How to stress test a correlation matrix

As part of a mean variance portfolio task, I am calculating portfolio risk and optimal allocations between assets given required level of return. Input: expected returns, volatility and correlation matrix. So far so good.

As a second part, I am supposed to stress input correlation matrix by some multiplier (say 1.3) and see how to it impacts the allocations and portfolio risk.

The question I have is: can I just multiply all fields in the correlation matrix by the given multiplier? It seems wrong to me as I would end up with "self correlation" > 1 on the diagonal, which makes no sense? Should I just keep diagonal as 1s and only multiply the rest? What if the multiplier is such that correlation between i and j will be >1 anyway? Any ideas appreciated, thank you.

NOTE: No risk free asset in this scenario, but it shouldn't matter.

• As an ad-hoc fix you could set $\rho_{ij}:=\max[-1,\min[1,1.3 \rho_{ij}]]$. That is multiply by 1.3 but then limit it to be between -1 and 1. – noob2 Mar 3 at 23:48
• thats what I ended up doing, thanks – NeverStopLearning Mar 6 at 18:44