Steve Reading wrote: ↑Mon Aug 31, 2020 9:53 am
Uncorrelated wrote: ↑Mon Aug 31, 2020 1:52 am
VIX is a measure of risk-neutral volatility (that means that it assumes options are priced by risk-neutral actors), but option traders are not risk neutral, this causes VIX to consistently under-estimate market volatility. Based on this explanation you might think that scaling VIX by some constant factor fixes this issue, but it turns out this doesn't work since the risk aversion of option traders changes quite substantially over time.
Gotcha. So you tried multiplying the VIX by some constant factor greater than 1.0 and used that as the future volatility estimate, and the results were inferior as well?
Exactly. I used a linear model (pred_vol = a + b * vix) to predict future volatility, and that results in worse out-of-sample utility. I also tried scaling the predicted volatility by various amounts, but a scaling factor of 1 gave the best results indicating that my linear model was already the best possible. I should point out that using VIX actually results in fairly decent in-sample performance, but there is a big drop in performance between in-sample and out-of-sample.
I also tried using VIX as a feature in other models, but that consistently resulted in worse out-of-sample results. This indicates the information present in VIX isn't all that good.
With out-of-sample I mean that I used k-fold cross validation to split the data in k different parts. Then all k parts except 1 are used to determine the parameters, the performance is assessed on the last part. The process is then repeated k times. This method prevents some (but not all!) forms of overfitting.
langlands wrote: ↑Mon Aug 31, 2020 11:45 am
If you are comparing constant percent allocation vs. target volatility or target variance, I think it's very important that you do all comparisons with daily rebalancing (if you did already, then great). Recall the numerous posts from people very happy about the fortuitous timing of their quarterly rebalancing this year along with a smaller number of other people who were less happy with their unfortunate timing. There's a lot of variance to the quarterly rebalancing back tests that I hope you took into account.
Notice as well that the quarterly rebalanced constant percent allocation that HEDGEFUNDIE uses has a very important ad-hoc volatility adjustment built into it. When volatility is decreasing, UPRO tends to be rising and when volatility is increasing, UPRO tends to be falling. If you are in between rebalancing periods, your UPRO/TMF portfolio is automatically following a volatility adjustment. In other words during the market crash in March if you aren't rebalancing UPRO, you are automatically following a target volatility type strategy since you are allowing your URPO allocation to decrease drastically (via market price) while volatility is high.
Edit: Target variance isn't really the right term (obviously targeting a constant volatility or variance is the same thing). By target variance, I just mean scaling by 1/vol^2 since target volatility is in essence scaling by 1/vol.
That was my method, indeed. I used daily rebalancing, k-fold cross validation for in-sample/out-of-sample splits and calculated the expected utility similar to the manipulation proof measure of performance you see around sometimes. I also assessed the performance with various holding periods, but that didn't change the conclusions.
With my best model, I also attempted to create an actual trading strategy. But this turned out to be extremely difficult: daily rebalancing results in the highest utility before transaction costs, but this causes excessive turnover and will never survive transaction costs. With longer rebalance intervals the expected utility is less impressive but the transaction costs are also lower. I tried to use a multi-period optimization algorithm from a paper but had poor results. My best model for balancing rebalance interval and transaction costs uses machine learning (reinforcement learning) to determine the right rebalance intervals. Combining all these idea's results in around 20% higher certainty equivalent return out-of-sample, about the same you can expect from a simple value tilt.
My claim is that if I have to pull out all these tricks to get a half-decent out-of-sample performance, then the average user certainly has no chance to beat the market with market timing strategies.
I don't believe HEDGEFUNDIE' rebalancing idea's have any merit. Pick your target allocation, rebalance when the current allocation deviates too far from the target allocation. No need to perform any weird tricks. If you believe weird tricks improve the expected utility, the rebalancing algorithm is not the right place to implement them.
langlands wrote: ↑Mon Aug 31, 2020 1:55 pm
Uncorrelated, is your interpretation of target volatility mine and tomphilly's or portfolio visualizer's? Maybe we're all talking past each other and don't even know it.
I'm aware of multiple variants of 1/σ:
1. Keep the stock volatility constant, allocate the rest to the risk-free asset. This is the variant I tested and you see most often in papers.
2. Keep the stock volatility constant, allocate the rest to TMF.
3. Keep the overall portfolio volatility constant by scaling the entire portfolio allocation. Allocate the rest to the risk-free asset.
4. Adjust the expected volatility of stocks and bonds independently, then run a mean-variance analysis and select the portfolio with the target variance.
I think variant 1 is best suited to test the overall theory as it allows you to isolate the volatility clustering effects in the selected asset class. Most users seem to use variant 2 or 3. Variant 2 can result in an asset allocation of 20/80 which is... really dumb and definitely does not succeed at keeping the volatility constant. Variant 3 appears to assume volatility clustering works similar in stocks and bonds (Which may be true, but I haven't seen any evidence). Variant 4 is one that I have not seen used anywhere, but appears to have the strongest theoretical basis (as as far as 1/σ strategies go, this one really isn't that bad. A long time ago before I discovered utility functions, I thought this was the best possible approach). I believe PV can simulate strategy 1, 2 and 3 by selecting the appropriate option as the out-of-market asset, but not 4.