Variance-Covariance method:

The Variance-Covariance method assumes that stock returns are normally distributed. In other words, it requires that we estimate only two parameters, the mean and standard deviation of the returns. The third method involves developing a model for future stock price returns and running multiple hypothetical  trials through the model.

A Monte Carlo simulation refers to any method that randomly generates trials, but by itself does not tell us anything about the underlying methodology. There are some disadvantages of using VaR. one disadvantage is that, if a large loss occurs, the VaR does not tell us much about the actual size of the loss. Moreover, while calculating VaR, it is usually assumed that normal market conditions prevail.

But sometimes markets can crash, or there may be extreme moves of market variables. Moreover, since VaR is a single number, does not say anything about which of the portfolio components is responsible for the largest risk exposure.  Yet another problem with VaR is that the VaR of a combination of two positions may be larger than the sum of the VaRs of the individual positions.  This goes against the diversification principle, that the risk of a diversified portfolio is no larger than the combined risk of the portfolio components.