Levered High Sharpe Ratio Portfolios

“you do not eat risk-adjusted returns”

How many times I have heard it. Well, not literally like this because, if you are able to frame it this way, you know it is not 100% true. Usually, it comes in the form of “stocks generate higher returns than that”. Meaning, why should I bother with a less volatile, higher Sharpe portfolio if, at the end of the day, I will earn less than allocating 100% to stocks?

For one, because of ergodicity. Even if you are comfortable with stock drawdowns and volatility and think your horizon is very long, you might need funds earlier than planned. While stocks are in said drawdown (if you are thinking that you have another “bucket” for that…well, then you are not 100% invested in stocks, meaning you are not earning the returns you think of). Or you might start investing at the wrong moment, in the sense that the returns going forward might differ from the recent and historical past.

It is returns AND the sequence of returns. It is the difference between arithmetic (what you think you are getting) and geometric returns (what you really get).

Thanks to Corey Hoffstein I recently discovered this blog; well, so far I just listened to the author in this podcast episode, to say the truth. But I hope to be able to do a deep dive soon about it.

Anyway, his latest post is an absolute gem about this topic.

“a higher Sharpe ratio portfolio is safer at any given common level of volatility compared to a lower Sharpe portfolio. And the easiest and surest way of increasing your Sharpe ratio is by increasing diversification.”

More importantly, Markku shows us that we can eat the Sharpe ratio. We just need to lever up the higher Sharpe portfolio to a higher volatility level.

In his example, if we bring the 60/40 up to the same volatility level of 100% stocks, we get higher returns. Conversely, we can get the same returns as a stock investor but with less volatility.

“The portfolio with the highest realized Sharpe ratio is guaranteed to have the highest mean growth rate among portfolios with equal volatility.” “In short, it is about maximizing the Sharpe ratio and leveraging to the desired level of risk.“

The cost of leverage obviously matters. As long as the cost-spread ABOVE the risk-free rate is less than the ratio between the levered overperformance vs the % of leverage, leverage adds value: any investor is better off investing in a levered high Sharpe ratio portfolio than allocating more to the high return/high volatility asset.

For example, in the case of the levered 60/40, Markku calculates that the cost-spread threshold is 1.33% (0.8 overperformance divided by 0.6 leverage). If you are familiar with IBKR margin spreads, the first tier (+1.5%) is not convenient but starting from the second one (+1.0%), even an IBKR margin loan makes sense.

Why am I mentioning this? Because the typical follow-up I receive for this reasoning is “Great, but how do I get leverage?” The good news for retail investors is that there are ETFs that offer leverage at a very low cost, very close to the risk-free rate. But even without them, if you are a “Europoor” like Twitter character Finumus loves to call European investors who cannot access US-listed instruments, you can do it with a simple (not optimal) Lombard loan from your broker (provided your portfolio is big enough).

Golden Butterfly

Even the thought of writing again about the 60/40 bores me to death, so today we will focus on the Golden Butterfly portfolio. This offers me as well the opportunity to discuss what some prominent (sigh) Italian YTers missed about the strategy (and its Weird Portfolio cousin) without alienating the good souls who have no clue what I am referring to (blessed you).

If the reason why you do not employ a Golden Butterfly (-esque) type of strategy is that it generates fewer returns than a 100% stock portfolio, may I introduce you to the Golden Butterfly levered up to the same volatility level:

Who’s winning the return race now?

As Markku said, if you want more profits you do not have to shift the portfolio allocation to the more volatile asset, you can simply add (or remove, if you want lower vol) leverage to the higher Sharpe mix available.

If your rebuttal at this point is about the fact that the Golden Butterfly (or any other portfolio) produces those results because of past correlations that might not replicate in the future, I invite you to listen to Meb Faber interviewing Jason Buck and Eric Crittenden. No one can be sure about that; but if you accept that the future can be uncertain, isn’t more diversification better than less?

Sure, in the case of the GB, maybe Small Cap Value might not offer the same overperformance it did in the past (actually, it did not provide it for the last 15 years and the portfolio is still ahead…), but the GB is just a variant of the Permanent Portfolio with a higher tilt to stocks. How wrong things can go while still living in a good environment for stocks?

