The Ultimate 401k Strategy

Many financial professionals would find the premise behind this post reckless.  I’m not going to argue with them.  Trading a 401k plan can be a terrible idea. It’s certainly foolish if you’re just using your gut or poor financial signals to time the trades.  But would Geometric Balancing work within the confines of a 401k?  Let’s find out, and in the process learn a bit more about creating a Geometrically Balanced portfolio.

Unique Aspects of 401ks

401ks and other similar savings plans are great.  You get to save money tax free, and often your employer will chip in additional funds to sweeten the deal further.  For many people (myself included), this is the largest investable asset they own.¹

However, these plans often come with restrictions. While these restriction make sense for the average investor, they can cause real problems to implementing a trading strategy, including Geometric Balancing.

• There are usually a limited number of investment choices.  Thankfully almost all plans offer a S&P 500 type fund and a government bond fund.
• Trading is often restricted.  Rebalancing frequently would not work. My 401k restricts reversing a trade for 30 days. I think this is common.
• You can’t truly go to cash. There should be a money market fund or a stable value fund, but often these are really just short term bond funds, or bank backed guarantees.
• Leverage is not an option.
• You’re not accessing the account any time soon without penalty. Therefore it makes sense to prioritize return over risk vs. return, especially if you are young. Although psychologically you still want to avoid huge drawdowns.

A strategy to maximize 401k growth has to be simple. Its only going to have the S&P 500 and government bonds available from my preferred list of assets.  No gold, and for now, I’m not going to consider a stable value fund a proxy for cash. And importantly it’s only going to rebalance the portfolio monthly.

Because we’re not touching this money any time soon, we can focus on increasing the future returns. We should maximize the geometric return.

To build this portfolio I’m going to use the structure outlined in the optimal portfolio for two assets.  If you’re not familiar with this post, you should go back and read it now.

The Model Inputs

Now the big question, what do we use for the inputs?

I’m going to walk you through a simple set of model inputs.  None of these match what I use for Geometric Balancing, although there are many similarities. But even in their simplicity these inputs still work very well.

First we’ll start with the standard deviation.

Standard Deviation.

I’m going to keep the predictor very simple. Standard deviation can change very quickly, so the model will take the standard deviation of the prior 20 days, nearly a month.  Then scale it to the proper period by multiplying by the square root of the number of days in the period.² In this case, use the standard deviation of the prior 20 daily returns and multiply by the square-root of 252 (a year in trading days), approximately 16.

That’s it.  Use the standard deviation of the last 20 days – scaled to the proper period – to predict the future standard deviation.³

Correlation.

Correlation is nearly as important as standard deviation.  It has an enormous impact on the portfolio construction, and can also change very quickly. 

To solve for correlation, use the same input as we did with standard deviation.  Take the correlation of bonds to stocks over the last 20 days.  There is no need to scale the correlation.

Return

Bonds

Now to the returns.  Let’s start with Bonds.  As explained in prior posts, sampling prior returns doesn’t do much good when it comes to estimating the future return. 

So what’s a reasonable prediction of the return of a bond?  Well if the yield doesn’t change, the return will be the yield itself. 

I have no idea how to predict the direction of yields. I’ve tried, and haven’t found anything trustworthy yet.  Therefore the most likely yield in the future, especially the near future, should be the same one as today.  The future return will be the bond’s yield.

But is this return the geometric return or the arithmetic return?

The geometric return is the long term return.  If a bond yield starts at 3%, changes over the year, but returns back where it started at 3%, the yield is the geometric return. Ok, then what was the monthly arithmetic return over that time? 

It has to be higher than the geometric return.  Per the formula:

Arithmetic Average = Geometric Average + Standard Deviation² / 2

The standard deviation squared is the variance. If the yield stays flat, the arithmetic return must be greater than the yield by half the bond’s variance.  You could make the estimate dynamic, using the variance input from above, but in order to keep the process simple, let’s just add a constant 0.7% (half the typical variance for long term bonds) to the yield to create the bond’s arithmetic return estimate.

Stocks.

What is the equivalent to bond yield in stocks?  Some might say dividends, but earnings yield is more appropriate.  It’s been shown the trailing price to earnings ratio does a fairly good job predicting long term stock return.  The earnings yield is just the inverse of the P/E ratio.

