Why High-Volatility VIX Futures May Receive Small Portfolio Weights
Summary
The document discusses portfolio optimization using an ETF and VIX futures, comparing minimum-variance and Sharpe-maximizing approaches across different rebalancing schedules. The response focuses on minimum-variance intuition: an asset’s weight is influenced by its relationship to the portfolio’s risk model and by its idiosyncratic variance. Because VIX exposure is described as substantially more volatile than the ETF examples, the response argues that a minimum-variance allocation may assign it only a small weight.
The answer points to a comparison of historical volatility and a portfolio-selection paper for further context. It does not directly resolve whether an ETF weight floor is appropriate, explain why allocations sometimes become concentrated, or analyze why adding VIX futures worsens the reported return and Sharpe statistics. Results depend on the sample, covariance estimates, constraints, and futures implementation, so the stated intuition is not a general guarantee about optimal weights.
Key ideas
- Minimum-variance weights depend on covariances as well as each asset’s own variance.
- An asset with much higher volatility can receive a small weight in a minimum-variance portfolio.
- A weight floor is a portfolio constraint that changes the optimization problem and its solution.
- The answer offers volatility intuition but does not explain the Sharpe-maximizing results or diagnose the user’s backtest.
Tags
Full text
# Portfolio Optimization with ETFs and Futures # Portfolio Optimization with ETFs and Futures I am looking to perform portfolio optimization with a single ETF (or two) and a VIX futures (with the possibility of adding an additional hedging instrument). Here are some features of my portfolio optimization: - I calibrate the covariance matrix using a historical rolling window of 21 days (a month, essentially). - I perform the rebalancing of weights with differently frequencies (daily, weekly and fortnightly). This means that everyday/5 days/10 days I compute my portfolio returns with new weights*realized returns for that day. The weekly and fortnightly returns are overlapping i.e. Monday to Friday for 1 weekly return, Tuesday to Monday for the next (same for fortnightly). - Besides the normal case where I assume all my holdings are in a ETF, I sometimes add in a VIX futures and run a simple portfolio optimization between the two assets. - I do this for both MVP (minimum-variance portfolio) and maximizing Sharpe ratio portfolio variants. - Lastly, this process is ran for a historical time series of 3 years, say 2018 to 2020. Many times, I obtain cases whereby my portfolio optimization allocates all my holdings to either the ETF or the VIX. This seems abnormal, should there be a restriction such that maybe I hold a minimum of 80.0% of my portfolio in the ETF? (I am asking with respect to financial intuition and not mathematical proofs). Also, when I perform the portfolio optimization with the ETF and the VIX futures, my portfolio statistics (expected return, realized volatility, Sharpe ratio - all are annualized from daily to a year with the assumption of IID - *252 or *252^0.5) usually turns out worse, is this normal? ## Answer by lehalle (score 2, accepted) https://quant.stackexchange.com/a/78246 I did the same experiment using yahoo finance to get charts. I took the SPY, the VIX and third ETF for comparison. First have a look at the volatility of the 3 vehicles: You can see that the VIX has 10 times more vol that the ETFs... And when you know that the weight of a instrument $k$ in a MVP is more or less proportional to $$\beta_k\over \sigma^2_k,$$ where $\beta_k$ is its beta relatively to the "market" (or your risk model), and $\sigma_k$ its idiosyncratic risk, it is natural that the VIX has a very small weight: For details about MVP (and others), have a look at C-A. L and Guillaume Simon. "Portfolio selection with active strategies: how long only constraints shape convictions" Journal of Asset Management 22, no. 6 (2021): 443-463.
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.