Lifecycle Investing - Leveraging when young

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sat Dec 07, 2019 10:12 pm

One small note to add to what has become a really interesting discussion: you're not obligated to stick to any one allocation forever. You're not even obligated to assume that assumptions around the risk premiums of asset classes will remain. I use a levered "risk parity" portfolio, but I also have a script that shows me the rolling correlation matrix of all the assets I hold, and I look for changes in regimes with respect to overall volatility and the covariance structure. I would never "set and forget" a so-called "risk parity" portfolio.

As a simple heuristic, the more leverage you use, the more actively involved you need to be, especially with monitoring and hedging risks. Medallion fund really took off once it could get leverage to 12.5:1, but they also have a sharpe ratio over 6 and make thousands of trades a day. In my case, I use leverage approaching 3:1 at times, yet my historical volatility is much less than SPY, and I have WAY less tail risk. If I could trade full time, I could use leverage ~5:1 safely. If I could employ a sizable team at an institution, I'd probably lever higher than that.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sat Dec 07, 2019 10:26 pm

Uncorrelated wrote:
Fri Nov 08, 2019 10:13 am
Just wanted to add a few thoughts to this discussion.
EfficientInvestor wrote:
Wed Nov 06, 2019 2:21 pm
Note that my backtests below for Portfolio 2 just uses the oldest bond mutual fund I could find a ticker symbol for. I implement my actual strategy with treasury futures.
Unfortunately that is not nearly enough data. See this chart from ERN in particular:

Image

Since 1980, bonds have done nothing but go up. There is no information in a backtest like this. Only huge potential for misinformation.


I have done some research on expected bond performance with a factor model (as opposed to backtesting). According to data from Fama & French 1963~1991, exposure to the TERM factor (20 years treasury) provides monthly returns of 0.06 with a standard deviation of 3.02. The mv-optimal ratio between stocks and TERM is approximately 77:23, this decreases the standard deviation of your portfolio by a grand total of 1% compared to a portfolio of stocks and cash with the same expected returns. According to own calculations on bond data since 1870, the TERM factor provides monthly returns of 0.12 with a standard deviation of 3.12. In this case, the optimal ratio between stocks and TERM is around 63:37 and such a portfolio decreases your standard deviation compared to a stocks + cash portfolio for the same expected return by around 10%. This is all without leverage.

Cash in this context means the return of RF in Fama & French factor model. Stocks means MKT-RF, TERM means the return of 20 years government bonds. The above might be a little hard to interpret, so here is a simple conclusion: based on data from 1963~1991, leveraging stocks/bonds in the optimal ratio (which can only be known after the fact) provides 1% higher sharpe ratio than a 100% stocks portfolio with the same expected return. Based on data since 1870, leveraging stocks/bonds in the optimal ratio (which can only be known after the fact) provides 10% higher sharpe ratio than a portfolio of 100% stocks.

This analysis assumes a correlation of 0 between stocks and bonds and that leverage occurs at the risk free rate, both of which I consider to be in favor of bonds. This analysis also assumes that the model captures all the variation on bond returns, this is likely a false assumption. Fama & French in "Common risk factors in the returns on stocks and bonds" seem to imply that treasuries with a duration lower than 10 years have statistically significant alpha of around 1% per year but they don't elaborate further. (if this is true, then leveraging long term treasuries is just plain stupid).

For reference SmB and HmL have approximately the same standard deviation as TERM, but the return of SmB is around 1.5 and 3.5 times higher and HmL around 3 to 7 times higher. The conclusion here is that according to Fama & French factor model, leveraging bonds is of little use even if you ignore the existence of SmB and HmL.
EfficientInvestor wrote:
Wed Nov 06, 2019 5:40 pm
The image below is based on historical data since 1955 and we can both agree that the future won't look like the past. So let's just use this image to discuss theory. I'm not trying to imply that the future will look like the past.
As 305Pelusa has mentioned, a risk party portfolio is not the same as MVO. Risk parity is a buzzword that doesn't seem to mean anything useful.

Everybody agrees that leveraging the MVO portfolio results in lower risk for the same return compared to any other portfolio. The problem in practice is that:
  • Gold returns are not statistically different from zero, but you're still using them anyway. Classic case of survivorship bias.
  • bond data since 1955 in no way represents future returns from bonds. There is a 60-year period where TLL (10 year) returned nothing. If you use that period as a basis for your analysis, you would get a completely MVO portfolio. This is less of an issue with stocks since stocks have performed well over basically any 60 year period.
  • Assumptions about the equity risk premium are much more fundamental than assumptions abound gold and bonds, and in my opinion have far lower chance of blowing up in your face.
  • Leverage is not free.
At the end of the day, the optimal investment policy depends on your assumptions. I would like to know what your return assumptions are.
EfficientInvestor wrote:
Wed Nov 06, 2019 10:29 pm
305pelusa wrote:
Wed Nov 06, 2019 9:50 pm
As for your retirement accounts, is that around 14x leverage? How does it compare returns-wise to the more brute, less efficient 229% that I'm using?
Yes, it's around 14x. But you have to remember that 12x of that 14x is in an asset that has had a max drawdown of -4% or so since 1955
I assume that drawdown is in nominal terms. According to PV data the real drawdown is around 12% for CASH and 18% for ITT (1977~1980). I don't have more data for ITT, but I know that CASH has a maximum drawdown of 48% between 1933 and 1952. Conveniently before the start of your backtesting period. One has to wonder how ITT fared in that time period.

I'm not saying that leveraging ITT is a bad idea, but It does have that distinct smell of data mining and recency bias. A leveraged stock portfolio appears to be a lot less susceptive to poor assumptions.
How are you determining the optimal portfolio? Is it the single set of weights that maximizes sharpe for the entire time period? Most modern risk parity strategies adjust weights as covariance structure changes over time.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Sun Dec 08, 2019 3:32 am

no simpler wrote:
Sat Dec 07, 2019 10:26 pm
How are you determining the optimal portfolio? Is it the single set of weights that maximizes sharpe for the entire time period? Most modern risk parity strategies adjust weights as covariance structure changes over time.
I use mean variance optimization with different assumptions. I generally reduce factor premium by half and reduce/zero out correlations. The resulting portfolio does not necessarily maximize the sharpe ratio, but hopefully is a robust estimator to maximize the return for a particular amount of risk. Maximizing the sharpe ratio is completely pointless unless you have free leverage, have an infinite time horizon, or when you have a coefficient of relative risk aversion exactly equal to 1.

Risk parity is a poor substitute to modern portfolio theory (released in 1952) and should just die. It's complete nonsense.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 08, 2019 11:49 am

Uncorrelated wrote:
Sun Dec 08, 2019 3:32 am
no simpler wrote:
Sat Dec 07, 2019 10:26 pm
How are you determining the optimal portfolio? Is it the single set of weights that maximizes sharpe for the entire time period? Most modern risk parity strategies adjust weights as covariance structure changes over time.
I use mean variance optimization with different assumptions. I generally reduce factor premium by half and reduce/zero out correlations. The resulting portfolio does not necessarily maximize the sharpe ratio, but hopefully is a robust estimator to maximize the return for a particular amount of risk. Maximizing the sharpe ratio is completely pointless unless you have free leverage, have an infinite time horizon, or when you have a coefficient of relative risk aversion exactly equal to 1.

Risk parity is a poor substitute to modern portfolio theory (released in 1952) and should just die. It's complete nonsense.
Risk parity is just a method to better discover an "efficient" portfolio, as per MPT, on real world data, e.g. with better generalization performance out of sample. The problem with mean variance optimization is that it overfits and is really unstable. Also, it doesn't reflect the highly non-stationary nature of variance and covariance of assets, particularly over a multi-decade time horizon, where as inter temporal risk parity can take this into account.

Risk parity isn't a substitute or rejection of MPT at all, it's just a practical implementation method for MPT. I subscribe to MPT, but the devil is in the details. How do you determine forward looking returns, variances, covariances, etc?

mathwhiz
Posts: 818
Joined: Tue Jul 01, 2008 7:58 pm

Re: Lifecycle Investing - Leveraging when young

Post by mathwhiz » Sun Dec 08, 2019 11:55 am

As someone that trains on the retirement plans in my organization, I find the vast majority of our employees have little to no interest and are not capable of managing their 401k plans. The lifecycle plans are like investment for dummies. They are easy, automatic, and should generate acceptable returns and prevent people from making mistakes.

I like to train on "professionally managed" portfolios and "set it and forget it" as this gives our employees confidence. They get intimidated and do bad things so generally I like lifecycle funds and recommend them to 95% of our employees.

Dottie57
Posts: 7494
Joined: Thu May 19, 2016 5:43 pm
Location: Earth Northern Hemisphere

Re: Lifecycle Investing - Leveraging when young

Post by Dottie57 » Sun Dec 08, 2019 12:05 pm

mathwhiz wrote:
Sun Dec 08, 2019 11:55 am
As someone that trains on the retirement plans in my organization, I find the vast majority of our employees have little to no interest and are not capable of managing their 401k plans. The lifecycle plans are like investment for dummies. They are easy, automatic, and should generate acceptable returns and prevent people from making mistakes.

