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Paul
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 2:14 pm

You did start off with "I don't even understand why a risk-less portfolio must earn the risk-free rate (as we can easily make a risk-less portfolio that always loses money, or doesn't lose and doesn't earn)." So I'm as confused by your questions as you are by my answers! Is it just a case of >= and <= rather than =   ? There is the unspoken assumption that we aren't just throwing money down the toilet, that we are trying to earn as much as possible! So the arbitrage limits how much we can make.
 
PierreBoulez
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 2:42 pm

I feel so stupid right now, because now I'm again confused by your previous message.
I don't agree with the concept.
Even though the portfolio is risk-free, why does it need to earn the risk-free rate? Do we assume that the risk-free rate influences *everything*?
Or is it more like the real world, where if you put money in bonds you can earn a certain rate, but if you put it under your bed you won't earn anything?
Again, thanks a lot for taking the time for helping!
 
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Paul
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 2:47 pm

The assumption is that anything risk free earns the risk-free rate. (Or you earn less, the mattress, but you can't earn more.) It doesn't matter what form the risk-free asset/portfolio/thing takes (bank account or option+/-stock). 

If you found two risk-free things that gave the same rate (long or short, i.e. if you borrow then you pay that rate) then you borrow at the lower rate and invest at the higher rate, as much as you could get away with.
 
PierreBoulez
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 3:00 pm

Thank you!
So, if you can earn less - why is the risk-less portfolio earning the risk-free rate?
Can you give a construction of the no arbitrage argument for the case where shorting the option doesn't give you enough money to buy the stock?
 
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Paul
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 3:05 pm

Yes. You give me a thousand pounds and I’ll give you a thousand pounds in a year.
 
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bearish
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 3:26 pm

There is an issue of distinguishing between the model world and the real world here. In the model world, cash doesn't actually exist (and there is no mattress). You store value without taking on risk by investing in the riskless asset. And the risk free rate does indeed influence everything, in that the expected return on any investment is given by the risk free rate plus a premium earned for taking on risk. Not all risks will be rewarded with a premium, and some "premiums" can be negative, but no risk no premium. 
 
PierreBoulez
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 3:32 pm

Thanks bearish! So, am I correct in assuming that when considering risk-free portfolios, there is absolutely no need for a no-arbitrage argument?
 
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Paul
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 3:35 pm

Do you need my account details for the deposit?!
 
PierreBoulez
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 4:22 pm

Paul! To be fair, I am wiling to pay money to get a correct no arbitrage argument in the above scenario (where shorting the option doesn't give you enough money to buy the stock), conversely also willing to pay money to get an explanation reasoning why such a scenario can't even exist.
 
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Paul
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

February 18th, 2019, 4:45 pm

Thanks bearish! So, am I correct in assuming that when considering risk-free portfolios, there is absolutely no need for a no-arbitrage argument?
This is precisely when you do use the no-arb argument! Otherwise we'd be talking about something like stat arb.
 
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daveangel
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

July 10th, 2019, 12:27 pm

I have been away from Wilmott for close to 4 years and I see nothing has changed !
knowledge comes, wisdom lingers
 
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bearish
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

July 11th, 2019, 1:35 am

Welcome back - however fleetingly! The biggest change is probably the sudden death of ppauper. Some people (trackstar -- I'm looking at you!) would argue that he was the irritant that stimulated the production of pearls around here. As far as I'm concerned, he was just an irritant. But, for whatever reason, the cadence of postings has slowed down. 
 
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trackstar
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Joined: August 28th, 2008, 1:53 pm

Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

July 11th, 2019, 2:37 am

I have been away from Wilmott for close to 4 years and I see nothing has changed !
This is more of a topic for the OT, but let's provide some highlights that have direct relevance to the current state of affairs around here:

1) Indeed ppauper is AWOL and has been for a few months. Will he return? Unknown.  Also absent: outrun, CrashedMint, frolloos, numbersix, and many others. Greener pastures? Time-consuming pursuit of hotties? Marriage and family?! Intergalactic travel? Unclear...

2) I have also been taking an extended break. My only posts since May 7 have been the July 5th "airports of 1776" commentaries on "Trump - the last 100 Days." That was too good not to share!

But more importantly, 4 years ago (circa your departure):

3) Donald Trump was not President.

4) The Brexit vote had not happened.

5) Artificial Intelligence and Machine Learning had not yet taken over the world. (Here and elsewhere.)

6) The stock market had not shrugged off bad news repeatedly, reaching new and unfathomable highs. Next time it will be different... Or?

7) When the next Crash does come, there may be a Renaissance here on the Forum.

Signing off and back into the silence for now. 

Nice to see you though and hope all is well in Pax Brexitania!

I will set out the Lady Carlyle bone china in your honor tomorrow.

* edited because I misspelled frolloos. Apologies to him, it’s been awhile since I saw that name in print. : )
Last edited by trackstar on July 11th, 2019, 10:49 am, edited 2 times in total.
 
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trackstar
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Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

July 11th, 2019, 2:58 am

A theme song for Fall 2019.  High fidelity (just the way I like it) and the light show is out of this world.

Run Like Hell - Pink Floyd Live at Earl's Court 1994

https://www.youtube.com/watch?v=0dB6MQlFLu8
I saw this tour in the US. ~Nirvana~ : )
 
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frolloos
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Location: Netherlands

Re: Arbitrage when risk-free portfolio earns less than riskless portfolio

July 11th, 2019, 9:43 am


1) Indeed ppauper is AWOL and has been for a few months. Will he return? Unknown.  Also absent: outrun, CrashedMint, froolos, numbersix, and many others. Greener pastures? Time-consuming pursuit of hotties? Marriage and family?! Intergalactic travel? Unclear...
Observing Blue Tits in the garden actually. And once in a while answering questions on the stack exchange - no OT there. As for the others, perhaps fleeing the reign of AI/ML/NN.

Well, things have not changed much here. Signing off again.
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