You heard that right! You can use leverage the smart way and reduce risk, all the while keeping the expected returns the same as in an unleveraged portfolio. Leverage has gotten a bad reputation, sometimes for a good reason, think Global Financial Crisis in 2008/9 or the LTCM debacle that almost sank the financial system in 1998. But every force can be used for good or bad, think Star Wars. So how do we change leverage from a Darth Vader to a Luke Skywalker?

To recap, there are several reasons to use leverage:

- The
**sucker bet**. People max out their credit cards to put money into a “sure bet,” a stock recommended by their hair stylist or brother in law. Or they buy levered ETFs, also a bad idea, see our earlier post on the pitfalls. This is the bad form of leverage because you use it to double (or triple) down on an already risky investment. Don’t do it! - The sucker bet that even the most sophisticated financial experts fall for: Google “LTCM leverage” to find the story of the hedge fund that blew up in 1998. It operated successfully for many years finding minute arbitrage opportunities and traded on those with huge leverage factors. It worked great until, well, until it stopped working and sank LTCM and almost the entire US financial sector over concerns about who LTCM’s counter-parties were. In finance it’s called picking up coins in front of the steamroller. Works most of the time, but sometimes the steamroller is faster.
- One could use leverage to
**adjust for the effect of marginal taxes**on your after-tax returns. If taxes reduce both your expected return and your risk (measured as standard deviation) by the same multiplicative factor of 1-tax rate then why not scale up your portfolio, as we detailed in our Synthetic Roth IRA post where we showed how to generate Roth IRA returns in a taxable account, without the constraints of annual contribution limits. - Using leverage the
**smart way to reduce risk.**Of course you don’t want to lever up the already risky part of your portfolio (equities). You want lever up your*diversifying*assets, most notably bonds. Levering up bonds can indeed*reduce*your overall risk, while keeping the expected return the same as in the unlevered portfolio.

And you guessed it, we don’t want to talk about the Synthetic Roth IRA again and definitely not the sucker bet type of leverage. Let’s look at how one can use leverage to **reduce risk**.

The finance theory behind this is that one can use the less than perfect correlation between stocks and bonds for diversification. In fact, lately, the correlation between stocks and bonds has been mostly negative (about -0.25 to -0.30 over the last few years), which means you can benefit a great deal from diversification.

### Efficient Frontier Analysis in a Stock-Bond-Cash Portfolio

Let’s start with the expected return, expected risk and correlations of the three assets:

An **efficient frontier** is the scatter-plot of expected risk (x-axis) vs. expected return (y-axis) pairs so that for every expected return target there isn’t another portfolio with lower risk. This is done using no leverage and no shorting. The efficient frontier is easy to compute in a three asset portfolio with two risky assets (stocks and bonds) and one risk-free asset (cash). It simply traces the risk/return profiles of portfolios with x% stocks and 100-x% bonds (and thus zero cash), see blue dots in the chart below. With more assets in the mix it would become slightly more complicated (quadratic constrained optimization) and would require some more programming beyond the capabilities of Excel.

Thanks to diversification between stocks and bonds, our efficient frontier has a parabola shape, twisted to the left. That’s because, for example, a 50%/50% portfolio has exactly the average return of the two assets, but significantly less then the average risk of the two assets.

*Side note: Real finance purist that we are we do not consider the lower portion of our blue dots (from 100% Bonds moving in a Northwestern direction up to the turning point) a part of the efficient frontier because that part is transparently inefficient as you can increase expected return while decreasing expected risk when moving to the upper left. But we find it easier to simply plot the entire parabola in Google Sheets, with this caveat attached.*

If we draw a tangent line between the cash dot and the efficient frontier we identify the tangency point, marked as the yellow dot. It gives you the highest Sharpe Ratio (excess return over cash per unit of risk). If we could use leverage to scale up this tangency portfolio we’d move to the Northeast along the green dots into an area significantly more attractive than the efficient frontier. The entire purple area is better than the efficient frontier, and of course the path along the green dots is the most attractive risk-return trade-off. It’s better through the force of leverage (which was not allowed in the construction of the efficient frontier).

The calculation of this efficient frontier, as well as the calculation of the tangency portfolio are in the Google sheet posted here, for folks to play around. Try your own parameters and see how the efficient frontier and the tangency line change:

Google Sheets link to Spreadsheet to generate Efficient Frontiers (sheet cannot be edited, but you can download and play around with the parameters)

### Results

The tangency portfolio has about 60% bonds and 40% stocks. Notice how the risk is only 6% annualized, but the expected return is quite measly: 3.68% (nominal). Nobody can save for or fund an early retirement with that!!!