I like to train on "professionally managed" portfolios and "set it and forget it" as this gives our employees confidence. They get intimidated and do bad things so generally I like lifecycle funds and recommend them to 95% of our employees.
As someone who did not know much I agree with your assessment. The really important idea for most retirement plans is the percentage saved. Combine lifecycle funds with high rate of saving and those employees should have a nice retirement.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 08, 2019 12:20 pm

no simpler wrote:
Sun Dec 08, 2019 11:49 am

Risk parity is just a method to better discover an "efficient" portfolio, as per MPT, on real world data, e.g. with better generalization performance out of sample.
Risk parity is simply the mean-variance optimized portfolio under the assumption that all assets have the same expected future returns. That's it. So gather all of the information you need for MVO, then say "ok I don't know what the future returns will be so I will assume they're the same" (dubious assumption IMO) and that's how you get risk parity.
no simpler wrote:
Sun Dec 08, 2019 11:49 am
The problem with mean variance optimization is that it overfits and is really unstable.
The trick is to set conditions ("no less than 20% in US stocks, not more than 50% bonds, etc") and let the optimizer solve for the last, say, 40% of the portfolio. This is Gibson's approach. It tends to give pretty stable solutions.
I certainly prefer that over making some assumption I know it's incorrect for sure (that bonds have the same expected return as stocks) and then using MVO to solve for that. Which, again, is all risk parity is.
no simpler wrote:
Sun Dec 08, 2019 11:49 am
Also, it doesn't reflect the highly non-stationary nature of variance and covariance of assets, particularly over a multi-decade time horizon, where as inter temporal risk parity can take this into account.
Since all risk parity is is MVO with a simplifying assumption on returns, both risk parity and MVO reflect (or don't) as much of the non-stationary nature of covariances, over however long you want.
no simpler wrote:
Sun Dec 08, 2019 11:49 am
Risk parity isn't a substitute or rejection of MPT at all, it's just a practical implementation method for MPT. I subscribe to MPT, but the devil is in the details. How do you determine forward looking returns, variances, covariances, etc?
I agree risk parity is some implementation of MPT. Your last question is strange though. You need to determine forward variances and covariances for the risk parity portfolio as well. IMO, you're also assuming forward returns; you assume they're the same across assets. I don't agree with this assumption so to me, risk parity is like MVO where you're purposefully putting in parameters you know are incorrect. Not my cup of tea.

langlands
Posts: 84
Joined: Wed Apr 03, 2019 10:05 pm

Re: Lifecycle Investing - Leveraging when young

Post by langlands » Sun Dec 08, 2019 12:47 pm

Uncorrelated wrote:
Sun Dec 08, 2019 3:32 am
no simpler wrote:
Sat Dec 07, 2019 10:26 pm
How are you determining the optimal portfolio? Is it the single set of weights that maximizes sharpe for the entire time period? Most modern risk parity strategies adjust weights as covariance structure changes over time.
I use mean variance optimization with different assumptions. I generally reduce factor premium by half and reduce/zero out correlations. The resulting portfolio does not necessarily maximize the sharpe ratio, but hopefully is a robust estimator to maximize the return for a particular amount of risk. Maximizing the sharpe ratio is completely pointless unless you have free leverage, have an infinite time horizon, or when you have a coefficient of relative risk aversion exactly equal to 1.

Risk parity is a poor substitute to modern portfolio theory (released in 1952) and should just die. It's complete nonsense.
Unless I'm mistaken, coefficient of relative risk aversion exactly equal to 1 means having log wealth utility. What is the relationship between maximizing sharpe ratio and having this utility function?

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Sun Dec 08, 2019 1:13 pm

no simpler wrote:
Sun Dec 08, 2019 11:49 am
Risk parity is just a method to better discover an "efficient" portfolio, as per MPT, on real world data, e.g. with better generalization performance out of sample. The problem with mean variance optimization is that it overfits and is really unstable. Also, it doesn't reflect the highly non-stationary nature of variance and covariance of assets, particularly over a multi-decade time horizon, where as inter temporal risk parity can take this into account.

Risk parity isn't a substitute or rejection of MPT at all, it's just a practical implementation method for MPT. I subscribe to MPT, but the devil is in the details. How do you determine forward looking returns, variances, covariances, etc?
The problem with covariance is that it is almost impossible to estimate with any statistical significance. I often hear in various threads that stocks and bonds have a covariance of -0.1 in the examined time period. But when I look at the data there is no way that the covariance is statistically different from zero. The problem isn't that the variance and covariance are non static, the problem is that people calculate the covariance and then run MPT, without realizing that the confidence bands are so bad that even the sign isn't reliable known. For most asset pairs you're looking at multi-century data before the sign of the covariance starts to become statistically significant.

With enough data, expected returns and volatility of asset classes can be estimated with sufficient accuracy. Factor research will even give you the confidence intervals. If you really think that the expected return estimators are so bad they are completely useless, then you shouldn't put any trust in volatility estimate either. And you definitely shouldn't put any faith in covariances.

The original idea behind risk parity is that all asset classes have the same expected return and volatility, this makes even less sense because many asset classes have overlapping risk factors. Selecting a portfolio with equal exposure to various risk factors (market, value, credit) is quite an interesting (but useless) optimization problem.
langlands wrote:
Sun Dec 08, 2019 12:47 pm
Uncorrelated wrote:
Sun Dec 08, 2019 3:32 am
no simpler wrote:
Sat Dec 07, 2019 10:26 pm
How are you determining the optimal portfolio? Is it the single set of weights that maximizes sharpe for the entire time period? Most modern risk parity strategies adjust weights as covariance structure changes over time.
I use mean variance optimization with different assumptions. I generally reduce factor premium by half and reduce/zero out correlations. The resulting portfolio does not necessarily maximize the sharpe ratio, but hopefully is a robust estimator to maximize the return for a particular amount of risk. Maximizing the sharpe ratio is completely pointless unless you have free leverage, have an infinite time horizon, or when you have a coefficient of relative risk aversion exactly equal to 1.

Risk parity is a poor substitute to modern portfolio theory (released in 1952) and should just die. It's complete nonsense.
Unless I'm mistaken, coefficient of relative risk aversion exactly equal to 1 means having log wealth utility. What is the relationship between maximizing sharpe ratio and having this utility function?
If just so happens that if you maximize the portfolio allocation with a logarithmic utility function, you will find the maximum sharpe ratio portfolio (the tangency portfolio). If you have a different utility function, then you will find a different result. In particular, a risk coefficient of 0 means to select the portfolio with the highest expected return irrespective of volatility.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 08, 2019 3:05 pm

Uncorrelated wrote:
Sun Dec 08, 2019 1:13 pm
no simpler wrote:
Sun Dec 08, 2019 11:49 am
Risk parity is just a method to better discover an "efficient" portfolio, as per MPT, on real world data, e.g. with better generalization performance out of sample. The problem with mean variance optimization is that it overfits and is really unstable. Also, it doesn't reflect the highly non-stationary nature of variance and covariance of assets, particularly over a multi-decade time horizon, where as inter temporal risk parity can take this into account.

Risk parity isn't a substitute or rejection of MPT at all, it's just a practical implementation method for MPT. I subscribe to MPT, but the devil is in the details. How do you determine forward looking returns, variances, covariances, etc?
The problem with covariance is that it is almost impossible to estimate with any statistical significance. I often hear in various threads that stocks and bonds have a covariance of -0.1 in the examined time period. But when I look at the data there is no way that the covariance is statistically different from zero. The problem isn't that the variance and covariance are non static, the problem is that people calculate the covariance and then run MPT, without realizing that the confidence bands are so bad that even the sign isn't reliable known. For most asset pairs you're looking at multi-century data before the sign of the covariance starts to become statistically significant.

With enough data, expected returns and volatility of asset classes can be estimated with sufficient accuracy. Factor research will even give you the confidence intervals. If you really think that the expected return estimators are so bad they are completely useless, then you shouldn't put any trust in volatility estimate either. And you definitely shouldn't put any faith in covariances.

The original idea behind risk parity is that all asset classes have the same expected return and volatility, this makes even less sense because many asset classes have overlapping risk factors. Selecting a portfolio with equal exposure to various risk factors (market, value, credit) is quite an interesting (but useless) optimization problem.
langlands wrote:
Sun Dec 08, 2019 12:47 pm
Uncorrelated wrote:
Sun Dec 08, 2019 3:32 am
no simpler wrote:
Sat Dec 07, 2019 10:26 pm
How are you determining the optimal portfolio? Is it the single set of weights that maximizes sharpe for the entire time period? Most modern risk parity strategies adjust weights as covariance structure changes over time.
I use mean variance optimization with different assumptions. I generally reduce factor premium by half and reduce/zero out correlations. The resulting portfolio does not necessarily maximize the sharpe ratio, but hopefully is a robust estimator to maximize the return for a particular amount of risk. Maximizing the sharpe ratio is completely pointless unless you have free leverage, have an infinite time horizon, or when you have a coefficient of relative risk aversion exactly equal to 1.

Risk parity is a poor substitute to modern portfolio theory (released in 1952) and should just die. It's complete nonsense.
Unless I'm mistaken, coefficient of relative risk aversion exactly equal to 1 means having log wealth utility. What is the relationship between maximizing sharpe ratio and having this utility function?
If just so happens that if you maximize the portfolio allocation with a logarithmic utility function, you will find the maximum sharpe ratio portfolio (the tangency portfolio). If you have a different utility function, then you will find a different result. In particular, a risk coefficient of 0 means to select the portfolio with the highest expected return irrespective of volatility.
Both rolling variance and covariance estimates have very statistically significant autocorrelation (and yes, I'm purging any overlap in trailing series). In the case of volatility, R^2 between two consecutive 21 day periods can exceed .7. Using implied volatility in options markets, you can also get decent estimates of higher moments (although true tail risk is still largely unpredictable). I have never found any stat sig autocorrelation in asset returns, at least using daily (or coarser) time series.

Using volatility clustering effects/autocorrelation, you can dynamically adjust both weights and leverage to control risk quite well.

The proper functioning of options markets completely flies in the face of the argument that changes in the moments of asset distributions aren't predictable. In fact, if you believe that volatility isn't heavily autocorrelated, then you should be able to make an absolute fortune betting on the mean reversion of the implied volatilities of options; you're basically saying there is huge unexploited inefficiency.

parval
Posts: 11
Joined: Tue Oct 22, 2019 9:23 pm

Re: Lifecycle Investing - Leveraging when young

Post by parval » Sun Dec 08, 2019 8:42 pm

I want to follow your strategy but couldn't find how you're executing? Can you talk more about your current allocation? I assume some % in LEAPs/futures? How do you calculate borrowing cost vs say LETFs?

