Historical VAR Vs Variance/Covariance Method

[passcfa2016]

Could someone please explain to me the difference between Historical VAR method and the Variane/Covariance Method? I’m stuck!

[sunseeker]

You mean the historical simulation method?

[cpk123]

Historical VAR - you are provided a table - looking at the Historical returns from the past — showing the Return on Portfolio vs. the probability of occurence of that return. (Look at Exhibit 4). You use that Historical analysis - and then decide what your VaR number would be.

Analytical VAR/Covariance method - The analytical or variance–covariance method begins with the assumption that portfo- lio returns are normally distributed. Use the number for the return, and the variance of the portfolio components - and covariance between components of the portfolio - arrive at Portfolio Variance using w1^2sd1^2 + w2^2sd2^2 + 2*w1*w2*cov(1,2) - arrive at portfolio std deviation - then do return - Z Score * Portfolio Std Deviation to get the VaR number.

The analytical or variance–covariance method’s primary advantage is its simplicity. Its primary disadvantage is its reliance on several simplifying assumptions, includ- ing the normality of return distributions. In principle, there is no reason why the calculation demands a normal distribution, but if we move away from the normality assumption, we cannot rely on variance as a complete measure of risk.

Using historical VAR - it is also called Historical Simulation method, we calculate returns for a given portfolio using actual daily prices from a user- specified period in the recent past, graphing these returns into a histogram. From there, it becomes easy to identify the loss that is exceeded with a probability of 0.05 (or 0.01 percent, if preferred).

so there is no assumption of the normality of returns,

The historical method has the advantage of being nonparametric (i.e., involving minimal probability-distribution assumptions), enabling the user to avoid any assump- tions about the type of probability distribution that generates returns. The disadvantage, however, is that this method relies completely on events of the past, and whatever distribution prevailed in the past might not hold in the future.

history is used in both cases - but slightly differently.

HTH

[zxfmontreal]

^ Can you also explain the advantages and disadvantages of each method + Monte Carlo method? (Those are all the three methods to calculate VaR right?)

On top of my head:

Historical method

adv: appropriate to use when portfolio contains options

disadv: future may not repeat the past

Analytical method

adv: market data is available to use

disad: variance/covariance matrix not stable over time; not appropriate when portfolios contain options

Monte Carlo method

Adv: appropriate when the model is complexe???

Disadv: results can only be as accurate as inputs

[zxfmontreal]

^ Crap…I didn’t read the quotes…