The second rebuttal is that GB overperformance can be linked to specific instances in the past, like the 2008 crisis. No shit mate! This is a feature, not a bug. If the portfolio, any portfolio available to anyone, would always outperform then everyone would have already invested in it (ok, not everyone. The dividend stans would still prefer to earn less). I would agree with this point if looking at 50 years of data (not the 20 everyone is checking) there would be only a single instance in which there was a positive divergence: sure, data mining. But if we are dealing with strategies that can underperform for 10 years and still be valid, and we are, the fact that we can pinpoint a few moments over 20 years where a DEFENSIVE strategy worked, ain’t that the whole point of the game?

This is hedge fund material without the associated 2 and 20 fees: track when things are good and protect when things are bad.

Levered Bonds

So, how do we get leverage at a reasonable cost? And would this leverage provide the same results that we just obtained?

Unfortunately, (good) leveraged ETFs are relatively new to the market. So for the lads that do not believe the previous backtest, I have limited options. But… look what happens if I use UBT, the 2X Long Treasury ETF from ProShares:

ProShares products are bad because they reset the leverage every day AND their cost is massive (0.95% for this beauty). And yet we get there!

If you are wondering where is $SHV 2x…good spot, I guess? $SHV is nothing but long cash, so we can net it out with the short cash position due to leverage. In the first example I left it there to make the step unlevered -> levered clearer but netting those positions out doesn’t change the end result (when trading costs are set at 0).

Full Levered Portfolio

Thanks to our friends at Wisdom Tree we can now create our levered GB with just 3 ETFs (plus one to just reach the right vol point):

For $1 invested in $GDE you get $0.9 of $SPY and $0.9 of $GLD (ok, it is not exactly $SPY because they do not want to pay S&P the fee but it is $SPY at the end of the day).

Here is the performance compared to the two previously described portfolios:

There is even a little room to lever the portfolio more and get higher returns! 😉

Or you can lever it down to get the same $SPY returns with less volatility. Any excuses left?

Oh yes, you live in Europe (ex-Switzerland) and you do not have access to $GDE. You do not have the instruments or you do not want them? Because $GDE is brought to you by the same guys behind $NTSX and last time I checked, you did not buy $NTSX even if you could. The UCITS version of $NTSX has 8m of AUM, if you do not have the instruments at this point is just your fault, I am sorry 🙂

Anyway, this wanted to be a simple example, so the next time someone tells you that you cannot eat the Sharpe ratio, you can throw this model in their teeth and check who can eat then.

BONUS POINTS

Another thing that makes me go like

is when lads complain “those lazy portfolios are made for US-based investors, if you need EURs the picture is different”.

Let’s go and check this with our beloved PortfolioCharts tool. You can see how a particular portfolio/allocation would perform in a different country by simply changing the “Home Country” field in the top-right box of the “My Portfolio” section. Since PC added the Membership tier, if you are not a member you can make these changes in the Charts section, one chart at a time.

The quality of the below images tells you why I chose a career in finance. Anyway, on the LHS you have the classic, US-based, Golden Butterfly while on the RHS you have the “Italian version”

In this instance, there are mainly two things that affect all the changes:

• EUR/USD exchange rate
• Italian inflation instead of the US one

The results are intuitive…up to a point. The Italian-GB has a higher average REAL return but the distribution has fatter tails (as expected, since we are adding the FX volatility) and positive skew (not expected).

Do we lose the very core pillars of the OG Golden Butterfly? Yes. Does it really matter? Up to a certain point.

The higher volatility brings the SWR of the Italian-GB down to 5.2% (compared to 6.1%) and the PWR from 4.6% to 4.0%.

This is not great, until you realise that the 100% stock portfolio has a SWR of 4.1% and a PWR of 3.1% for a US investor and 3.5% (SWR) / 2.7% (PWR) for an Italian one. The Golden Butterfly is still miles ahead even for an investor that has to suck up all the FX volatility, if their goal is to have a smoother ride and, possibly, extract more juice from their portfolio during the retirement phase.

World exposure instead of US-only

That said, no one in Europe has a 100% USD-only portfolio. To make our experiment more credible, let’s use a portfolio like this:

The 50/50 split should represent a World Index-like risk exposure. (What it does not do is invest ONLY in Italian Bonds, because that’s stupid)

We do not get 100% there but we are close enough, innit? Meaning, even if you live in Europe and you spend EUR, this very simple (took more to do the print screens than to think about the allocations) World Golden Butterfly would do it for you.

What I am reading now:

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