####### backtest #######
This is a function conducting backtesting using specific strategy function results

## input ##
1. data: historical trading data (has to be the same form of the testdata).
2. initial.time: the timepoint you start backtesting.
3. initial.money: the money you have at the initial.time (default=100).
4. rebalance: the time gay between each rebalance (default=1).
5. method: the name of strategy function,e.g. GMVP, SHARPE, PerfInd, etc (default=GMVP).
6. lower: the lower bound for the weight of each asset in the portfolio (default=0).
7. upper: the upper bound for the weight of each asset in the portfolio (default=1).
8. rf: risk free rate. If you set rf=0, the program will calculate the return rate using the return of the index/benchmark (default=0).

## output ##
1. timeset: a sequence of rebalancing time.
2. total.money: a sequence of money achieved from strategy.
3. index.money: a sequence of money achieved from investing index.
4. weight: a sequence of weight used in each rebalancing.
5. block: total number of rebalancing.
6. weighted.means: a sequence of average portfolio returns at each rebalancing time point.
7. variances: a sequence of variance of portfolio returns at each rebalancing time point.
8. index.means: a sequence of average index returns at each rebalancing time point.
9. index.variances: a sequence of variance of index returns at each reblancing time point.
10. sharpe.ratio: a sequence of sharpe.ratio of portfolio.
11. A 2 by 2 plot.




####### GMVP #######
This is a strategy function searching portfolio weights by minimizing the variance of portfolio.

## input ##
1. data: historical trading data (has to be the same form of the testdata).
2. lower: the lower bound for the weight of each asset in the portfolio (default=0).
3. upper: the upper bound for the weight of each asset in the portfolio (default=1).
4. rf: risk free rate (not necessary in GMVP)

## output ##
1. name: a sequence of asset names in the portfolio.
2. weight: the GMVP strategy weight for each asset.
3. comb: A combination of name and weight.



####### SHARPE #######
This is a strategy function searching portfolio weights by maximizing the sharpe ratio of portfolio.

## input ##
1. data: historical trading data (has to be the same form of the testdata).
2. lower: the lower bound for the weight of each asset in the portfolio (default=0).
3. upper: the upper bound for the weight of each asset in the portfolio (default=1).
4. rf: risk free rate. If you set rf=0, the program will calculate the return rate using the return of the index/benchmark (default=0).

## output ##
1. name: a sequence of asset names in the portfolio.
2. weight: the SHARPE strategy weight for each asset.
3. comb: A combination of name and weight.
4. sharpe.ratio: the maximum of sharpe ratio.
5. exdvar: excess return over variance (used as initial value of theta in PerfInd function).

####### PerfInd #######
This is a strategy functino searching portfolio weights by minimizing the Performance Index.

## input ##
1. data: historical trading data (has to be the same form of the testdata).
2. lower: the lower bound for the weight of each asset in the portfolio (default=0).
3. upper: the upper bound for the weight of each asset in the portfolio (default=1).
4. rf: risk free rate. If you set rf=0, the program will calculate the return rate using the return of the index/benchmark (default=0).

## output ##
1. name: a sequence of asset names in the portfolio.
2. weight: the PerfInd strategy weight for each asset.
3. comb: A combination of name and weight.
4. theta: estimated theta.
5. Performance.Index: estimated performance index




####### MaxDR #######
This is a strategy function searching portfolio weights by maximizing the Diversification Ratio of portfolio.

## input ##
1. data: historical trading data (has to be the same form of the testdata).
2. lower: the lower bound for the weight of each asset in the portfolio (default=0).
3. upper: the upper bound for the weight of each asset in the portfolio (default=1).
4. rf: risk free rate. If you set rf=0, the program will calculate the return rate using the return of the index/benchmark (default=0).

## output ##
1. name: a sequence of asset names in the portfolio.
2. weight: the SHARPE strategy weight for each asset.
3. comb: A combination of name and weight.
4. Diversification.Ratio: the maximum of diversification ratio.