-edit I thought harder about this, does this make sense?

Say SPY is at $315, instead of paying $31,500 for 100 shares, I buy 3 LEAP calls at ~$200 strike to mimic the 3x exposure?

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Mon Dec 09, 2019 12:48 am

parval wrote:
Sun Dec 08, 2019 8:42 pm
I want to follow your strategy but couldn't find how you're executing? Can you talk more about your current allocation? I assume some % in LEAPs/futures? How do you calculate borrowing cost vs say LETFs?

-edit I thought harder about this, does this make sense?

Say SPY is at $315, instead of paying $31,500 for 100 shares, I buy 3 LEAP calls at ~$200 strike to mimic the 3x exposure?
I highly recommend that if you're interested, that you acquire the book.You can probably figure it out reading through the thread but you do have to work out some numbers eventually (like your future discounted savings) and the book does an OK job at taking you through that. I update my allocation every 3 months and update the original post.

Borrowing cost calculations can be found on page 3-5.

As for your example, one LEAP call at a low enough strike price will be like controlling/emulating 100 shares of SPY. The strike price of $200 is low enough.

If you bought 3 LEAP calls, that would provide an exposure to around 300 shares of SPY.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Mon Dec 09, 2019 10:45 am

I just realized the source of the disconnect w.r.t inter temporal risk parity, and the stability of parameter estimates.
One very counterintuitive finding - not only are many parameters NOT scale invariant for different time horizons, but increasing time scale can often lead to weaker parameter estimates. Longer time scale does NOT result in more "statistical significance." This is why the highest performing/highest sharpe funds often work on very short time scale, and even the same managers will be unable to achieve anywhere near the same sharpe if they launch a longer time scale/higher capacity fund. Keep in mind that shorter time scale does NOT mean less data - often it's quite the opposite (you can have thousands of intraday ticks, etc).

How this applies to risk parity: on shorter time scales, both variance and covariance autocorrelations are much, much more pronounced than on longer time scales. In fact, the autocorrelation declines rapidly after increasing a window beyond 21 days in the case of volatility.

I would also argue that the more leverage you use, the shorter the time scale you need to be concerned with. Brokers already enforce this by way of having stricter overnight margin requirements than intraday.

In any case, I agree that on very long, multi-decade time scale, returns and risk premiums are more "knowable" than volatilities or correlations. But on shorter time scale, the opposite is the case.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Sat Dec 14, 2019 3:21 pm

With all the recent discussions about LETF I was curious how your risk tolerance changes when using lifecycle investing. Recall this graph that I made earlier:

Image

In this graph, where we assume our retiree has a risk aversion coefficient of 3..
60% stocks corresponds to a risk aversion coefficient of 3.
90% stocks corresponds to a risk aversion coefficient of 1.75
120% stocks corresponds to a risk aversion coefficient of 1.2
150% stocks corresponds to a risk aversion coefficient of 1 (equal to the kelly criterion, or maximizing the geometric returns)
180% stocks corresponds to a risk aversion coefficient of 0.8
210% stocks corresponds to a risk aversion coefficient of 0.72
240% stocks corresponds to a risk aversion coefficient of 0.62
300% stocks corresponds to a risk aversion coefficient of 0.5

The numbers above are approximations based on the same assumptions that I used to generate the figure.

Apparently, your risk aversion coefficient becomes more or less arbitrary low at the start of your career. This has implications for selecting the optimal portfolio. A risk tolerance below one results in the rational selection of a portfolio that has significant volatility drag. Below is an image for illustrative purposes that displays, for various risk coefficients, the optimal portfolio assuming an universe of leveraged funds:

Image

Use the top image to choose the optimal volatility (X axis) for your risk tolerance, and then lookup the same X coordinate on the bottom left image to find the optimal portfolio. Fund selection kept simple for illustrative purposes.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 15, 2019 11:51 am

Uncorrelated wrote:
Sat Dec 14, 2019 3:21 pm
Apparently, your risk aversion coefficient becomes more or less arbitrary low at the start of your career. This has implications for selecting the optimal portfolio. A risk tolerance below one results in the rational selection of a portfolio that has significant volatility drag. Below is an image for illustrative purposes that displays, for various risk coefficients, the optimal portfolio assuming an universe of leveraged funds:
Super interesting. I read an abstract for a paper recently that suggested that when you're young it makes sense to take on MORE risk than optimizing for geometric return, eg risk aversion below 1. I'll be honest, I never got to understanding the rationale for that - do you know why this makes sense?

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 15, 2019 11:59 am

Uncorrelated wrote:
Sat Dec 14, 2019 3:21 pm
With all the recent discussions about LETF I was curious how your risk tolerance changes when using lifecycle investing. Recall this graph that I made earlier:

Image

In this graph, where we assume our retiree has a risk aversion coefficient of 3..
60% stocks corresponds to a risk aversion coefficient of 3.
90% stocks corresponds to a risk aversion coefficient of 1.75
120% stocks corresponds to a risk aversion coefficient of 1.2
150% stocks corresponds to a risk aversion coefficient of 1 (equal to the kelly criterion, or maximizing the geometric returns)
180% stocks corresponds to a risk aversion coefficient of 0.8
210% stocks corresponds to a risk aversion coefficient of 0.72
240% stocks corresponds to a risk aversion coefficient of 0.62
300% stocks corresponds to a risk aversion coefficient of 0.5

The numbers above are approximations based on the same assumptions that I used to generate the figure.

Apparently, your risk aversion coefficient becomes more or less arbitrary low at the start of your career. This has implications for selecting the optimal portfolio. A risk tolerance below one results in the rational selection of a portfolio that has significant volatility drag. Below is an image for illustrative purposes that displays, for various risk coefficients, the optimal portfolio assuming an universe of leveraged funds:

Image

Use the top image to choose the optimal volatility (X axis) for your risk tolerance, and then lookup the same X coordinate on the bottom left image to find the optimal portfolio. Fund selection kept simple for illustrative purposes.
This is really great work overall, and thankful for you sharing. My one piece of feedback would be again, to consider that the optimal portfolio is highly non-stationary. Forget risk parity for sake of argument - let's assume it's suboptimal. As a simple thought experiment - chop up your sample period into quarters, then find the optimal portfolio for each quarter, then compute geometric return; you will likely end up with some insanely high performance. Obviously this is massively overfitting and impossible to achieve out of sample, but that's the point.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Sun Dec 15, 2019 12:17 pm

no simpler wrote:
Sun Dec 15, 2019 11:51 am
Uncorrelated wrote:
Sat Dec 14, 2019 3:21 pm
Apparently, your risk aversion coefficient becomes more or less arbitrary low at the start of your career. This has implications for selecting the optimal portfolio. A risk tolerance below one results in the rational selection of a portfolio that has significant volatility drag. Below is an image for illustrative purposes that displays, for various risk coefficients, the optimal portfolio assuming an universe of leveraged funds:
Super interesting. I read an abstract for a paper recently that suggested that when you're young it makes sense to take on MORE risk than optimizing for geometric return, eg risk aversion below 1. I'll be honest, I never got to understanding the rationale for that - do you know why this makes sense?
The difference lies in how the individual outcomes are weighted. The geometric return maximizes the probability of outperforming, but the arithmetic return maximizes the average terminal value.

For example, suppose the following set of possible outcomes at the maximum geometric return portfolio:
$4000, $4000, $5000

Or the following set of possible outcomes at the maximum arithmetic return portfolio:
$2000, $2000, $15000

Choosing the maximum arithmetic return portfolio results in higher average terminal value, but maximizing the geometric return maximizes the probability of ending with the highest terminal value. The best one depends on your personal utility function. (I'm super disappointed there have been zero mentions of this in the LETF threads...)
no simpler wrote:
Sun Dec 15, 2019 11:59 am
This is really great work overall, and thankful for you sharing. My one piece of feedback would be again, to consider that the optimal portfolio is highly non-stationary. Forget risk parity for sake of argument - let's assume it's suboptimal. As a simple thought experiment - chop up your sample period into quarters, then find the optimal portfolio for each quarter, then compute geometric return; you will likely end up with some insanely high performance. Obviously this is massively overfitting and impossible to achieve out of sample, but that's the point.
I have only seen limited evidence that it it possible to beat a static prediction of the future ERP out-of-sample. In fact, prominent researchers such as Fama & French have released papers that claim that the shape of the yield curve and earnings information offer no information regarding future ERP and/or risk premia. I'm not going to waste my time with an exercise in overfitting.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 15, 2019 12:25 pm

Uncorrelated wrote:
Sun Dec 15, 2019 12:17 pm
no simpler wrote:
Sun Dec 15, 2019 11:51 am
Uncorrelated wrote:
Sat Dec 14, 2019 3:21 pm
Apparently, your risk aversion coefficient becomes more or less arbitrary low at the start of your career. This has implications for selecting the optimal portfolio. A risk tolerance below one results in the rational selection of a portfolio that has significant volatility drag. Below is an image for illustrative purposes that displays, for various risk coefficients, the optimal portfolio assuming an universe of leveraged funds:
Super interesting. I read an abstract for a paper recently that suggested that when you're young it makes sense to take on MORE risk than optimizing for geometric return, eg risk aversion below 1. I'll be honest, I never got to understanding the rationale for that - do you know why this makes sense?
The difference lies in how the individual outcomes are weighted. The geometric return maximizes the probability of outperforming, but the arithmetic return maximizes the average terminal value.

For example, suppose the following set of possible outcomes at the maximum geometric return portfolio:
$4000, $4000, $5000

Or the following set of possible outcomes at the maximum arithmetic return portfolio:
$2000, $2000, $15000

Choosing the maximum arithmetic return portfolio results in higher average terminal value, but maximizing the geometric return maximizes the probability of ending with the highest terminal value. The best one depends on your personal utility function. (I'm super disappointed there have been zero mentions of this in the LETF threads...)
What utility has a preference for maximizing average terminal value? That sounds like the kind of thing most probably don't want. Do you need RRA < 1 for that?

