There is $7.4BN in AUM allocated to levered short ETFs of which $6.4 BN is allocated to the ticker TBT (Proshares Ultrashort 20+ Yr ETF). This ETF’s underlying is the Barclays’ 20 Yr Bond Index, whose historical chart is shown below.

The next chart shows two hypothetical paths that the underlying follows from now to 6 months into the future. Which of the two paths do you think leads to a positive payoff from buying the 2x short levered ETF and holding it for the entire duration?

The answer is neither. In Path #1, the underlying returns -3.5% over the time horizon, but a 2x levered short ETF would have returned -0.34% over the same period. This does not also account for management fees and interest expenses that the investor would also incur. In Path #2, the underlying returns -1.96%, but the 2x levered short ETF would have returned -5.5% over the same time horizon. The chart below shows three lines for each path: the trajectory of the underlying, the profitability from shorting the underlying with 2x leverage and the profitability of holding a 2x levered short ETF (TBT equity).

To be fair, holding a levered ETF past 1 day does not always lead to underperformance relative to buying/shorting the underlying with leverage. During the first month of Path#2, for example, the 2x levered short ETF outperforms shorting the underlying with 2x leverage.

Understanding what drives the divergence in performance

So what are some of the factors that drive the difference in payoff between buying/shorting the underlying on your own with leverage and buying a levered ETF? The first factor is the degree of serial correlation (streakiness) or mean reversion in the underlying. A path demonstrating a higher degree of mean reversion, all else being equal, will lead to a drag in performance of the levered ETF, while a path showing more serial correlation with give the levered ETF a bump in performance relative to levering up and buying/shorting the underlying.

The second factor is the length of your holding period: the longer you hold a levered ETF the more its performance is likely to diverge from simply levering up the underlying. The video below discusses these two factors in more detail, along with simulations of different scenarios. The video talks about the case of a 2x long levered ETF, but all the principles apply for a 2x short ETF as well.

The third factor influencing the relative under/outperformance of a levered ETF is the size of the moves in the underlying. The larger the daily moves in the underlying, the more a levered ETF will be likely to diverge in performance from simply levering the underlying.

The fourth factor we discuss is the amount of leverage in the ETF. A more highly levered ETF will cause more price divergence than a less levered ETF. These last two factors are discussed in more detail and with the aid of computer simulations in the video below:

Conclusion

Many investors who are betting on price declines in treasuries are buying levered short ETFs and holding them past one day. When investors do this they are making a highly complex bet on the future path and volatility of the underlying bond index. Therefore if investors want to short treasuries using a levered ETF, they should think through what path they expect treasuries to follow and whether those price declines are likely to take place during a high or low volatility regime.

If the expected decline in treasuries coincides with higher volatility and/or a higher degree of mean reversion in bond prices (perhaps reflecting short term uncertainty in the market), then holding onto a levered short treasury ETF over that period will likely underperform simply shorting an unlevered bond fund (e.g TLT equity) using leverage. It is entirely possible that investors who end up being right on the direction of the underlying bond index and would have profited from shorting it, may instead lose money buying a levered short ETF.

Describes a number of things that can cause the banking system to stop functioning. This includes a liquidity crisis when depositors demand their money back immediately, or insolvency when a banks assets are worth less than its liabilities. This video also addresses the common conception that during the Gold Standard era every dollar in circulation was backed fully by gold.

Videos to watch before

How did the banking system come into existence?

Explains how society evolved from using Gold coins for transactions to having a banking system that creates credit/loans from the savings/deposits of others. The banking system described is similar to the banking system under the Gold Standard (i.e when currency was backed by a commitment by the government to exchange each note for a fixed amount of gold).

Videos to watch before

None needed

This video discusses how interest rates determine the money supply in an economy. An interest rate increase causes a tightening of lending by causing money to be loaned to those who are most likely to produce a higher returns. The interest rate also affects the incentives of savers to keep money in the bank as opposed to spending/investing it.

Videos to watch before

How did the banking system come into existence?

A look at an advantage of the Gold Standard system. We examine how a commitment to the Gold Standard meant that governments could not print/spend money indiscriminately. Because people holding a currency could redeem gold for their currency at any time, any loss in confidence in a currency would cause gold reserves held by a central bank to become quickly depleted and undermine the currency they were attempting to print/spend.

Videos to watch before

1. What can cause the banking system to break down?
2. What restrictions did the Gold Standard impose on member countries?

This video talks about a disadvantage of the Gold Standard. Specifically we discuss how a country with high unemployment often found itself with some unpleasant options to choose from when trying to stimulate job creation. The most common way to decrease unemployment was to first decrease wages in an economy such that exports were made cheaper, creating more demand for goods and leading to an inflow of gold, which ultimately lead to an increase in employment. This first step of decreasing wages was often extremely difficult for governments to do.

Videos to watch before

What restrictions did the Gold Standard impose on member countries?

We examine how an increase in money supply without a corresponding increase in the amount of goods/services can lead to inflation. We then look at the real historical example of Europe from 1500-1600 and the causes of the “price revolution” at that time.

Videos to watch before

None needed

A short example illustrates how having a common currency makes trading goods in an economy more efficient by making it a simpler to find someone to exchange goods with.

Videos to watch before

None needed

An examination of how the Gold Standard kept price levels in check. An increased/decreased price level in one country was countered by a flow of gold out of/into the country through the trade imbalance mechanism. This offsetting flow of gold would neutralize the change in the price level.

