As shown above, x-axis represents the level of risk, as measured by standard deviation, for each asset while y-axis represents expected return of each asset. The visualized chart using R unequivocally highlights that the Optimal Investment Portfolio is efficient investment asset compared to other asset as it has relatively very low risk but generates reasonable expected return compared with other investment assets.

Value at Risk (VaR) Analysis using R

Financial Concepts

VaR

Value at Risk measures the amount of potential loss that could happen in an investment or a portfolio of investments over a given time period. Value at Risk does not measure the actual amount of loss.

For example, if 1 week VaR at 95% confidence level is $10,000, this means the followings:

1) The probability that the amount of loss on investment position due to risk factors in 1 week will be less than $10,000 is 95%. We are 95% confident that the potential loss would be less than $10,000.

2) The probability that the amount of loss on investment position due to risk factors in 1 week will be greater than $10,000 is 5%. We are 5% confident that the potential loss would be greater than $10,000.

VaR Calculations

There are two main methods to compute VaR:

1. Historical Method: re-organize actual historical returns, putting them in order form worst to best. Depending on confidence level, the VaR will be different. This method assumes that history will repeat itself, from a risk perspective.

2. Variance-Covariance Method: assumes that stock returns are normally distributed. Similar to historical method except that this method uses familiar curve instead of actual data.

Optimal Investment Portfolio Value at Risk (VaR)

In order to compute VaR for the portfolio, historical method was used, assuming that stock returns are not normally distributed. The target period was between 2010-01-01 and 2015-12-31. The confidence level of 95% or 5% Value at Risk (VaR) was computed during the project and 1 month was chosen for the VaR time period.

As mentioned before, the optimal portfolio is composed of 10 stocks. In order to compute the optimal portfolio 1 month 5% VaR, 1 month 5% VaR of each stock must be computed, applied to optimal portfolio ratios and summed together.

Data for each stock's monthly return between 2010-01-01 and 2015-12-31 was acquired.

The following histograms show each stock's historical monthly return distribution between 2010-01-01 and 2015-12-31. The histograms were plotted using R and aforementioned data.

2016.11