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Sun Dec 15, 2019 1:13 pm

305pelusa wrote:
Sun Dec 15, 2019 12:25 pm

What utility has a preference for maximizing average terminal value? That sounds like the kind of thing most probably don't want. Do you need RRA < 1 for that?
Correct. But if you use lifecycle investing and you reverse the asset allocation calculation to find the risk aversion coefficient, you can find a risk aversion coefficient below 1.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 15, 2019 1:36 pm

Uncorrelated wrote:
Sun Dec 15, 2019 1:13 pm
305pelusa wrote:
Sun Dec 15, 2019 12:25 pm

What utility has a preference for maximizing average terminal value? That sounds like the kind of thing most probably don't want. Do you need RRA < 1 for that?
Correct. But if you use lifecycle investing and you reverse the asset allocation calculation to find the risk aversion coefficient, you can find a risk aversion coefficient below 1.
I understand what you mean. If you ignore the human capital from someone using lifecycle investing and just look at what they invest, then it looks incredibly aggressive, past both the stock market's Kelly Criterion (overbetting) as well as what any rational human might want in risk (extremely risk-seeking).

I guess the thing I'm confused is that I'm not sure what you're arguing. Are you ultimately for lifecycle investing or not? BTW, when I say "lifecycle investing", I'm broadly talking about any strategy that uses leverage (and in fact, heavy leverage) early on to expose some of the future savings contributions to the stock market today. Whether that's a wealth adaptive or just a constant % allocation (what I use).

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Sun Dec 15, 2019 2:45 pm

I'm for evidence based asset allocations. Life cycle investing is one of the best in that regard.

I just wanted to write down my latest research experiments :wink: . A problem with my optimal variable asset allocation and lifecycle investing is that it only supports combinations of two assets. When you try to add in factor investing it becomes difficult to choose the right asset allocation. Perhaps we can use this method to aid in the selection of the optimal portfolio.

In theory we can run my optimizer with an arbitrary frontier, but one step at a time...

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 15, 2019 6:14 pm

Uncorrelated wrote:
Sun Dec 15, 2019 12:17 pm
no simpler wrote:
Sun Dec 15, 2019 11:51 am
Uncorrelated wrote:
Sat Dec 14, 2019 3:21 pm
Apparently, your risk aversion coefficient becomes more or less arbitrary low at the start of your career. This has implications for selecting the optimal portfolio. A risk tolerance below one results in the rational selection of a portfolio that has significant volatility drag. Below is an image for illustrative purposes that displays, for various risk coefficients, the optimal portfolio assuming an universe of leveraged funds:
Super interesting. I read an abstract for a paper recently that suggested that when you're young it makes sense to take on MORE risk than optimizing for geometric return, eg risk aversion below 1. I'll be honest, I never got to understanding the rationale for that - do you know why this makes sense?
The difference lies in how the individual outcomes are weighted. The geometric return maximizes the probability of outperforming, but the arithmetic return maximizes the average terminal value.

For example, suppose the following set of possible outcomes at the maximum geometric return portfolio:
$4000, $4000, $5000

Or the following set of possible outcomes at the maximum arithmetic return portfolio:
$2000, $2000, $15000

Choosing the maximum arithmetic return portfolio results in higher average terminal value, but maximizing the geometric return maximizes the probability of ending with the highest terminal value. The best one depends on your personal utility function. (I'm super disappointed there have been zero mentions of this in the LETF threads...)
no simpler wrote:
Sun Dec 15, 2019 11:59 am
This is really great work overall, and thankful for you sharing. My one piece of feedback would be again, to consider that the optimal portfolio is highly non-stationary. Forget risk parity for sake of argument - let's assume it's suboptimal. As a simple thought experiment - chop up your sample period into quarters, then find the optimal portfolio for each quarter, then compute geometric return; you will likely end up with some insanely high performance. Obviously this is massively overfitting and impossible to achieve out of sample, but that's the point.
I have only seen limited evidence that it it possible to beat a static prediction of the future ERP out-of-sample. In fact, prominent researchers such as Fama & French have released papers that claim that the shape of the yield curve and earnings information offer no information regarding future ERP and/or risk premia. I'm not going to waste my time with an exercise in overfitting.
yes, changes in returns and risk premium are definitely not predictable out of sample. But again, variance and covariance definitely are very predictable - so you should be able to get lower variance out of sample (while assuming returns stay roughly constant) by more frequent optimization. Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.

In fact, if you're optimizing the geometric mean, you must take into account the non-stationarity of variance. Modern betting algorithms based on Kelly Criterion depend on some volatility forecast, and you definitely cannot just use some fixed volatility estimate for a multi decade period. During a long period, volatility can go from persistent single digits all the way to over 50%. And again, leverage makes this disparity even larger since you multiply the volatility by the square of leverage to get the volatility drag. Once you get to higher leverage levels, you will see what I'm talking about - you MUST do some kind of active volatility management or you will blow up.

https://en.wikipedia.org/wiki/Kelly_cri ... ngle_asset

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 15, 2019 6:38 pm

no simpler wrote:
Sun Dec 15, 2019 6:14 pm
Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.
This strategy, as I've implemented it, does not have volatility decay.
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
But again, variance and covariance definitely are very predictable
I didn't know variance and correlations were "very predictable". Whoever can predict variance would make a lot of money in options actually.
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
Once you get to higher leverage levels, you will see what I'm talking about - you MUST do some kind of active volatility management or you will blow up.
That doesn't sound promising though. The implication is that you'd sell exposure when volatility goes up to maintain the correct risk. But that's precisely when the markets are riskiest, the premiums are highest, and the more disciplined investors who keep holding on and reinvesting tend to come out best.

You and I have disagreed on this since the very beginning. You like LETFs because they sell exposure when the market drops. And presumably, you'd sell those LETFs once volatility spikes due to the higher volatility decay. And I don't want to sell when the markets drop and I don't want to make a stance on volatility (meaning, whether volatility goes up and down, I maintain exposure). For people following the strategy how I am, we don't need to do these "active volatility managements", we don't need to try to predict volatilities or correlations (if that's even a thing), and we don't suffer from volatility decay.

And the borrowing costs are cheaper too :sharebeer

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 15, 2019 6:42 pm

Uncorrelated wrote:
Sun Dec 15, 2019 2:45 pm
I'm for evidence based asset allocations. Life cycle investing is one of the best in that regard.

I just wanted to write down my latest research experiments :wink: . A problem with my optimal variable asset allocation and lifecycle investing is that it only supports combinations of two assets. When you try to add in factor investing it becomes difficult to choose the right asset allocation. Perhaps we can use this method to aid in the selection of the optimal portfolio.

In theory we can run my optimizer with an arbitrary frontier, but one step at a time...
Gotcha. Yeah, your stuff is certainly really interesting. Thank you for taking the time.

Interestingly, first time I read about Lifecycle Investing, it wasn't even evidence-based. It was purely theoretical (it was John Campbell's "Strategic Asset Allocation"). It was later when I came to the paper from the econ professors. All they really did was grab that theoretical result developed already, and actually put it through the data and evidence. And it did very well.

For me, the fact that it works from a fundamental, theoretical sense is the most important thing. It just makes intuitive sense. That it has backtested excellently is a bonus.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 15, 2019 6:45 pm

305pelusa wrote:
Sun Dec 15, 2019 6:38 pm
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.
This strategy, as I've implemented it, does not have volatility decay.
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
But again, variance and covariance definitely are very predictable
I didn't know variance and correlations were "very predictable". Whoever can predict variance would make a lot of money in options actually.
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
Once you get to higher leverage levels, you will see what I'm talking about - you MUST do some kind of active volatility management or you will blow up.
That doesn't sound promising though. The implication is that you'd sell exposure when volatility goes up to maintain the correct risk. But that's precisely when the markets are riskiest, the premiums are highest, and the more disciplined investors who keep holding on and reinvesting tend to come out best.

You and I have disagreed on this since the very beginning. You like LETFs because they sell exposure when the market drops. And presumably, you'd sell those LETFs once volatility spikes due to the higher volatility decay. And I don't want to sell when the markets drop and I don't want to make a stance on volatility (meaning, whether volatility goes up and down, I maintain exposure). For people following the strategy how I am, we don't need to do these "active volatility managements", we don't need to try to predict volatilities or correlations (if that's even a thing), and we don't suffer from volatility decay.

And the borrowing costs are cheaper too :sharebeer
When it comes to math, there aren't really opinions though. The predictability of volatility is well documented, going back to Mandelbrot, and Nobel prizes have been awarded for research in this area. And the optimal betting criteria for optimizing long run geometric growth is a function of the betting period's volatility. Note that when the market drops, I stay exposed to the market, but both expected returns and volatility spike during market drops. This is means your strategy is inherently irrational, because it means you should be taking on more leverage when the market is calm to get the same exposure you are comfortable with during market drops. Right now you're saying your risk preferences are highly transitory.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 15, 2019 7:03 pm

no simpler wrote:
Sun Dec 15, 2019 6:45 pm

When it comes to math, there aren't really opinions though. The predictability of volatility is well documented, going back to Mandelbrot, and Nobel prizes have been awarded for research in this area.
Can you please link me to a paper that shows how to predict volatility? I know how to make delta-hedged volatility positions with options. Wouldn't mind having a free lunch on the side.
no simpler wrote:
Sun Dec 15, 2019 6:45 pm
This is means your strategy is inherently irrational, because it means you should be taking on more leverage when the market is calm to get the same exposure you are comfortable with during market drops.
You keep missing the point of Lifecycle Investing because you keep looking at the portfolio in isolation. You are forgetting about human capital, by far the largest asset of young people.

