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9

Sharpe ratio is defined as $\frac{(x - r)}{\sigma}$ where $x$ is return, $r$ is the risk free rate and $\sigma$ is volatility. Now levering up $n$ times multiplies both the return and volatility by $n$. But shouldn't the ratio change since $r$ stays the same? Ah, but remember, leverage isn't free. You have to fund leverage, and that cuts out of your return. ...


7

The key to this is to think about the enterprise value of a business separately from how it is financed. For simplicity sake, consider a business that comprises a sole gold bar (no workers, no extraction costs, etc). The value of the business is clearly just the value of the gold bar. If it were a listed company, with no debt, then the equity ...


4

The textbook academic answer is that Sharpe ratio is not impacted by leverage as explained by other answers. However, reality tells a different tale entirely: Imagine you lever up your investments by such amount that your future performance will critically hinge on the following conditions: That those who extended credit to you will not re-call their ...


4

Generally no. Sharpe ratio should vary linearly. Use leverage: the return increases, but so does volatility. De-lever" the return decreases but, so does volatility.


3

First of all you need a model to generate future returns, I assume you already have this. Since its just a model, there will be an unexplained component in the predictions made for every period $t$ and for every asset $i$. Let $\varepsilon_{t, i}$ denote this random innovation and $\mathrm{E}[r_{t, i}] = f(\varepsilon_{t, i})$ the expected asset return as ...


3

It depends obviously on which specific leverage you attempt to measure but you can certainly build some sort of index from, for example, the below: Aggregate smoothed equity P/E ratio divergence from long term mean (in a sense it reflects how money is levered to buy stocks at multiples of their long term P/E mean). Broad money in circulation -> Money ...


3

It depends a lot on the structure of the ETF, it could be : * In the "terms and conditions" of the (highly possible) total return swap of the fund * Portfolio insurance * Option combination (or cap & floor) I think it's in the swap details, already saw that a few times.


3

To answer your questions: 1) Yes, the above table is correct 2) Your results are correct except..... 1X loss = 9.6%. When you combine both positive and negative changes, it is the MEDIAN value that is of interest. Here are some links: http://www.futuresmag.com/Issues/2010/March-2010/Pages/Trading-with-leveraged-and-iinverse-ETFs.aspx ...


2

cost of leverage for equity only long/short investing is a function of the margin deal you can negotiate with your broker, if you have a large amount of capital. If you don't have significant capital to start with, then it's likely you'll only be able to get 2x leverage with a loan rate between 4% and 10% (retail reg-t margin rates at most brokers) This ...


2

High level Flow of funds comparative analysis for the U.S., Japan, and Euro Area by the bank of Japan. Country level report from the ECB. It is an 800+ page report so the link may take time to load (alternatively go to ECB data warehouse/reports/Euro Area accounts). Canadian financial flow accounts data.


1

I'd question the assertion in your question, what proof do you have that leveraged ETFs must go to zero? A plausible price pattern can easily be constructed that leads to a leveraged ETF that climbs forever. That same leveraged portfolio would climb forever as well.


1

Your math is right. If we normalize $W_{0}=1$, we have a return of $$ r\left(P\right) = P-1 $$ and a price-elasticity of return of $$ \epsilon\left(P\right) = \frac{P}{P-1} \mathrm{.} $$ If your price $P$ goes from its initial value $W_{0}=1$ to $P=2$, you make a return of $r\left(2\right) = 1$. If your investment has a final price of $P=3$, your return ...


1

It is true that you don't change your risk/return ratio but you can scale the ingredients of this ratio, meaning that you can e.g. scale up the level of risk you are prepare to take to also lever up your returns. Through that mechanism you can make use of very small spreads.


1

The key reason why you observe divergent performance patterns is related mostly to the following: The biggest reason is the different cost to hedge those products. The costs to implement and especially maintain the hedge on the long vs short side can be very different. Either the hedge is implemented through an index replication in which case the manager ...


1

There are three prices to consider when discussing an ETF: the ideal price as represented by the index, the NAV of the fund based on that day's holdings, and the market value traded on a stock exchange. This third price is what you see. In your example, Russell has calculated a cap-weighted value based on the annual membership. Direxion then determines ...


1

In a nutshell, the client only manages their own position, with the client credit line provided by the broker, whereas the broker manages all their clients' positions, using the broker credit line with their provider banks. You can work it out from there. Interest is presumably to do with cash deposits and loans.


1

Even in a perfect world, a 3X leveraged ETF cannot achieve a compound return three times that of the underlying. In the case of periodic discrete rebalancing, we call this effect the "arithmetic of loss and recovery," but even in the limit of continuous rebalancing, this effect does not disappear. Ito's formula tells us that $$\mathrm d ...


1

Your example could be correct but you're on the wrong track. Leveraged ETFs are designed for day trading, it isn't a leveraged 3x position that will return 3x the long term average of the name. The leverage is reweighted each day which will affect your performance. Eg if the market goes 100->99->100 the market is unchanged over 2 days. But a 3x ETF will go ...



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