Scale up the tangency point to match the expected return of stocks and we start getting somewhere! At 7% return we now have a risk of only 12.31%, instead of 15% in the all-equity portfolio. That’s a sizable reduction in risk, through the power of leverage.

Alternatively, we could scale up the portfolio all the way to match the stock risk (15%) and gather the extra return of 8.45%, 145 basis points better than the stock portfolio.

We also include some other examples:

- An 80/20 portfolio vs. an 80/100 portfolio (80% stocks, 20% bonds, another 80% bonds on margin). You get roughly the same risk with the leverage portfolio but much bigger expected return. Also notice that an 80/20 portfolio has essentially a perfect correlation (0.995) with stocks. That’s unappealing. The 80/100 portfolio has a lower correlation.
- A 60/40 portfolio has pretty measly expected return and also very high correlation with stocks. A 60/100 portfolio juices up the return, with slightly higher risk and much lower stock correlation.
- Note that both the 80/100 and 60/100 portfolio are not on the tangency line, but they are pretty darn close, with a Sharpe Ratio only marginally below the optimal Sharpe Ratio.

### Implementation

Implementing even large degrees of leverage is relatively easy with futures contracts. We wrote briefly about the ins and outs of equity futures investing in our Synthetic Roth IRA post and the mechanics here are similar. Probably the most elegant way to implement a sample portfolio of about 80% equities and 120% bonds would be to hold the entire equity portion in physicals (e.g. Stocks, ETFs, mutual funds) another 18% in bond funds and the remaining 102% bond futures. The 2% leftover cash is more than enough for the margin on Treasury futures.

### Robustness checks

What happens when we change some of the assumptions?

- Corporate bonds instead of 10Y Treasury bonds: you get higher yield, but also higher correlation with stocks. One would need over 100% of bond exposure (hard to accomplish since there are no corporate bond futures) and another close to 60% stock exposure. To mimic this portfolio one would probably have to hold the bonds as an ETF (slightly under 100%), keep the remaining portfolio cash in cash to be used as margin for equity futures. The reduction in portfolio risk relative to the all stock portfolio is over 18%. 12.25% risk instead of 15%.
- Junk (high-yield) bonds: you further increase the yield, but the correlation is now substantial. 108% target weight in junk bonds would be hard to accomplish, but one could get close by holding almost the entire portfolio in bond ETFs and the equity exposure in stock futures.
- Treasuries, but assume zero correlation instead of negative correlation. This is still easy to implement: keep one asset as physicals the other as futures on margin. Reduction in expected risk is much lower though, less than 1/10.
- Higher cash expected returns: Still very high bond weight, reduction in expected risk also less than 1/10.

### Limitations/What can go wrong?

- All the other drawbacks of trading futures apply here as well, and we outlined those already in our Synthetic Roth IRA post. Those include the large size of single futures contracts ($130,000+ for the current 10 year future, $100,000 for S&P500 e-mini futures), the need to “roll” the contracts once a quarter, etc.
- The negative correlation between stocks and bonds could break down. An inflation shock a la 1974 would drag down both bonds and stocks. What is the likelihood of that? OPEC has lost its bite and US central bank policy has gained a lot credibility and transparency since then, so we doubt this is really in the cards going forward.
- Parameters for the tangency point and thus the desired portfolio will change (e.g., Treasury Yields!!!). When assumptions change we have to recalculate the weights and adjust the portfolio.

I like to keep it simple, and these strategies seem unsimple.

If it works as advertised, I would imagine one could invest in a fund that is using these strategies. Are you aware of any funds available to investors that deliver an equal risk with higher expected return, or equal expected return with lower risk by utilizing leverage?

Best,

-PoF

We like simplicity too. But sometimes the analogy of losing your keys in the bushes but searching for them under the street light (because it’s easier) would apply.

Bonds are celebrated as diversifies, but an 80/20 portfolio still has a stock correlation of 0.995. Add more bonds and you reduce the expected return so much that FIRE becomes a lot harder. There are no simple solutions to this conundrum.

The products that I know of are for institutional investors only. There are a few products for retail (I believe AQRIX) that do similar stuff, but from a slightly difference angle: risk parity. Problem is that they have high fees that invalidate the small advantage. They also appear to weight purely on risk (or 1/risk) and they don’t take expected returns into account. I would not invest in that.

