | 0.0018221 | 0.0020180 | 0.0072603 | 0.0022859 | 0.0030890 | 0.0029749 | | VIC | 0.0020202 | 0.0024626 | 0.0011345 | 0.0028170 | 0.0011131 | 0.0018594 | 0.0022859 | 0.0064643 | 0.0009622 | 0.0017002 | | HPG | 0.0027855 | 0.0048307 | 0.0024260 | 0.0029619 | 0.0017396 | 0.0027920 | 0.0030890 | 0.0009622 | 0.0076791 | 0.0034633 | | SSI | 0.0034875 | 0.0032298 | 0.0020834 | 0.0032546 | 0.0018961 | 0.0038513 | 0.0029749 | 0.0017002 | 0.0034633 | 0.0071576 |

## Tangency Portfolio

we provide necessary inputs to the TangencyQP to find the weight of optimal portfolio with maximum Sharpe Ratio.

tangency_result <- quantport::TangencyQP(ret=mean_vec,covmat=cov_mat,short=F,rf=0,freq="monthly")
optimal_weight <- data.frame(tangency_result$weight)  tangency_result <- quantport::TangencyQP(ret=mean_vec,covmat=cov_mat,short=T,rf=0,freq="monthly") optimal_weight <- data.frame(tangency_result$weight)


Portfolio return and standard deviation are also stored and accessed using $ operator print(tangency_result$portfolioret)
#> [1] 0.4095923
print(tangency_result$portfoliosd) #> [1] 0.2320305 print(tangency_result$SharpeRatio)
#> [1] 0.5095843


## Efficient Frontiers

There are other useful functions you could find in the vignettes of this package. Below is the efficient frontier with short-sale constraints. The dots to the right of the curve is single asset risk-return trade-off point. The red dot is tangency portfolio and the green dot is minimum variance portfolio. Mean return and standard deviation are both annualized assuming 252 trading days.

ef <- quantport::ShowEfficient(ret=mean_vec,covmat=cov_mat,short=F,rf=0.05,freq="monthly",simpoints=200,assetpoints=T)


## Equal weight and Inverse volatility (risk-parity) portfolio

The weight and statistics information of several popular porfolios could be calculated using UltimateWeight function as below:

final_result <- UltimateWeight(ret=mean_vec,covmat=cov_mat, short=F,rf=0,freq="monthly")
kable(round(final_result[[1]],4))


| | Tangency | MinimumVariance | InverseVolatility | EqualWeight | | --- | -------: | --------------: | ----------------: | ----------: | | FPT | 0.0000 | 0.1803 | 0.1889 | 0.1 | | GAS | 0.0000 | 0.0000 | 0.0522 | 0.1 | | GMD | 0.0460 | 0.1014 | 0.0682 | 0.1 | | VCB | 0.0000 | 0.0142 | 0.1047 | 0.1 | | VNM | 0.2042 | 0.2517 | 0.1233 | 0.1 | | REE | 0.0000 | 0.0277 | 0.1092 | 0.1 | | MSN | 0.0000 | 0.0612 | 0.0899 | 0.1 | | VIC | 0.3932 | 0.2287 | 0.0911 | 0.1 | | HPG | 0.3566 | 0.1043 | 0.0783 | 0.1 | | SSI | 0.0000 | 0.0306 | 0.0942 | 0.1 |

kable(final_result[[2]])


| | WeightType | SD | Return | SharpeRatio | WeightEntropy | Herfindahl | DiversificationRatio | | ----------------- | :---------------- | --------: | --------: | ----------: | ------------: | ---------: | -------------------: | | Tangency | Tangency | 0.1922628 | 0.3012658 | 1.566948 | 1.200775 | 0.6744166 | 1.482326 | | MinimumVariance | MinimumVariance | 0.1773560 | 0.2389767 | 1.347440 | 1.898773 | 0.8250242 | 1.535520 | | InverseVolatility | InverseVolatility | 0.1872915 | 0.2157626 | 1.152015 | 2.245068 | 0.8874638 | 1.494049 | | EqualWeight | EqualWeight | 0.1913088 | 0.2193945 | 1.146808 | 2.302585 | 0.9000000 | 1.525267 |

## Sequential Quadratic Programming for lower and upper boundary

With additional constraints for single asset weight, we have another tools to come up with the exact solution. The Sequential Quadratic Programming is implemented by the function TangencySP. Upper boundary and lower boundary must be passed as two arguments of the function.

