Capital assets pricing model including a risk-free asset.

Description

Compute the capital assets pricing model including a risk-free asset.

Usage

capm(x, Rf = 0.2/270, sh = FALSE, eRtn = NULL)

Arguments

Details

Let \xi_1 , \ldots,\xi_n be random asset returns and w_1 , \ldots, w_n the portfolio weights. The expected returns are r_m = E\xi_m , m = 1, \ldots, n. In addition to these risky investments, there is a risk-free asset (a bond or bank account) available, which has return r_0. Denoting the weights of w_0 for the risk-free asset. The return of portfolio given by

R_p = w^t r

where, r = (r_1, \ldots, r_n)^t.

Risk is measure by a deviation functional \Sigma. It is a variance-covariance of asset returns. The risk-free component w_0 ignore in the objective. So, the standard deviation of portfolio is given by \sigma_p = w^t \Sigma w.

To obtain the optimum value of w_i, i = 1,\ldots, n, we solve the following model:

\min w^t \Sigma w,\;\;s.t:\;\; w^t r + w_0 r_0 > \mu \;\; and \;\;\sum w_i + w_0 = 1

Note that, the portfolio weights may be negative (selling short is allowed). Market portfolio is named MP where, the risk free weight w_0 is zero (see, the function of prtf()).

For any portfolio p,

E(R_p) = r_0 + \beta(p) (r_{MP} - r_0)

where, r_{MP} is return of market portfolio and \beta(p) is the beta coefficient of the portfolio p. It is given by \beta(p) = Cov( r_{MP}, r_p )/ SD(r_{MP}).

Value

References

Pflug and Romisch (2007, ISBN: 9789812707406)

Examples

## Not run: 
x <- rnorm(500,0.05,0.02)
y <- rnorm(500,0.01,0.03)
z<-cbind(x, y)
colnames(z) <- c("prt1","prt2")

capm( z, sh = FALSE, Rf= 0.2/270, eRtn=0.02 )

## End(Not run)

Download Historical Dataset from Tehran Stock Exchange (TSE)

Description

getTSE function is an easy way to download and organize the historical dataset from websites of TSE and www.tsetmc.com. Since, the raw data are not recorded in a standard format, we provide the function for organize the data in user friendly way. Daily data updated after 13:30 UTC. The market is closed on Friday and Wensday and national holidays.

Usage

	getTSE(file, symbols=NA)

Arguments

Details

The list of symbols or assets can be named, and the list names will be used as names for the variables. Component data is an array with xts time series object. The name for dimensions are: Open, High, Low, Close, Volume, Last. The value of symbols are appear in Global Environment.

Value

The output is an object of the “assets” name which get all the name of assets list to download.

Examples

## Not run: 
	fpath<-system.file("extdata", "sample.dat", package="TSEtools")
	getTSE(fpath)
	
## End(Not run)

Matrix Conversion in Portfolio

Description

mcPrt function compound the vector of assets in matrix form to using the multivariate data analysis. The assets must be included the items of Open, Close, High, Low and Volumn. The function also calculate the rate of return and Sharpe ratio for portfolio selection.

Usage

mcPrt(asset, sub = "::", pstvRtn = FALSE, pr = "daily", Rf = 0.0)

Arguments

Details

The values of function contain Sharpe ratio and rate of return. Sharpe ratio is defined as:

SR=\frac{\bar{R}-R_f}{\sigma_R}

where \bar{R} is the mean asset return, R_f is the risk free rate of return and \sigma_R is the standard deviation (volatility) of the asset.

Let X_t is the closing price of the asset at time t and its value after a period of length \Delta t, say X_{t+\Delta t}. The return over that period is defined as:

R_t=\frac{X_{t+\Delta t}}{X_t}-1

Note that the return equation is equivalent to log return asset when the ratio value of the asset is close to 1 (see, Carmona 2003). To check the goodness of fit test on return value, maximum and minimum of prices, suggested to use the package of gnFit.

Value

The values of function involve close, return, max and min as a matrix and xts format. The columns are a value of assets which is ordered by date. The mean return, volatility and Sharpe ratio are assigned in the out. The plot of return vs volatility and also the graph of Sharpe ratio are outputs of function.

References

Carmona (2003, ISBN:0387202862)

Examples

## Not run: 
fpath<-system.file("extdata", "sample.dat", package="TSEtools")
getTSE(fpath)
rtn<-mcPrt(asset0, sub="2016::", pstvRtn=TRUE, pr="weekly")$return

## End(Not run)

Design the Portfolio of assets

Description

Compute the efficient frontier function for some selected risk functionals in a portfolio optimization setting.

Usage

prtf (x, Rf = 0.0, sh = FALSE ,eRtn = NULL)

Arguments

Details

Let \xi_1 , \ldots,\xi_n be random asset returns and w_1 , \ldots, w_n the portfolio weights. The expected returns are r_m = E\xi_m , m = 1, \ldots, n. In addition to these risky investments, there is a risk-free asset (a bond or bank account) available, which has return r_0. Denoting the weights of w_0 for the risk-free asset. The return of portfolio given by

R_p = w^t r

where, r = ( r_1, \ldots, r_n)^t.

Risk is measure by a deviation functional \Sigma. It is a variance-covariance of asset returns. The risk-free component w_0 ignore in the objective. So, the standard deviation of portfolio is given by \sigma_p = w^t \Sigma w.

To obtain the optimum value of w_i, i=1,\ldots, n, we solve the following model:

\min w^t \Sigma w\;\; s.t:\;\;w^t r > \mu \;\; and\;\; \sum w_i = 1.

where, \mu is a constant value. Note that, the portfolio weights may be negative (selling short is allowed).

Value

The minimum weights show with MIN which is the portfolio with the minimum volatility. Market portfolio is given by MP where, the risk free weight w_0 is zero. MP is the tangency point between the market line and efficient frountier curve. A list containing the following components:

References

Pflug and Romisch (2007, ISBN: 9789812707406)

See Also

portfolio.optimization, portfolio.optim

Examples

## Not run: 
x <- rnorm(500,0.05,0.02)
y <- rnorm(500,0.01,0.03)
z<-cbind(x, y)
colnames(z) <- c("prt1","prt2")

prtf (z, sh = FALSE)

## End(Not run)