0One of the most widely used risk measures is the Value at Risk or VaR. VaR summarizes the worst expected loss over a target horizon within a given confidence interval.
Historical Simulation is non-parametric method that utilizes past returns to generate a VaR . It does not require any statistical assumption beyond stationarity of the distribution of returns or, in particular, their volatility. Suppose we have returns from day 1 to day t . To get the v\return of day t , we need to apply the formula:
Return(t) = ln (Stock Price (t)/ Stock Price(t-1))
The value of risk with confidence level p% is calculated as :
VaR = Portfolio Amount*(PERCENTILE(Return(t=1):Return(t=t),(100%-p%)))
Historical Simulation for portfolio is performed in two ways :
- Constant Mix : In this we maintains constant percentage of mixture of stocks in portfolio . For example if we have Stock A comprising of of 33% and Stock B is of 67%. In the constant mix we simultaneously pick shares from on stock to another as the prices of stock changes and as a result their composition changes . To maintain composition , it is important to shift shares from one stock to another.
When we have daily returns of the each stock in percentage basis, we multiply each stock with the each stocks composition percentage. As per provided above, we need to multiply stock A with 33% and stock B with 67% to maintain constant composition on the daily return.
- Buy and Hold : In this stock prices changes on the daily basis and due to which their composition also changes in the portfolio on the daily basis.
When we have daily returns of the each stock in percentage basis, we check out how much of the returns it shows on daily basis on the monetary basis, we check how much each stock comprises of total composition as we get varying composition of daily return.
