Choosing Robust Parameter Regions from Return and Volatility Grids
Summary
The document asks how to identify robust parameter regions in a discrete strategy grid when each parameter pair has an associated return and volatility. It proposes filtering grid points by minimum return, maximum volatility, and separate stability-radius thresholds for the return and volatility surfaces. The aim is to find parameter choices that meet performance requirements while remaining stable under nearby parameter changes.
It then asks how to compare acceptable regions when their return and volatility stability radii trade off, and how to rank many such regions. The document supplies no selected metric, analysis, or empirical evidence; it is a question rather than a worked method. Any answer would need to define the neighborhood used for stability, account for the scale and units of each measure, and state how return and risk priorities are combined. The proposed thresholds and candidate filtering are illustrative, not validated guidance.
Key ideas
- The proposed screening rule requires minimum return and maximum volatility at each grid point.
- It measures parameter robustness with separate stability radii for returns and volatility.
- The document asks how to rank regions when their two stability measures conflict.
- No comparison metric or empirical validation is provided.
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Full text
# robust regions in grid search
# robust regions in grid search
I have a strategy f that takes parameters x,y (for x,y taking values in integer ranges). I get two grids (of returns and volatility values) from computing f(xi,yi) for integer ranges x1 <= xi <= x2 and y1 <= yi <= y2.
My question: what is the standard optimization techniques of determining areas in this discrete grid that are robust with respect to both returns and volatility values? The simplest way that comes to mind is given by this pseudo-code
```
threshold_ret = ...; // minimum required threshold
threshold_vol = ...; // maximum allowed volatility
threshold_rr = ...; // minimum required returns stability radius
threshold_rv = ...; // minimum required volatility stability radius
candidates = empty list;
foreach (xi,yi) do
ret = returns at xi,yi;
vol = volatility at xi,yi;
rr = maximum stability radius for returns grid at xi,yi;
rv = maximum stability radius for volatility grid at xi,yi;
if (ret > threshold_ret) and (vol < threshold_vol) and
(rr > threshold_rr) and (rv > threshold_rv) then
add (xi,yi,rr,rv) to candidates list;
end if
end for
```
Also, assume I have two acceptable regions R1 and R2 from the candidates list. For R1, let stability radius for returns grid be rr1, and for volatility grid be vr1. similarly, let these quantities be rr2 and vr2 for region R2. Given that there are different cases such as
```
(rr1 > rr2) and (vr1 < vr2)
(rr1 < rr2) and (vr1 < vr2)
(rr1 > rr2) and (vr1 > vr2)
(rr1 > rr2) and (vr1 > vr2)
```
what is the reasonable metric to use to select from these regions? What if there are many such regions?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.