Myers-Read in simulation

1. Myers-Read in simulation • Myers-Read capital allocation can be done in simulations using the “conditional risk” algorithm (Ruhm-Mango-Kreps). • No derivatives need to be calculated. • This is probably the easiest way to implement Myers-Read in a simulation.

2. Myers-Read in simulation • Example: • 2 independent normal risks: • Risk A:μ = 100, σ = 30 • Risk B:μ = 200, σ = 40 • Total:μ = 300, σ = 50 • Capital = 2σ  97.725 %ile ruin level

4. Myers-Read in simulation 1) Simulate the variables, sum them to get total portfolio. In example, 10K iterations. 2) Sort by total portfolio result. 3) Take a small sample of iterations on either side of the “ruin point”: These receive weight = 1, all others receive weight = 0. 4) Take weighted averages of each variable to get “funding” amounts. Subtract expected values to get capital allocation.

5. Other risk measures possible • Myers-Read uses p(ruin) as its central risk criterion. • The “Risk Function” column can be used to implement almost any risk measure instead, such as Default Rate of Surplus, Risk Coverage Ratio or TVaR.

6. Why does it work? • How can you get Myers-Read allocations without taking any derivatives? • Myers-Read is an additive method. • Any additive risk-allocation method can be implemented with the Ruhm-Mango-Kreps conditional-risk method, by using a suitable risk function (Ruhm-Mango theorem, from paper submitted to NAAJ).