Risk Budgeting for Nonlinear Portfolios Through Return Streams
Summary
The document asks how to assign equal risk contributions across asset classes in a portfolio that includes nonlinear instruments such as options. One response recommends first converting each instrument into a return stream, estimating risk parameters from those streams, and then applying a portfolio method such as equal risk contribution or minimum variance. This frames nonlinear holdings in terms of their observed portfolio returns before optimization.
A second, explicitly speculative response suggests estimating option risk from simulated option-price returns. It proposes sampling volatility from its historical distribution and repricing options to form a return distribution, while acknowledging that the assumptions are unsupported and may be flawed. The discussion provides possible workflows, not an established method, and leaves key modeling choices and validation unresolved.
Key ideas
- Return streams for portfolio instruments can serve as inputs to risk estimation and weighting.
- Equal risk contribution and minimum variance are suggested as possible allocation methods.
- A speculative alternative estimates option-return risk by sampling volatility and repricing options.
- The proposed option method lacks mathematical support and is acknowledged as potentially flawed.
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Full text
# How to perform risk budgeting for non-linear portfolios? # How to perform risk budgeting for non-linear portfolios? I am using this question to compute optimal weights following a risk budgeting approach. The problem is I am using non-linear portfolios (options,equity,fixed income,fx). What I am looking for is that each asset class contributes the same amount of risk to the portfolio, and I am sure I can't use the regular approach if I have derivatives in my portfolio. ## Answer by Kyle Balkissoon (score 2) https://quant.stackexchange.com/a/19123 An approach to consider is: - Computing the total return streams of all the instruments in the portfolio - Calculate the risk parameters using 1 - Weight appropriately (Equal risk contribution, min variance etc) ## Answer by milkmotel (score 2) https://quant.stackexchange.com/a/31636 Just brainstorming here, could you possibly approach risk of an option from a probabilistic perspective? Because the price of the option ($S - X$, where $S$ is lognormally distributed) is lognormally distributed with the same standard deviation as $S$ (aside from being truncated at 0 and having the probability go to infinity as $S$ decreases or $X$ increases, which would pose issues) we can assume that the volatility of the distribution of $P$ is most sensitive to changes in $\sigma_S$, not $S$. Therefore, based on the historical distribution of $\sigma_S$, could you not compute the implied distribution of values of the price of the option? Essentially run a low-iteration Monte Carlo sampling from the historical distribution of volatility, then use the output of option prices to estimate a distribution of returns for $P$, and therefore the risk. Just find the optimal volatility by running volatility for different periods and finding which one most closely matches the current implied vol. I understand that the math to support this is completely absent and there is likely a huge flaw in the assumptions made, but it may be a solution. Just choose a holding period and only calculate for that one $t$, or iterate across all $t$ and have a dynamic volatility that would require automatic rebalancing.
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