When the market drops, your human capital is intact but your savings drop significantly. So you need to invest more into stocks (via increasing leverage) to maintain a constant proportion of your wealth in stocks. Increasing leverage once the market drops in Lifecycle Investing is nothing more than rebalancing back to policy targets.

Once you stop thinking about risk as "% loss of your savings" and think about it as "% loss of your total wealth", then you'll understand that not increasing exposure (and especially selling exposure) after market drops is decreasing your risk. I want to maintain constant risk.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Sun Dec 15, 2019 7:22 pm

305pelusa wrote:
Sun Dec 15, 2019 7:03 pm
no simpler wrote:
Sun Dec 15, 2019 6:45 pm

When it comes to math, there aren't really opinions though. The predictability of volatility is well documented, going back to Mandelbrot, and Nobel prizes have been awarded for research in this area.
Can you please link me to a paper that shows how to predict volatility? I know how to make delta-hedged volatility positions with options. Wouldn't mind having a free lunch on the side.
no simpler wrote:
Sun Dec 15, 2019 6:45 pm
This is means your strategy is inherently irrational, because it means you should be taking on more leverage when the market is calm to get the same exposure you are comfortable with during market drops.
You keep missing the point of Lifecycle Investing because you keep looking at the portfolio in isolation. You are forgetting about human capital, by far the largest asset of young people.

When the market drops, your human capital is intact but your savings drop significantly. So you need to invest more into stocks (via increasing leverage) to maintain a constant proportion of your wealth in stocks. Increasing leverage once the market drops in Lifecycle Investing is nothing more than rebalancing back to policy targets.

Once you stop thinking about risk as "% loss of your savings" and think about it as "% loss of your total wealth", then you'll understand that not increasing exposure (and especially selling exposure) after market drops is decreasing your risk. I want to maintain constant risk.
Options markets already take into account volatility prediction, so there's no free lunch there. Options premiums are determined largely by their Implied Volatility, which are forward looking and represent the market's expectation of future volatility. There is also a Variance Risk Premium, which is to say sellers of options earn a persistent premium over the actual, realized volatility as payment for taking risk (eg negative gamma).

In any case, here's a review of research on volatility clustering, GARCH, etc:
http://public.econ.duke.edu/~boller/Pap ... 7_0910.pdf
Even if you can't make riskless profit in options market, you can adjust portfolio allocations based on volatility predictions.

I understand better now where you're coming from, re: ratio of financial assets to human capital. Let me think this over.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Sun Dec 15, 2019 7:36 pm

no simpler wrote:
Sun Dec 15, 2019 7:22 pm

Options markets already take into account volatility prediction, so there's no free lunch there. Options premiums are determined largely by their Implied Volatility, which are forward looking and represent the market's expectation of future volatility. There is also a Variance Risk Premium, which is to say sellers of options earn a persistent premium over the actual, realized volatility as payment for taking risk (eg negative gamma).
If there's a VRP (and I know there is, it's very logical) isn't that fundamentally saying that whatever variance options imply isn't actually what ends up occurring? The comments seem to be at odds:
"Variance is very predictable. Options's implied volatility reflect that predictable variance."
"Whatever variance options predicted has historically, on average, not occurred and you would've in fact made a profit by betting it would be lower."

So when you're predicting variance, do you look at implied volatility and then subtract something to account for the VRP phenomenon? 0_o

langlands
Posts: 84
Joined: Wed Apr 03, 2019 10:05 pm

Re: Lifecycle Investing - Leveraging when young

Post by langlands » Sun Dec 15, 2019 11:46 pm

Nosimpler is saying that since we're only using variance in portfolio risk management, not in alpha generation (making money off vol arb in options, for example), it's good enough to take the variance in the recent past as a reasonable estimate of variance going forward as an input to the optimization problem. The point is really that variance is reliably a positive number while returns can be positive or negative. This makes variance a much more robust input into the optimization problem while solutions to the optimization are extremely sensitive to assumptions about returns.

Obviously, if you're trying to use predictions of vol. to make money directly, your predictions have to be much better and by the usual efficient market arguments, that's very difficult (which is what I think 305pelusa is getting at).

langlands
Posts: 84
Joined: Wed Apr 03, 2019 10:05 pm

Re: Lifecycle Investing - Leveraging when young

Post by langlands » Mon Dec 16, 2019 12:09 am

305pelusa wrote:
Sun Dec 15, 2019 6:38 pm
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.
This strategy, as I've implemented it, does not have volatility decay.
Lifecycle investing can be implemented without taking on any net leverage, i.e. you use leverage > 1 when young and < 1 when old. But volatility decay doesn't disappear with a leverage multiple of 1. It disappears at a leverage multiple of 0, i.e. investing at the risk-free rate. Volatility decay is literally the difference between the arithmetic return and the geometric return, which will always be positive as long as returns have any uncertainty.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Mon Dec 16, 2019 4:55 am

no simpler wrote:
Sun Dec 15, 2019 6:14 pm
yes, changes in returns and risk premium are definitely not predictable out of sample. But again, variance and covariance definitely are very predictable - so you should be able to get lower variance out of sample (while assuming returns stay roughly constant) by more frequent optimization. Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.

In fact, if you're optimizing the geometric mean, you must take into account the non-stationarity of variance. Modern betting algorithms based on Kelly Criterion depend on some volatility forecast, and you definitely cannot just use some fixed volatility estimate for a multi decade period. During a long period, volatility can go from persistent single digits all the way to over 50%. And again, leverage makes this disparity even larger since you multiply the volatility by the square of leverage to get the volatility drag. Once you get to higher leverage levels, you will see what I'm talking about - you MUST do some kind of active volatility management or you will blow up.

https://en.wikipedia.org/wiki/Kelly_cri ... ngle_asset
Some comments here. The kelly criterion is a special case of optimizing the the best portfolio with a risk tolerance of exactly one. The image I have shown finds the best portfolio for multiple risk tolerances at the same time. Of course I know what the kelly criterion is, but it isn't relevant unless we are talking about a risk tolerance of one (of course the formula can be easily adjusted for other risk tolerances by simply multiplying sigma squared in the formula by the risk aversion coefficient).

Volatility is predictable. However it's not clear what you can do with that. It is reasonable to assume that the option markets are efficient enough that you can't make free money of volatility predictions. But why wouldn't that be the same for the equity market? If the market follows a brownian motion model with stochastic volatility, adjusting your asset allocation as a response to volatility forecasts results in higher risk adjusted returns. However, there are other models where it doesn't work. Just the fact that volatility is predictable isn't sufficient to claim that asset allocation should be adjusted with short term volatility forecasts.

The paper "Forecasting the Equity Risk Premium: The Role of Technical Indicators", 2012 version (older versions lack this information), tests various switching strategies and finds that a volatility-based indicator hooked up to a agent that maximizes the geometric return results in an annualized alpha of -0.52% before trading costs. I believe that was even an in-sample test.

305pelusa wrote:
Sun Dec 15, 2019 7:03 pm
Once you stop thinking about risk as "% loss of your savings" and think about it as "% loss of your total wealth", then you'll understand that not increasing exposure (and especially selling exposure) after market drops is decreasing your risk. I want to maintain constant risk.
I'm fairly certain that if the markets go down, lifecycle investing requires to to reduce your position. Take a look at the lifecycle investing chart I posted earlier. At the far left side of the image $1_000_000 corresponds to an asset allocation of 60% stocks and $500_000 corresponds to an asset allocation of 90% stocks. That indicates that if your net worth moves down from $1_000_000 to $500_000 you are required to sell some of your options to reduce your exposure. I'm sure the exact math is detailed in the lifecycle investing paper.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Mon Dec 16, 2019 8:23 am

langlands wrote:
Mon Dec 16, 2019 12:09 am
305pelusa wrote:
Sun Dec 15, 2019 6:38 pm
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.
This strategy, as I've implemented it, does not have volatility decay.
Lifecycle investing can be implemented without taking on any net leverage, i.e. you use leverage > 1 when young and < 1 when old. But volatility decay doesn't disappear with a leverage multiple of 1. It disappears at a leverage multiple of 0, i.e. investing at the risk-free rate. Volatility decay is literally the difference between the arithmetic return and the geometric return, which will always be positive as long as returns have any uncertainty.
Ok fair. What I meant to say is that if the underlying index gets more volatile (but same compound return), this strategy produces the same compound return it would’ve had it not gotten more volatile. This is in stark contrast to LETFs whose compound returns are a function of volatility.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Mon Dec 16, 2019 8:40 am

Uncorrelated wrote:
Mon Dec 16, 2019 4:55 am
I'm fairly certain that if the markets go down, lifecycle investing requires to to reduce your position. Take a look at the lifecycle investing chart I posted earlier. At the far left side of the image $1_000_000 corresponds to an asset allocation of 60% stocks and $500_000 corresponds to an asset allocation of 90% stocks. That indicates that if your net worth moves down from $1_000_000 to $500_000 you are required to sell some of your options to reduce your exposure. I'm sure the exact math is detailed in the lifecycle investing paper.
It looks to me like not only should you not sell any exposure (ETFs, contracts, options), but you should actually buy 440k in exposure to stocks after the drop in your example. Am I missing something?

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Mon Dec 16, 2019 8:48 am

305pelusa wrote:
Sun Dec 15, 2019 7:36 pm
no simpler wrote:
Sun Dec 15, 2019 7:22 pm

Options markets already take into account volatility prediction, so there's no free lunch there. Options premiums are determined largely by their Implied Volatility, which are forward looking and represent the market's expectation of future volatility. There is also a Variance Risk Premium, which is to say sellers of options earn a persistent premium over the actual, realized volatility as payment for taking risk (eg negative gamma).
If there's a VRP (and I know there is, it's very logical) isn't that fundamentally saying that whatever variance options imply isn't actually what ends up occurring? The comments seem to be at odds:
"Variance is very predictable. Options's implied volatility reflect that predictable variance."
"Whatever variance options predicted has historically, on average, not occurred and you would've in fact made a profit by betting it would be lower."

