23 votes

Sharpe ratio and leverage

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 $...
  • 349
10 votes

Sharpe ratio and leverage

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 ...
  • 14.1k
6 votes

Sharpe ratio and leverage

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.
  • 581
5 votes
Accepted

Why does rebalancing leveraged portfolios buy winners and sell losers?

Portfolio as it stands: 300% A -100% B Total: +200%. Ratio 1.5:0.5 Short additional 50% B. Now: ...
  • 3,619
5 votes

What is stopping me from using high leverage on high Sharpe strategies?

Not sure if "3-4 Sharpe" indicates the value of the Sharpe ratio you're earning since such magnitude is meaningless without some benchmark to compare against, due to it being a purely ...
  • 2,825
4 votes
Accepted

Max option leverage strike

Ciao, I'm studying this problem from a while. Let me post the graph obtained numerically. I've used the following parameters: $$ \left\{ \begin{array}{rcl} S &=& 2 \\ r &=& 0.01 \\ \...
  • 445
4 votes

How to trade leveraged ETFs

Quite a good article can be found here: http://seekingalpha.com/article/3140956-investing-in-leveraged-etfs-theory-and-practice Just selling a pair of leveraged ETFs to harvest the "volatility decay" ...
  • 27k
4 votes

Should the Sharpe ratio of a portfolio change when it is leveraged?

Let us assume: a constant risk-free rate $r$ a risky asset with returns $X$ with expected value $\mathbb{E}(X)=\mu_X$ and variance $\text{Var}(X)=\sigma_X^2$ a portfolio investing $w$ in the risky ...
  • 10.9k
4 votes

Use of interest rate swaps in liability-driven investing

Based on a Bloomberg article by Matt Levine, this is how it works: Pension funds have long-term liabilities: say a liability of £100 in 30 years from now. This liability will have a net present value, ...
  • 5,376
3 votes

What does it mean for an option strategy to be leveraged

There is a little known Greek called "lambda" or leverage which equals Delta times Stock price divided by option price $\lambda=\frac{\Delta . S}{c}$. So if $\lambda>1$ the option could be said to ...
  • 9,657
3 votes
Accepted

What is the source of the money in a leverage transaction?

You borrow that money from your broker. If you are retail client with for example IG they will offer this service to you. They will charge you some interest for the lending. There will be a margin ...
  • 1,411
3 votes

In FX trading, is the risk for long positions higher than for short positions, or vice versa?

I you take a long position in a stock the worst that can happen is the stock goes to zero, and you lose your investment. If you take a short position in a stock, you have the potential for unlimited ...
  • 5,638
3 votes
Accepted

Implementing leveraged Risk Parity Portfolio using Direxion 3X ETF

Apologies in advance for being hyper-critical. I have somewhat strong feelings about this =P The purpose of risk parity is to improve portfolio efficiency via achieving better diversification. (We ...
  • 10.9k
3 votes
Accepted

How does the Collateral in Collateralized Loan Obligations (CLOs) Work?

The loans are placed in a vehicle company (“special purpose vehicle” or SPV). This company issues various tranches of debt and purchases the loans from the marketplace. There is no specific posting ...
  • 14.3k
3 votes
Accepted

The relationship between volatility of underlying asset, leverage and the volatility of the derivative

The key variable is indeed the derivative's elasticity $\Omega$ (aka leverage, Lambda). It is defined by $$\Omega=\frac{\frac{\partial V}{V}}{\frac{\partial S}{S}}=\frac{\partial V}{\partial S}\frac{S}...
  • 14.1k
3 votes
Accepted

What kind of option would best be suited for a price based algorithm?

You may be looking for synthetic longs/shorts which would be buying/selling an ATM call and selling/buying an ATM put. This will give you leverage while nearly replicating the underlying. I would ...
3 votes

How do leveraged ETFs achieve their investment objectives?

Q1 How leveraged ETFs achieve their leverage: Depending on the fund house's strategy, leverage is typically achieved by investing in futures, swaps, by borrowing funds, or a combination of above. You ...
  • 31
3 votes

Leveraged ETF pair trade, where's the gamma/convexity?

Both products actually have positive convexity, they will buy more underlying (SP500) when the price goes up and sell it when it goes down. However, if you hedge every day, you will just cancel out ...
  • 2,878
3 votes

Leveraged ETF pair trade, where's the gamma/convexity?

I disagree that these products are convex*. At any point in time, the ETF exposure to the underlying is linear, it's just that it changes through time. A 2x ETF will just have 2x exposure to the ...
  • 2,446
3 votes

Leveraged ETF pair trade, where's the gamma/convexity?

As @Lliane explains, you are actually describing a position in which the underlying is rebalanced everyday, hence the compounding effect of the leveraged ETF vanishes. Maybe a bit of modelling can be ...
3 votes
Accepted

Operating Leverage Interpretation

Operating leverage $k$: $$k=\frac{Quantity*(Price-AVC)}{Profit}$$ but profit (actually operating profit) is: $$Profit=Quantity*(Price-AVC)-FixOpCosts$$ If quantity sold increases by $a\%$ then our new ...
  • 836
2 votes

How to trade leveraged ETFs

One standard strategy is to short both "bull" and "bear" ETFs (usually called "double short"). A bit naive heuristics is that if you're loosing money holding a long position due to volatility, you can ...
  • 1,533
2 votes
Accepted

How does tranching cause leverage?

The leverage is conceptual (as you're not borrowing something to buy more of something in the standard form of leverage). I think it'll become clear when you compare an equity tranche position to a ...
2 votes

Data on banks’ leverage

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 (...
  • 1,335
2 votes

Why does the Sharpe ratio not change when the strategy is leveraged?

Sharpe ratio = $\frac{r_p - r_f}{\sigma_p}$, where: $r_p$ is the expected portfolio return $\sigma_p$ is the portfolio's standard deviation $r_f$ is the risk free rate. When you leverage '$n$' ...
  • 758
2 votes
Accepted

What does it mean for an option strategy to be leveraged

In general any investment position is said to be leveraged, if it is financed by a debt position. This is with regards to options, stocks or any other security. Say you buy an option with maturity in ...
2 votes
Accepted

Leveraged Permanent Portfolio Using ITM Call Options

I can see the genius is your investment thesis. I looked at the probability analysis in TOS and found that it is highly unlikely that the above options will go OTM on Jan 2019. Which means, this is ...
  • 48
2 votes

Are leveraged ETFs cheaper than using leverage?

Leveraged ETF have negative gamma: the higher the volatility of the underlying index the bigger the negative drag. This is a big pitfall of those instruments because one can be correct with the ...
  • 2,137
2 votes
Accepted

Do I need that extra cash to exercise call or put options?

This would depend on whether the option you bought is cash- or physically-settled. Let $V_t$ be the intrinsic value of your option at time $t$, $T$ its maturity and $y$ the number of shares it gives ...
2 votes
Accepted

In FX trading, is the risk for long positions higher than for short positions, or vice versa?

[Your] analysis is correct. The long trade is worth 100 - 100/FX, and the short trade is worth 100/FX -100, where FX=ending EURUSD exchange rate. The first expression has unlimited downside as FX -> 0,...
  • 9,167

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