## Black-Litterman

### Canonical Black-Litterman

We provide the function to calculate the posterior mean return and covariance matrix based on He and Litterman (1999) paper. We provide a simple example as below:

First we limit our asset pool with only 4 assets

kable(head(dataset1[,1:5],2))


| Date | FPT | GAS | GMD | VCB | | :--------- | ----------: | --------: | --------: | ----------: | | 2013-02-28 | -0.0771388 | 0.0292289 | 0.1640979 | -0.0149015 | | 2013-03-29 | 0.0212766 | 0.1631420 | 0.3123053 | -0.0091842 |

data2 <- dataset1[,2:5]

mean_vec2 <- apply(data2,2,mean)
cov_mat2 <- cov(data2)
kable(mean_vec2)


| | x | | --- | --------: | | FPT | 0.0175349 | | GAS | 0.0205154 | | GMD | 0.0171414 | | VCB | 0.0184696 |

kable(cov_mat2)


| | FPT | GAS | GMD | VCB | | --- | --------: | --------: | --------: | --------: | | FPT | 0.0042614 | 0.0033102 | 0.0021415 | 0.0024455 | | GAS | 0.0033102 | 0.0116427 | 0.0025431 | 0.0035473 | | GMD | 0.0021415 | 0.0025431 | 0.0088099 | 0.0026539 | | VCB | 0.0024455 | 0.0035473 | 0.0026539 | 0.0069645 |

Presumbably, we have the market capitalization weight of those four assets and the (\delta) parameter of 2.4 suggested by He and Litterman, then the (\Pi) as below

market <- c(0.1,0.4,0.1,0.4)
PI <- PiCal(2.4,cov_mat2,market)
print(PI)
#>            [,1]
#> FPT 0.007062136
#> GAS 0.015987202
#> GMD 0.007617427
#> VCB 0.011315181


We will express our subjective views through matrix P and vector Q. The first view is that the 1st asset will outperform the 3rd asset by 1%. The second view is that the 3rd asset will have mean return of 3%. Then we formulate the views as below:

P <- matrix(c(1,0,0,-1,0,1,0,0), ncol=4, byrow = T)
Q <- c(0.01, 0.03)


Then the (\tau) parameter is estimated as (1/n) which is 0.25. The mean return and covariance matrix will be calculated accordingly:

BL <- BLcanon(mean_vec2,cov_mat2,P,Q,PI,0.25)
kable(BL$BLmean)  | | | | :-- | --------: | | FPT | 0.0111561 | | GAS | 0.0228588 | | GMD | 0.0085949 | | VCB | 0.0083554 | kable(BL$BLvar)


| | FPT | GAS | GMD | VCB | | --- | --------: | --------: | --------: | --------: | | FPT | 0.0051415 | 0.0037283 | 0.0026042 | 0.0030944 | | GAS | 0.0037283 | 0.0130977 | 0.0028598 | 0.0039803 | | GMD | 0.0026042 | 0.0028598 | 0.0109382 | 0.0031775 | | VCB | 0.0030944 | 0.0039803 | 0.0031775 | 0.0081739 |

To come up with the weight, we just input the mean return and the covariance matrix into optimizer to find the tangency portfolio:

result_BL <- TangencyQP(BL$BLmean, BL$BLvar, F, 0.05, "monthly")
barplot(result_BL$weight, names.arg = names(mean_vec2), col = "#C92F3A")  head(result_BL$weight)
#> [1] 0.2378 0.7622 0.0000 0.0000