So when you're predicting variance, do you look at implied volatility and then subtract something to account for the VRP phenomenon? 0_o
Implied Vol is still highly predictive of realized vol, even if there is a persistent premium. Just like inches and feet are different units, but they are perfectly correlated. You can also use trailing historical vol to predict future realized vol and you will be on the same scale.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Mon Dec 16, 2019 8:57 am

Uncorrelated wrote:
Mon Dec 16, 2019 4:55 am
no simpler wrote:
Sun Dec 15, 2019 6:14 pm
yes, changes in returns and risk premium are definitely not predictable out of sample. But again, variance and covariance definitely are very predictable - so you should be able to get lower variance out of sample (while assuming returns stay roughly constant) by more frequent optimization. Reduction in variance (even modestly) becomes extremely important in the context of this thread, e.g. applying leverage, since volatility decay is quadratic w.r.t to the leverage ratio.

In fact, if you're optimizing the geometric mean, you must take into account the non-stationarity of variance. Modern betting algorithms based on Kelly Criterion depend on some volatility forecast, and you definitely cannot just use some fixed volatility estimate for a multi decade period. During a long period, volatility can go from persistent single digits all the way to over 50%. And again, leverage makes this disparity even larger since you multiply the volatility by the square of leverage to get the volatility drag. Once you get to higher leverage levels, you will see what I'm talking about - you MUST do some kind of active volatility management or you will blow up.

https://en.wikipedia.org/wiki/Kelly_cri ... ngle_asset
Some comments here. The kelly criterion is a special case of optimizing the the best portfolio with a risk tolerance of exactly one. The image I have shown finds the best portfolio for multiple risk tolerances at the same time. Of course I know what the kelly criterion is, but it isn't relevant unless we are talking about a risk tolerance of one (of course the formula can be easily adjusted for other risk tolerances by simply multiplying sigma squared in the formula by the risk aversion coefficient).

Volatility is predictable. However it's not clear what you can do with that. It is reasonable to assume that the option markets are efficient enough that you can't make free money of volatility predictions. But why wouldn't that be the same for the equity market? If the market follows a brownian motion model with stochastic volatility, adjusting your asset allocation as a response to volatility forecasts results in higher risk adjusted returns. However, there are other models where it doesn't work. Just the fact that volatility is predictable isn't sufficient to claim that asset allocation should be adjusted with short term volatility forecasts.

The paper "Forecasting the Equity Risk Premium: The Role of Technical Indicators", 2012 version (older versions lack this information), tests various switching strategies and finds that a volatility-based indicator hooked up to a agent that maximizes the geometric return results in an annualized alpha of -0.52% before trading costs. I believe that was even an in-sample test.

305pelusa wrote:
Sun Dec 15, 2019 7:03 pm
Once you stop thinking about risk as "% loss of your savings" and think about it as "% loss of your total wealth", then you'll understand that not increasing exposure (and especially selling exposure) after market drops is decreasing your risk. I want to maintain constant risk.
I'm fairly certain that if the markets go down, lifecycle investing requires to to reduce your position. Take a look at the lifecycle investing chart I posted earlier. At the far left side of the image $1_000_000 corresponds to an asset allocation of 60% stocks and $500_000 corresponds to an asset allocation of 90% stocks. That indicates that if your net worth moves down from $1_000_000 to $500_000 you are required to sell some of your options to reduce your exposure. I'm sure the exact math is detailed in the lifecycle investing paper.
Simulate a portfolio at higher levels of leverage (3:1+). Then look at what happens during periods of high volatility. This will give you an intuitive understanding of why it makes no sense to keep leverage fixed when volatility spikes.

For unlevered portfolios, it is ok to increase risk when vol spikes because you get higher expected returns as well. So sharpe stays roughly the same or even goes up (e.g. classic distressed/value investing). For levered portfolios, yes, you need to be more serious about using volatility for both adjusting leverage and allocation.

Volatility cannot predict returns because returns aren't predictable. Volatility can predict volatility, and knowing volatility is critical for virtually any allocation scheme.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Mon Dec 16, 2019 9:55 am

305pelusa wrote:
Mon Dec 16, 2019 8:40 am
Uncorrelated wrote:
Mon Dec 16, 2019 4:55 am
I'm fairly certain that if the markets go down, lifecycle investing requires to to reduce your position. Take a look at the lifecycle investing chart I posted earlier. At the far left side of the image $1_000_000 corresponds to an asset allocation of 60% stocks and $500_000 corresponds to an asset allocation of 90% stocks. That indicates that if your net worth moves down from $1_000_000 to $500_000 you are required to sell some of your options to reduce your exposure. I'm sure the exact math is detailed in the lifecycle investing paper.
It looks to me like not only should you not sell any exposure (ETFs, contracts, options), but you should actually buy 440k in exposure to stocks after the drop in your example. Am I missing something?
You're right I messed up. When the market goes down you should decrease your notional exposure. But because the value of your contracts dropped faster than your desired notional exposure, you should add some contracts. (when max leverage is not yet reached).
no simpler wrote:
Mon Dec 16, 2019 8:57 am
Simulate a portfolio at higher levels of leverage (3:1+). Then look at what happens during periods of high volatility. This will give you an intuitive understanding of why it makes no sense to keep leverage fixed when volatility spikes.

For unlevered portfolios, it is ok to increase risk when vol spikes because you get higher expected returns as well. So sharpe stays roughly the same or even goes up (e.g. classic distressed/value investing). For levered portfolios, yes, you need to be more serious about using volatility for both adjusting leverage and allocation.

Volatility cannot predict returns because returns aren't predictable. Volatility can predict volatility, and knowing volatility is critical for virtually any allocation scheme.
They did exactly that in the paper I mentioned, with a max leverage of 150%, and found that switching asset allocations in the optimal way based on recent volatility way did not improve expected utility. Expected utility was improved with other estimators (recent volatility was the third worst estimator before fees, out of 28 estimators).

If what you say is true, then high frequency traders would long volatility decay when predicted volatility is low and short volatility decay when predicted volatility is high. If enough traders do that the inefficiency will disappear.

You can't just add "volatility decay is bad for LETF" and "volatility is predictable" to arrive at the conclusion that market timing volatility results in higher risk adjusted performance. That is a contradiction of the efficient market hypothesis.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Mon Dec 16, 2019 3:06 pm

Uncorrelated wrote:
Mon Dec 16, 2019 9:55 am
305pelusa wrote:
Mon Dec 16, 2019 8:40 am
Uncorrelated wrote:
Mon Dec 16, 2019 4:55 am
I'm fairly certain that if the markets go down, lifecycle investing requires to to reduce your position. Take a look at the lifecycle investing chart I posted earlier. At the far left side of the image $1_000_000 corresponds to an asset allocation of 60% stocks and $500_000 corresponds to an asset allocation of 90% stocks. That indicates that if your net worth moves down from $1_000_000 to $500_000 you are required to sell some of your options to reduce your exposure. I'm sure the exact math is detailed in the lifecycle investing paper.
It looks to me like not only should you not sell any exposure (ETFs, contracts, options), but you should actually buy 440k in exposure to stocks after the drop in your example. Am I missing something?
You're right I messed up. When the market goes down you should decrease your notional exposure. But because the value of your contracts dropped faster than your desired notional exposure, you should add some contracts. (when max leverage is not yet reached).
no simpler wrote:
Mon Dec 16, 2019 8:57 am
Simulate a portfolio at higher levels of leverage (3:1+). Then look at what happens during periods of high volatility. This will give you an intuitive understanding of why it makes no sense to keep leverage fixed when volatility spikes.

For unlevered portfolios, it is ok to increase risk when vol spikes because you get higher expected returns as well. So sharpe stays roughly the same or even goes up (e.g. classic distressed/value investing). For levered portfolios, yes, you need to be more serious about using volatility for both adjusting leverage and allocation.

Volatility cannot predict returns because returns aren't predictable. Volatility can predict volatility, and knowing volatility is critical for virtually any allocation scheme.
They did exactly that in the paper I mentioned, with a max leverage of 150%, and found that switching asset allocations in the optimal way based on recent volatility way did not improve expected utility. Expected utility was improved with other estimators (recent volatility was the third worst estimator before fees, out of 28 estimators).

If what you say is true, then high frequency traders would long volatility decay when predicted volatility is low and short volatility decay when predicted volatility is high. If enough traders do that the inefficiency will disappear.

You can't just add "volatility decay is bad for LETF" and "volatility is predictable" to arrive at the conclusion that market timing volatility results in higher risk adjusted performance. That is a contradiction of the efficient market hypothesis.
I don't think it's a violation of EMH at all. You're just updating your priors to construct the most efficient portfolio, given all available information, at time T. You're not conducting any sort of arbitrage or trying to generate alpha with respect to a given index.

UberGrub
Posts: 108
Joined: Wed Aug 21, 2019 3:47 pm

Re: Lifecycle Investing - Leveraging when young

Post by UberGrub » Mon Dec 16, 2019 3:51 pm

UberGrub wrote:
Sun Nov 17, 2019 12:08 pm
305pelusa wrote:
Fri Nov 15, 2019 8:17 pm
UberGrub wrote:
Fri Nov 15, 2019 6:07 pm
I'm considering another set of options. I have done very well with this first set. However, the markets have gone up a lot thus far so I'm afraid of buying at the peak (yeah yeah, I know that's market timing but still).

Any thoughts 305pelusa?
Buy additional market exposure to hedge your ideosyncratic lifetime sequence of returns risk. It has nothing to do with current prices.