Also we’re not arguing that this is the only way. Nor are we arguing that one should go all the way to 120% bond weight. Any step in that direction, though, should help with diversification. Example: buy ETFs that have some implicit bond beta built in already, such as high dividend, preferred stock, etc.

We did the study on REITs a while ago and found that they look like there’s a lot of bond exposure:

https://earlyretirementnow.com/2016/06/02/reits-pros-and-cons/

But there’s also the disadvantage that there’s a lot of uncompensated risk on top of that.

Have you fine gentelmen researched adding managed futures to a traditional portfolio of stocks, bonds and real estate?

Good article ERN. While this is a good synthesis of macro level data between asset classes, I feel even the 100% stock portfolio need not have the highest risk and volatility. For example, I have a 100% equity portfolio comprised of dividend stocks with a beta of 0.85 (equal in theory to 85:15 SPY:Cash portfolio) and on or close to the efficient frontier. Yet, I find the actual volatility to be significantly lower as equity sub classes like Utilities and Cons Staples act as a strong lever to bring down overall volatility during market downturns. I saw this during the last 3 ‘minor’ drawdowns over the past few years but it is something I am watching with more than academic curiosity. I would love to have you participate in my blog and share your comments.

That’s an important point! Dividend stocks have some bond-like features built in already. They have lower equity betas and significant to bonds. We did some calculations here: https://earlyretirementnow.com/2016/06/02/reits-pros-and-cons/

(The post is about REITs but we also look at high dividend stock, Vanguard VYM)

But: ideally one wants to have up to 120% bond allocation. Much more than any stock or stock sector we are aware of would display in a factor regression.

It would be hard to improve much beyond the efficient frontier without bonds on leverage. But I agree, some sectors like the ones you mention would be a good first step.

Cheers!

Good to read this. I am very familiar with the efficient frontier and this article took my knowledge to the next level.

Hearing about futures makes me want to explore this asset class a little further. Sounds like a good holiday plan!

Thx for sharing this insight.

Since you know about options already (and not just know about them but actually trade them, big difference) it shouldn’t take much effort to pick that up. Good luck!!!

The 10 ounce contract looks tempting

Awesome, best of luck! 🙂

Interesting idea… What are the tax implications of this?

All the usual rules apply:

1: Keep physical bonds in the tax deferred accounts ONLY

2: Keep physical stocks (individual securities, Mutual Funds, ETFs) in the taxable account (or tax-deferred account if tax-deferred is filled up with bonds)

3: The futures positions: Depends. You can keep them in the taxable account, but then take into account that the income is taxed at 60% Long-term gains, 40% short-term gains. One might want to apply the trick we described here

https://earlyretirementnow.com/2016/06/07/synthetic-roth-ira/

Scale up by 1/(1-taxrate) to compensate for effect of income taxes.

What are your thoughts on implementing the “Match Stock Risk” portfolio? I’m mixing treasury futures diversification and the synthetic roth strategy on paper and it’s looking like:

~$120k in cash turns into:

1 E-mini S&P future – say $120k

1 10yr Treasury future – say $130k

cash: $36k (30% E-Mini value) + $13k (10% Treasury value) = $49k

IEF (10yr Treasury ETF): $71k

I saw in a post you mentioned leaving 30% equity future value in cash to avoid margin calls. Above you mention 2% of treasury futures being sufficient when a portion of the 18% bond fund is counted as marginable cash. I put in 10% to further decrease risk of margin call considering the leverage by adding the treasury futures.

Could you poke holes in this strategy?

No holes in that strategy, really. One concern is that in the event of an inflation shock you would lose on both stocks and bonds.

Also in terms of the margins, you are actually a bit too conservative. Equity futures require around $5,000 maintenance margin and bond futures around $1,300. (check the exact numbers here:

http://www.cmegroup.com/trading/interest-rates/us-treasury/10-year-us-treasury-note_performance_bonds.html#sortField=exchange&sortAsc=true&clearingCode=21§or=INTEREST+RATES&exchange=CBT&pageNumber=1

and

http://www.cmegroup.com/trading/equity-index/us-index/e-mini-sandp500_performance_bonds.html#sortField=exchange&sortAsc=true&clearingCode=ES§or=EQUITY+INDEX&exchange=CME&pageNumber=1)

With $100,000 you will not get a margin call because brokers should allow you to use 75% of the IEF as margin. So, you could actually increase the ETF holding a little bit.

But make sure you check out my blog post here: https://earlyretirementnow.com/2017/04/26/have-bonds-lost-their-diversification-potential/

It doesn’t take much of an increase in bond yields to wipe out the benefit of bonds.