Videos to watch before

1. What restrictions did the Gold Standard impose on member countries?
2. Does an increasing money supply always cause inflation?

A look at what macro economic factors make Gold attractive to hold. We look at the relationship between real interest rates and Gold prices and point out how other currencies in the world looking unattractive makes Gold look attractive.

Transcript

In this video we take a look at how gold competes with other currencies and look at what factors make holding gold relatively more or less attractive compared to other currencies in the world.

Setting up the example

Similar to our previous video, we are going to assume that there are only three currencies in the world: the US dollar, gold and rest of the world (ROW) currencies. If you watched our previous videos you know that the reason we are treating gold as the currency is because a lot of people who hold gold look at it as a store of wealth/value and so they often compared gold to other currencies when they’re trying to decide how to keep their wealth.

We are going to assume that the exchange rate between US dollars and gold is that 1 unit of gold = 1000 US dollars and as we talked about before, because gold is denominated in US dollars, this exchange rate is the price of gold in the market. We are also going to assume that the exchange rate between US dollars and ROW currency is such that 1 US dollar = 2 ROW currencies. Finally, we know from the previous videos that defining these two exchange rates defines the third exchange rate between gold and ROW currency such that 1 unit of gold = 2000 ROW currency.

What makes holding dollars attractive?

Question: if you are sitting in the US, what makes it attractive to hold US dollars? One way to answer the question is to think: “If I’m holding US dollars, the safest thing that I can do with my US dollars is to buy government bonds with it”. Now when you buy a government bond you earn an interest rate that depends upon the interest rate in the economy, so you could argue the attractiveness of the currency depends upon that interest rate. Imagine the interest rate in the US is now 5%. This means you can buy, let’s say, a 3 year government bond that will pay you 5% a year to just keep your money there.

Someone might look at that 5% return and argue that it doesn’t capture the entire picture. So let’s imagine that we have 100 dollars and we put it in a 3 year government bond that pays 5%. So at the end of 1 year we have 100 dollars that we put into the bond plus the 5% percent interest, so we have 105 dollars. Now these 105 dollars 1 year later might not be worth the same as 105 dollars the year before. The reason for this is because you might be able to buy less with those 105 dollars a year later because in that time the price level in the economy might have gone up. Let’s say the price in the economy went up by 1%. That 1% is the inflation rate and we’re going to define the real interest rate as = nominal interest term — inflation rate. So in our example the real interest rate is 5%-1% = 4%. So we think that this 4% real interest rate captures the attractiveness of holding money in US dollars because it is a measure of what we can buy a year later.

When is holding Gold attractive?

Let’s go ahead and think about how attractive each of these other two currencies are by the same metrics. We’ll assume the nominal interest rate in the ROW is 6% and the inflation rate is 1%, so the real interest rate is 5%. What should the nominal interest rates be for gold? When you buy gold you can’t take that gold and invest it in anything, all you can really do is have it sitting around somewhere. So we’re going to assume that the nominal interest rate for gold is 0%. In reality, it’s probably slightly negative because you actually have to pay money to store gold.

What should the inflation rate for gold be? It makes logical sense is to assume that the inflation rate is equal to how much new gold is brought into the whole gold market every year. We know from our previous video that there are about 2,600 tons of gold that are brought into the gold market (that has a total of 165,000 tons of gold in it) every year by miners and that implies an inflation rate of around 1.5% (2600/165000). So this implies that the real interest rate on gold is around -1.5% (0%-1.5%). So when the real interest rate in the US is 4% and ROW is 5%, gold with its -1.5% real interest rate does not look particularly attractive. However, lets imagine the economic situation changes such as a nominal interest rate in the US is equal to 0%, the inflation rate is equal to 5% implying the real interest rate is equal to -5% and in the ROW, the nominal interest rate is 0%, the inflation rate is 4% and the real interest rate is -4%. In this scenario gold with its -1.5% inflation rate starts looking more attractive. When the real interest rate gets lower and lower in world currencies, gold seems like a more and more attractive way to store the value of the money that you’ve learned. In this case where the real interest rates across the world is about -5%, you’d expect a lot of money from the US and the ROW might go into buying gold. All the money flowing into buying gold would likely change this exchange rate between gold and the US dollar such that 1 unit of gold becomes = 1500 US dollars instead of 1000 US Dollars.

Real Interest rates vs. the Price of Gold

So what you might expect to see historically is a relationship between the real interest rate in world currencies and the price of gold.The chart [SLIDE 5] shows the price of gold in US dollars (the pink line) and the real interest rate (blue line) in the US. I’ve excluded the real interest rate in the rest of the world partly to keep things simple and partly because people generally perceive the US dollar as being more safe than ROW currencies and so that data isn’t as important.

The green line on the chart shows where the real interest rate is about -1.5% which is what we are assuming is roughly the inflation rate of gold. Our hypothesis is that when the real interest rate in currencies approaches the real interest rate of gold people will start seeing gold as a alternative currency.The chart confirms this hypothesis to some extent. The circles on the blue lines show periods where the real interest rate is close to or below -1.5% and we see that they often occur at the same time as rallies in the price of gold.

Conclusion

The big picture here is that the price of gold might be related to the attractiveness of keeping money in other currencies and so when you go out and buy gold you are effectively betting that keeping money in other currencies will be increasingly unattractive.

Sources:
Gold data from Bloomberg
Real Interest Rate calculated from 3 Month Tbill Yields and CPI YOY from Bloomberg

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