I like MT's advice:

"Take your exposure to risky asset classes on your current allocation path for the next 10-15 years, multiply it by, say, 1.01, and fund this by reducing exposure to cash and bonds. Reduce exposure in real dollar terms to these risky asset classes by the same amount after 10-15 years. If your means allow, increase the multiplier by 1.02, 1.03, etc. It's a free lunch, thanks to intertemporal diversification."
ebot wrote:
Fri Nov 15, 2019 6:48 pm
Can you provide some insight into which specific LEAPS you are buying (which S&P ETF, how far out, strike price, etc)? Are you using any stop limits to in case of a large drop?
I did earlier. Here's a set I bought/sold:
viewtopic.php?p=4709613#p4709613

Here's the process for figuring them out:
viewtopic.php?p=4712716#p4712716

No stop limits. I recommend that if you leverage with margineable derivatives (like options and futures) you keep leverage low enough so that your salary/savings contributions can stabilize the portfolio against the harshest environments and avoid liquidation. I believe the one thing where this can go wrong is forced liquidation. It is also why I do not use Leveraged ETFs. The systematic buying high and selling low is effectively being long volatility, which is not a position that has been generally rewarded historically.
Just my 2 cents.
Thank you for the response. I will acquire another set this upcoming week.
Really glad I did this then. Thank you for the help 305pelusa

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Tue Dec 17, 2019 3:39 pm

UberGrub wrote:
Mon Dec 16, 2019 3:51 pm
UberGrub wrote:
Sun Nov 17, 2019 12:08 pm
305pelusa wrote:
Fri Nov 15, 2019 8:17 pm
UberGrub wrote:
Fri Nov 15, 2019 6:07 pm
I'm considering another set of options. I have done very well with this first set. However, the markets have gone up a lot thus far so I'm afraid of buying at the peak (yeah yeah, I know that's market timing but still).

Any thoughts 305pelusa?
Buy additional market exposure to hedge your ideosyncratic lifetime sequence of returns risk. It has nothing to do with current prices.

I like MT's advice:

"Take your exposure to risky asset classes on your current allocation path for the next 10-15 years, multiply it by, say, 1.01, and fund this by reducing exposure to cash and bonds. Reduce exposure in real dollar terms to these risky asset classes by the same amount after 10-15 years. If your means allow, increase the multiplier by 1.02, 1.03, etc. It's a free lunch, thanks to intertemporal diversification."
ebot wrote:
Fri Nov 15, 2019 6:48 pm
Can you provide some insight into which specific LEAPS you are buying (which S&P ETF, how far out, strike price, etc)? Are you using any stop limits to in case of a large drop?
I did earlier. Here's a set I bought/sold:
viewtopic.php?p=4709613#p4709613

Here's the process for figuring them out:
viewtopic.php?p=4712716#p4712716

No stop limits. I recommend that if you leverage with margineable derivatives (like options and futures) you keep leverage low enough so that your salary/savings contributions can stabilize the portfolio against the harshest environments and avoid liquidation. I believe the one thing where this can go wrong is forced liquidation. It is also why I do not use Leveraged ETFs. The systematic buying high and selling low is effectively being long volatility, which is not a position that has been generally rewarded historically.
Just my 2 cents.
Thank you for the response. I will acquire another set this upcoming week.
Really glad I did this then. Thank you for the help 305pelusa
Yeah markets have kept going up. I am also glad I took the plunge this summer. It’s really soothing to actually root for markets to go up (which is what they tend to do). Before, I’d always get upset because it would mean I’d buy at higher prices.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

Re: Lifecycle Investing - Leveraging when young

Post by Uncorrelated » Wed Dec 18, 2019 2:34 pm

Uncorrelated wrote:
Sun Dec 15, 2019 2:45 pm
I'm for evidence based asset allocations. Life cycle investing is one of the best in that regard.

I just wanted to write down my latest research experiments :wink: . A problem with my optimal variable asset allocation and lifecycle investing is that it only supports combinations of two assets. When you try to add in factor investing it becomes difficult to choose the right asset allocation. Perhaps we can use this method to aid in the selection of the optimal portfolio.

In theory we can run my optimizer with an arbitrary frontier, but one step at a time...
I've finally gotten around to reading the lifecycle investing paper in detail and ran my optimizer with the same assumptions as used in the paper. My optimizer arrives at exactly the same assumptions as the paper. That's good news, because my optimizer can:
Calculate the optimal asset allocation for arbitrary utility functions, instead of just CRRA.
Calculate the optimal asset allocation for arbitrary combinations of assets, planned expenses, etc. etc.
Calculate the optimal asset allocation for arbitrary margin call logic, options contracts, tax logic etc. etc. As long as it can be approximated by a probability distribution on a discrete time basis.

If anyone wants to have anything specific simulated, send me a message. I'm out of inspiration right now.


I also spent some time to read this thread in it's entirely. I ran a few mean-variance optimizations on factor funds and it appears that options can be used to leverage factor funds and/or create poor mans long/short factor funds. For example by selling put options on SPY (large cap growth) and buying call options on small cap value. Has anyone leveraging factor funds with options. If not, why not?

langlands
Posts: 84
Joined: Wed Apr 03, 2019 10:05 pm

Re: Lifecycle Investing - Leveraging when young

Post by langlands » Wed Dec 18, 2019 2:47 pm

I still don't understand the reasons for using options instead of futures for leverage. And most leveraged ETFs are essentially using futures, so I don't mind paying them a fee for handling all the hard work for me (not to mention tax benefits of only paying LTCG instead of 60/40 LTCG/STCG). So basically, for retail investors that don't have to push around millions, I don't see a compelling reason not to use levered ETFs.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Wed Dec 18, 2019 2:57 pm

Uncorrelated wrote:
Wed Dec 18, 2019 2:34 pm
Uncorrelated wrote:
Sun Dec 15, 2019 2:45 pm
I'm for evidence based asset allocations. Life cycle investing is one of the best in that regard.

I just wanted to write down my latest research experiments :wink: . A problem with my optimal variable asset allocation and lifecycle investing is that it only supports combinations of two assets. When you try to add in factor investing it becomes difficult to choose the right asset allocation. Perhaps we can use this method to aid in the selection of the optimal portfolio.

In theory we can run my optimizer with an arbitrary frontier, but one step at a time...
I've finally gotten around to reading the lifecycle investing paper in detail and ran my optimizer with the same assumptions as used in the paper. My optimizer arrives at exactly the same assumptions as the paper. That's good news, because my optimizer can:
Calculate the optimal asset allocation for arbitrary utility functions, instead of just CRRA.
Calculate the optimal asset allocation for arbitrary combinations of assets, planned expenses, etc. etc.
Calculate the optimal asset allocation for arbitrary margin call logic, options contracts, tax logic etc. etc. As long as it can be approximated by a probability distribution on a discrete time basis.

If anyone wants to have anything specific simulated, send me a message. I'm out of inspiration right now.


I also spent some time to read this thread in it's entirely. I ran a few mean-variance optimizations on factor funds and it appears that options can be used to leverage factor funds and/or create poor mans long/short factor funds. For example by selling put options on SPY (large cap growth) and buying call options on small cap value. Has anyone leveraging factor funds with options. If not, why not?
I use options for leverage by creating synthetic longs. Options are flexible enough you can create just about any exposure you want. However, with ETFs, there's a huge ceveat - the options on the ETF may not have enough liquidity without paying huge spreads. SPY has a ton of liquidity and is very cheap to leverage using options, but many factor funds do not have much liquidity.

Also, going long a call of one factor and short a put of another will not create the exposure you want. If you want pure factor exposure, then you want to be delta and gamma neutral, and you don't want your factor exposure to change with changes in the market. So you would want a long call/short put in one fund and and then a short call/long put in another fund, all with same strike and time to maturity.

but tl;dr: yes, you can get factor exposure through options, and you can lever to your heart's content.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Wed Dec 18, 2019 3:16 pm

no simpler wrote:
Wed Dec 18, 2019 2:57 pm
Uncorrelated wrote:
Wed Dec 18, 2019 2:34 pm
Uncorrelated wrote:
Sun Dec 15, 2019 2:45 pm
I'm for evidence based asset allocations. Life cycle investing is one of the best in that regard.

I just wanted to write down my latest research experiments :wink: . A problem with my optimal variable asset allocation and lifecycle investing is that it only supports combinations of two assets. When you try to add in factor investing it becomes difficult to choose the right asset allocation. Perhaps we can use this method to aid in the selection of the optimal portfolio.

In theory we can run my optimizer with an arbitrary frontier, but one step at a time...
I've finally gotten around to reading the lifecycle investing paper in detail and ran my optimizer with the same assumptions as used in the paper. My optimizer arrives at exactly the same assumptions as the paper. That's good news, because my optimizer can:
Calculate the optimal asset allocation for arbitrary utility functions, instead of just CRRA.
Calculate the optimal asset allocation for arbitrary combinations of assets, planned expenses, etc. etc.
Calculate the optimal asset allocation for arbitrary margin call logic, options contracts, tax logic etc. etc. As long as it can be approximated by a probability distribution on a discrete time basis.

If anyone wants to have anything specific simulated, send me a message. I'm out of inspiration right now.


I also spent some time to read this thread in it's entirely. I ran a few mean-variance optimizations on factor funds and it appears that options can be used to leverage factor funds and/or create poor mans long/short factor funds. For example by selling put options on SPY (large cap growth) and buying call options on small cap value. Has anyone leveraging factor funds with options. If not, why not?
I use options for leverage by creating synthetic longs. Options are flexible enough you can create just about any exposure you want. However, with ETFs, there's a huge ceveat - the options on the ETF may not have enough liquidity without paying huge spreads. SPY has a ton of liquidity and is very cheap to leverage using options, but many factor funds do not have much liquidity.