Earnings Yield = Earnings / Price

Once again, since these are long term returns, the earnings to price ratio is a geometric return.  The arithmetic return should be half the variance higher than the earnings yield. 

But, and this is key, it’s not the variance of the S&P 500 you have to add to the earnings yield.  The S&P 500 is a collection of stocks.  The earnings to price ratio we see is roughly the average ratio of all the index’s component stocks.  Therefore use the variance of the individual stocks to find the arithmetic return of the index.  The variance of an average stock is around 8% (28% standard deviation).  Half this is 4%. Add 4% to the earnings/price ratio to generate the estimated future arithmetic returns.

Put it all together

Now take these inputs and put them into the model. I’m going to use SPY and TLT as a proxy for the two funds. The current market is quite tame and calls for 100% stocks which makes for a boring example. So lets look at September 1, 2019:

And then the mixing (from this post):

Bonds % = 2.64% / 14.3 = 19%

Therefore the optimal portfolio was:

81 % SPY,    19% TLT

The Backtest

To evaluate if the strategy works, let’s run a backtest on the strategy to 1978. At the start of each month, the test will rebalance to the newly calculated optimal portfolio.⁴

The strategy beat the S&P 500’s compound returns by a percent and a half per year, with two thirds the volatility, 50% of the draw down, and a 50% improvement in Sharpe ratio (details in footnotes). 

The portfolio is unique in its stability.  I preach re-balancing, but when you aim for maximum return without leverage, the portfolio will often just sit in 100% stocks for years. 1978 to early 1981. Mid 1988 to late 1989.  Mid 1993 to early 1997.  Late 2003 to mid 2007.  Early 2012 to end of 2015.  And early 2016 to early 2018.  All very good times to invest in stocks. 

Maybe that’s a coincidence. But it seems unlikely.  The optimal portfolio’s heavy weight in stocks may be the reason the markets grew so strongly during these periods.

Now this isn’t a perfect portfolio by any measure. There are individual years that didn’t do so well, especially in relation to the market (’99 and ’09). But these “bad” years are always in relation to extreme out performance in neighboring years (’00, ’08). 

And more importantly, it is a very raw portfolio. The model inputs work just fine but they are rough around the edges. All of them can be improved, which if done right will improve the overall portfolio. You can add cash to this.⁵ Also, you can sometimes get around the 30 day limit which can make a big difference.⁶ Nearing retirement? Move the portfolio to maximize return/risk as opposed to just return.⁷

The key point: this framework is the starting point. It’s the foundation to all sorts of wonderful portfolios.

Pure Kelly Criterion.

The Geo Balanced 401k is pure Kelly criterion, without leverage.  It’s chasing the highest geometric return capable from the two assets.  It’s not going after the best risk return ratio, just return. 

Most people think investing at “full Kelly” is extremely dangerous.  They are correct if you use leverage.  But if you don’t use leverage, and you only invest in tradition assets, (respectable stocks and bonds), “full Kelly” is safe.  The unlevered “full Kelly” portfolio reduces volatility and drawdowns, while increasing returns because the strategy runs away from extreme volatility not towards it.  Don’t let anyone tell you an unlevered “full Kelly” portfolio is dangerous.

Once you see its power, you’ll realize balancing a portfolio to maximize geometric return is the only way to invest. 

1-I’m not including a house in in investable asset.

2-Technically you should scale everything to the time period you plan to rebalance.  Since we are rebalancing monthly, we should be scaling this data to a monthly value (multiply by the square root of 20).  However that produces very small numbers which don’t conceptualize well.  It’s much easier to relate to annual values, which is why I’ve used annual values for this experiment. The return should technically also be scaled to monthly values.

3-Many people have asked if I use the VIX for volatility. I don’t and haven’t even tried it in the model yet. That said I expect most of the time it would work well.

4- To take the backtest to 1978 I’m using the long bond yield to determine bond’s returns.

5- Adding cash will add nearly a percent to the returns while slightly improving volatility and drawdown.

6- As an example, “target date” funds are all the rage. These funds are really just a stock and bond fund that changes it’s portfolio weight percentage towards bonds the closer it gets to retirement age. As an example, in December 2018 I moved mid month into the 2025 target date fund since I couldn’t move back into the standard bond fund yet. It put the money in a near equal weight stock/bond fund which is what I was what my portfolio called for then.

7- I will write on this later.