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6 votes
Accepted

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, ...
Jan Stuller's user avatar
  • 6,178
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: ...
Phil H's user avatar
  • 3,679
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 ...
develarist's user avatar
  • 3,030
5 votes
Accepted

If someone is comfortable with 100% stocks, why shouldn't they just build a stock/bond portfolio and lever it to match the volatility of 100% stocks?

I think @nbbo2 nailed the answer to this question in comments (upvoted). But, to answer the question solely by its title: One reason you would not run a levered portfolio with matched volatility is ...
Brian B's user avatar
  • 14.9k
4 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 ...
Chris Taylor's user avatar
  • 5,931
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 ...
SRKX's user avatar
  • 11.1k
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 \\ \...
clarkmaio's user avatar
  • 455
4 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 ...
dm63's user avatar
  • 17.2k
4 votes

How do you define the NAV of a leveraged ETF?

Are you familiar with how a futures trading account works? You deposit a certain amount of cash. When you "buy" a future this does not use up any cash, nor is the future shown on your ...
nbbo2's user avatar
  • 11.4k
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 ...
Quantoisseur's user avatar
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}...
Kevin's user avatar
  • 16k
3 votes

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

How it works has been described clearly by dm63. I commend that answer. I would like to add a few words about "collateral", what does it refer to? Obviously the buyers of the debt tranches ...
nbbo2's user avatar
  • 11.4k
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 ...
Daneel Olivaw's user avatar
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 ...
will's user avatar
  • 2,581
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 ...
Lliane's user avatar
  • 2,908
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 ...
Jacobi's user avatar
  • 31
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 ...
Helin's user avatar
  • 11.8k
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 ...
nbbo2's user avatar
  • 11.4k
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 ...
emot's user avatar
  • 876
3 votes

How do you define the NAV of a leveraged ETF?

I am not 100% sure, but I think taking a close look at one leverage ETF, it's NAV and holdings may help. Let's take an example: TQQQ - UltraPro QQQ (which is a 3x leveraged NASDAQ ETF) If I download ...
phdstudent's user avatar
  • 8,421
3 votes
Accepted

Optimal leverage for strategy with normal returns

Assuming you are compounding returns, the optimal strategy is given by: μ/σ^2 For your strategy this is 0.05/0.01 = 5x, but because of your constraint of a maximum of 2x, then you'd choose 2x. From a ...
Newquant's user avatar
  • 804
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 ...
Fuce's user avatar
  • 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 ...
Ezy's user avatar
  • 2,187
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 ...
Daneel Olivaw's user avatar
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,...
Alex C's user avatar
  • 9,382
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 ...
dms_quant's user avatar
2 votes
Accepted

Volatility of a leveraged CFD portfolio

Here is an Excel example that I happened to have on my desktop. There are two assets (Asset1 and Asset2). Their respective weights are below their names. In this example, Asset1 has a "1" as the ...
amdopt's user avatar
  • 4,348
2 votes

How do leveraged ETFs achieve their investment objectives?

The daily holdings for TQQQ is available here https://www.proshares.com/funds/tqqq_daily_holdings.html. They use a combination of swap contracts on the Nasdaq 100 with different banks, futures ...
Freelunch's user avatar
  • 1,086
2 votes

Implementing leveraged Risk Parity Portfolio using Direxion 3X ETF

Here is my take on trying to answer this question. My backtest goes as far as December 1979 (just before the great bond bull run). I used daily total return index for Wilshire 5000 and 10-year ...
Bruno Carneiro's user avatar
2 votes

What does leverage have to do with beta?

Your leverage will be the amount of money you borrow to buy the risky portfolio P. Intuitively, the more you borrow money to buy P, the more you are exposed to market behaviour and so β will be high. ...
JeanGuillaume's user avatar

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