Also, going long a call of one factor and short a put of another will not create the exposure you want. If you want pure factor exposure, then you want to be delta and gamma neutral, and you don't want your factor exposure to change with changes in the market. So you would want a long call/short put in one fund and and then a short call/long put in another fund, all with same strike and time to maturity.

but tl;dr: yes, you can get factor exposure through options, and you can lever to your heart's content.
Great post! I will just add that selling puts can be quite tax inefficient. I'm not sure it makes sense to try to get factor exposure long-short when 40+% of your profits go to Uncle Sam.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Wed Dec 18, 2019 3:28 pm

langlands wrote:
Wed Dec 18, 2019 2:47 pm
I still don't understand the reasons for using options instead of futures for leverage.
Options are literally cheaper in my case, once you account for taxes. As if that wasn't enough, they also would require no cash for collateral (no cash drag), no mark-to-market or quarterly rolling. I literally haven't checked on them at all. In my particular circumstances, I can't think of a reason for using futures instead of options.
langlands wrote:
Wed Dec 18, 2019 2:47 pm
So basically, for retail investors that don't have to push around millions, I don't see a compelling reason not to use levered ETFs.
LETFs target a certain leverage, regardless of the dollar exposure. In Lifecycle Investing, you want the opposite: a dollar exposure regardless of leverage. You should be more leveraged once the market drops, and less leveraged once it rises. Options and futures do this automatically. LETFs don't.

The amount of work I put to monitor my options is legit zero. I'm saving on that 1% annual fee with little work. Markets would have to go sharply down before I'd need to even pay attention. LETFs also borrow at higher costs (at least UPRO did), and then there's the volatility decay (which options/futures avoid). Uncorrolated has the exact dates but I think since ~1940 to today, UPRO has basically returned the same as the S&P500. I'd probably just go 100/0 with heavy tilts a la Bernstein to diversify temporally before I did it with LETFs.

no simpler
Posts: 108
Joined: Sat Jul 13, 2019 4:54 pm

Re: Lifecycle Investing - Leveraging when young

Post by no simpler » Wed Dec 18, 2019 4:27 pm

305pelusa wrote:
Wed Dec 18, 2019 3:28 pm
langlands wrote:
Wed Dec 18, 2019 2:47 pm
I still don't understand the reasons for using options instead of futures for leverage.
Options are literally cheaper in my case, once you account for taxes. As if that wasn't enough, they also would require no cash for collateral (no cash drag), no mark-to-market or quarterly rolling. I literally haven't checked on them at all. In my particular circumstances, I can't think of a reason for using futures instead of options.
langlands wrote:
Wed Dec 18, 2019 2:47 pm
So basically, for retail investors that don't have to push around millions, I don't see a compelling reason not to use levered ETFs.
LETFs target a certain leverage, regardless of the dollar exposure. In Lifecycle Investing, you want the opposite: a dollar exposure regardless of leverage. You should be more leveraged once the market drops, and less leveraged once it rises. Options and futures do this automatically. LETFs don't.

The amount of work I put to monitor my options is legit zero. I'm saving on that 1% annual fee with little work. Markets would have to go sharply down before I'd need to even pay attention. LETFs also borrow at higher costs (at least UPRO did), and then there's the volatility decay (which options/futures avoid). Uncorrolated has the exact dates but I think since ~1940 to today, UPRO has basically returned the same as the S&P500. I'd probably just go 100/0 with heavy tilts a la Bernstein to diversify temporally before I did it with LETFs.
LETFs are a bit unusual in that they rebalance leverage daily. This isn't actually good or bad - it's just...different. When volatility is high and the market chops sideways, LETFs are really bad. When you're in a low vol, directional bull or bear market, they're great.

I can't rebalance my synthetic longs daily, because the contract sizes are too big. In many regimes, this is a good thing, because I have less volatility decay and I don't pay management fees. But there are times, like the last couple months, where I wish I was in daily rebalanced LETFs.

A sophisticated strategy could combine synthetic longs with cash underlying, and then change the rebalancing frequency anywhere from quarterly to daily, based on the market regime. But that would be a ton of work.

Anyhow, I agree that people are overly afraid of options. Synthetic longs with time to maturity out more than a year are really not much work. It is a little annoying when you do need to rebalance, both because of contract size and just reporting difficulty; there's def a fintech opportunity here.
Also, putting aside taxes, synthetic longs for SPY and TLT should not be more expensive than futures. You just need to be mindful of how you submit orders to get your spreads down. For anything with a lot of liquidity, any sort of replicating position should be damn near identical cost wise, thanks to put-call parity. Generally when people think they've found a "cheaper" way to replicate a position, they're not accounting for something.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Wed Dec 18, 2019 5:05 pm

no simpler wrote:
Wed Dec 18, 2019 4:27 pm
LETFs are a bit unusual in that they rebalance leverage daily. This isn't actually good or bad - it's just...different. When volatility is high and the market chops sideways, LETFs are really bad. When you're in a low vol, directional bull or bear market, they're great.
You're talking about LETFs in general. I won't comment on that. I'm talking about LETFs in the context of Lifecycle Investing. In Lifecycle Investing, you need to up exposure to stocks after market drops and vice-versa. Uncorrolated's graph shows this. Logic shows this. And the math shows this. These LETFs are doing the opposite. This really should be the end of that argument: they're not quite what you'd want here.

There might be other applications where they're a great choice and options/futures aren't. That's cool. I just don't think one of those is here.

Lee_WSP
Posts: 1361
Joined: Fri Apr 19, 2019 5:15 pm
Location: Arizona

Re: Lifecycle Investing - Leveraging when young

Post by Lee_WSP » Wed Dec 18, 2019 5:19 pm

305pelusa wrote:
Wed Dec 18, 2019 5:05 pm
no simpler wrote:
Wed Dec 18, 2019 4:27 pm
LETFs are a bit unusual in that they rebalance leverage daily. This isn't actually good or bad - it's just...different. When volatility is high and the market chops sideways, LETFs are really bad. When you're in a low vol, directional bull or bear market, they're great.
You're talking about LETFs in general. I won't comment on that. I'm talking about LETFs in the context of Lifecycle Investing. In Lifecycle Investing, you need to up exposure to stocks after market drops and vice-versa. Uncorrolated's graph shows this. Logic shows this. And the math shows this. These LETFs are doing the opposite. This really should be the end of that argument: they're not quite what you'd want here.

There might be other applications where they're a great choice and options/futures aren't. That's cool. I just don't think one of those is here.
I agree with the logic there, but disagree with the robustness of the strategy. Increasing leverage would increase the chance of a margin call or options becoming worthless (or near worthless enough to not matter). Does the strategy have some sort of limit to the exposure?

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Wed Dec 18, 2019 5:29 pm

no simpler wrote:
Wed Dec 18, 2019 4:27 pm
Generally when people think they've found a "cheaper" way to replicate a position, they're not accounting for something.
I can't comment on TLT but I actually tend to find options to be significantly cheaper than futures. I might be doing something wrong but I can't figure out why. Maybe you can help.

Just now I looked at a synthetic option position and it has a borrowing rate of ~1.8%. This makes sense, that's basically what the Tbills/LIBOR/etc are at. However, I'm looking at the March 2020 future on the S&P 500 E-Mini. I see right now:

Contract cost = 3199.25
The S&P 500 closed just an hour ago at = 3191.14
The dividend yield is at ~1.9%

So you can buy the S&P at 3191.14. Or get the contract, pay an extra 8.11 in cost basis ("contango") and miss a dividend of ~15 dollars. So you're overpaying by 23.11 to have exposure to the index for about a quarter. That would annualize to ~92.44 dollars on an exposure of 3191.14, which is ~2.8%. Am I missing something?

langlands
Posts: 84
Joined: Wed Apr 03, 2019 10:05 pm

Re: Lifecycle Investing - Leveraging when young

Post by langlands » Wed Dec 18, 2019 5:41 pm

305pelusa wrote:
Wed Dec 18, 2019 5:29 pm
no simpler wrote:
Wed Dec 18, 2019 4:27 pm
Generally when people think they've found a "cheaper" way to replicate a position, they're not accounting for something.
I can't comment on TLT but I actually tend to find options to be significantly cheaper than futures. I might be doing something wrong but I can't figure out why. Maybe you can help.

Just now I looked at a synthetic option position and it has a borrowing rate of ~1.8%. This makes sense, that's basically what the Tbills/LIBOR/etc are at. However, I'm looking at the March 2020 future on the S&P 500 E-Mini. I see right now:

Contract cost = 3199.25
The S&P 500 closed just an hour ago at = 3191.14
The dividend yield is at ~1.9%

So you can buy the S&P at 3191.14. Or get the contract, pay an extra 8.11 in cost basis ("contango") and miss a dividend of ~15 dollars. So you're overpaying by 23.11 to have exposure to the index for about a quarter. That would annualize to ~92.44 dollars on an exposure of 3191.14, which is ~2.8%. Am I missing something?
I hope someone can weigh in on the math here as this as this is something I'd really like to know. But it just seems extremely implausible to me that the implied financing on the futures could be higher than options since the SPY futures market is one of the most liquid in the world, certainly much more liquid than options. To put it another way, why do almost all leveraged ETFs choose to use futures instead of options to replicate their positions? The money seems too free.

User avatar
Topic Author
305pelusa
Posts: 1251
Joined: Fri Nov 16, 2018 10:20 pm

Re: Lifecycle Investing - Leveraging when young

Post by 305pelusa » Wed Dec 18, 2019 5:54 pm

langlands wrote:
Wed Dec 18, 2019 5:41 pm
To put it another way, why do almost all leveraged ETFs choose to use futures instead of options to replicate their positions? The money seems too free.
There are some disadvantages to options. They're not perfect synthetic positions like futures are.

That said, if I had to guess, it's because the sheer volume of options you'd need to buy/sell for a mutual fund might be quite large. And daily reconstitution potentially very obnoxious and pricey. At least futures come in much larger sizes. Even then, they're probably a pain for large institutions. My understand is that LETFs like UPRO use neither; they use actual derivative swaps that they negotiate with other financial institutions and that are specific to them. These swaps, in UPRO's case at least, have higher costs than the risk-free rate as well. Once again, probably because with the sheer volume of daily trades, it's easier to have contracts with specific institutions to gain your exposure instead of going into the market place every day.

Post Reply