Ern,

Thanks for pointing me in the right direction here – I’m learning a ton and am fascinated by improving the risk/return ratio.

With the recent inversion of the yield curve, would you still be executing this levered bond strategy? Would you make any changes? Obviously it’s not really juicing returns because the spread on the 10 year and risk free rate is currently negative, but in terms of risk-parity do you still see validity?

With implementing 5-6x leverage on bonds with margin and IEF(or Munibond) holdings of collateral, have you had any experiences coming close to a margin call? Or do you just actively rebalance to avoid this problem.

Many thanks – your ideas and articles are opening a new world to me!

Cheers.

Hi Big Ern!

I’m a bit late to the party. Love this post and the simple introduction on how to introduce leverage in your portfolio. I have one question: You say that the most elegant way of implementing this portfolio is by owning physical equities and the bond part in futures. I wonder if there’s any drawbacks of doing it the other way around, i.e., holding physical bonds and invest in index futures. The new Micro E-mini contracts makes this a lot easier too.

The reason I’m thinking along these lines is because of tax withholding on dividends for non US citizens on US stocks. I’m in Hong Kong and thus pay 0% tax on capital gains and dividends. But my broker still have to withold 30% tax on all dividends I would receive from US stocks or ETFs (this can be reduced to 15% if I buy ETFs domiciled in e.g., Ireland, but I still like the prospect of 0% tax on the returns of US futures. Every little bit helps).

Is the reason that you’re recommending holding the equity portion of the portfolio in physical instruments mainly based on the assumption taxes for US citizens or is there something fundamentally different on how the portfolio performs based on which asset classes you hold in physicals vs derivatives?

Thanks again for an absolutely phenomenal blog!

Yes, works that way too. If your tax situation is different, feel free to implement that way! 🙂

I noticed that you show the max-Sharpe ratio as 40/60 in both this post from 2016 and your most recent post about beating the stock market. I am in the process of implementing strategy #4 using treasury futures to generate leverage while maintaining the max-Sharpe ratio. This might be a stupid question, but is it safe to assume the max-Sharpe ratio will remain fairly stable at 40/60 over a decades long retirement?

I don’t actually know how to calculate the max-Sharpe ratio myself and I couldn’t find the current ratio through a Google search. I suppose I could just ask you to calculate it for me every few years! 😀

(expected return minus risk-free rate)/risk

And that’s pretty stable at 40/60, very true! No need to recalculate every day. 🙂

This article from a year ago makes an interesting case for a 50/50 weighting as a good proxy for the max-Sharpe ratio which is unknowable in advance. https://www.alpha-week.com/risk-parity-gorilla-room

Thanks for the link! Whether it’s 40/60 or 50/50 also depends on the duration of the bonds. 30-year bonds might be closer to 50/50.

Correction: The article proposes a 50/50 risk parity weighting (as opposed to a 50/50 nominal weighting) as a proxy for the max-Sharpe ratio.

The author also mentioned that “In 2018, Fixed Income was approximately 60% of the public securities outstanding in the United States versus 40% Equities.” I don’t know if it is purely coincidental, but I thought it was interesting that the Market Portfolio in 2018 matches the max-Sharpe ratio you listed in your posts during that time frame.

In any case, it is a good article that can be easily consumed by a layperson such as myself.

Yeah, true. Good artcile. I’m not a huge fan of the pure RP approach because when looking only at risk you lose the portfolio optimization that takes into accounts expected returns as well. But as an easy starting point, RP is pretty neat! 🙂

I finally noticed your spreadsheet for generating efficient frontiers and I downloaded it and played around with it last night. That is a great tool that allowed me to see how the max-Sharpe ratio changes by adjusting the assumptions for expected return, risk, and correlation.

I wonder if adding a low correlation asset like gold might improve the Sharpe ratio a bit. Is there a way to add another asset class to the spreadsheet?

The efficient frontier calc in a 2-asset world is trivial. You simply map around the weights = (x,1-x) and you got the frontier. Once you add assets, you can no longer calculate the frontier so easily in Excel. I use Matlab/Octave for that. It’s a constrained quadratic optimization (quadprog).

But yes, adding more assets will shift the frontier to the “good” direction. It’s just no longer tricial to compute the frontier! 🙂

Thanks! I just realized I can use your SWR Toolbox 2.0 spreadsheet to run simulations to my heart’s content including adding gold and leverage. Love it!

You bet! Glad you enjoy the new features! 🙂