wilmott.com

The volatility of a portfolio of assets derived using the standard variance-covariance approach depends on three factors - the allocation to a particular asset (the more the allocation to a particular asset, the more it contributes), the volatility of the asset itself (the more the volatility, the more it contributes), and the correlation of a particular asset with respect to other assets within the portfolio (the lesser the correlation, the less it contributes).Are there any studies done that discuss the sensitivity of contribution to risk to the three factors described above. In particular, does one factor dominate the other? I would like to know if there is a way to quantify using either a simulation or closed-form solution to see how much of the contribution to risk is driven by each of the three factors.Any help is greatly appreciated.Thanks in advance.

Perhaps I am missing something, but surely the closed form solution you are looking for is:Where there are N assets with weight w(i) and standard deviation sigma(i), and correlation sigma(ij) between the i-th and the j-th assets for i is not equal to j. Or if the covariance-variance matrix is V (V = [sigma(ij)]i,j=1,...,N) and the weight column matrix is w, then:The three 'risks' are then seen as:1. w(i)2. sigma(i)3. sigma(ij) , for j = 1,..., i-1, i+1,..., NThe above equation is central in Markowitz mean-variance portfolio optimisation, which provides an interesting framework (even though it is about 50 years old) to understand the risk of a portfolio in a holistic manner. I think it would be difficult to break down the portfolio risk into the mentioned components, partly because they are driven by choice and by portfolio optimisation.Hope I haven't missed the point completely.

Using very simple partial derivatives and matrix fundaes the dis-aggregation you wantto do looks do-able. But i don't know how much technically correct it might be to breakdown overall risks intofactors like standard deviations and correlations. Personally i would not do that, becauseits best to think of risks in terms of risk-factors which are market observable rather thanfactors which go into price calculation. Historical Correlation is an output of two time series.what sense would it make to change correlations then.