Fear and Greed: The Market Price of Risk

FearAndGreed

The Market Price of Risk is a much-neglected quantity. It is a concept that you’ll find in models of incomplete markets. In a nutshell, if a market is incomplete and you can’t hedge away some risk then you have to say how that risk is valued. The Market Price of Risk (MPR) quantifies this, and allows you to price all derivatives on the same underlying(s) consistently with each other. (If they have the same source(s) of risk then those risks ought to be treated alike.)


You don’t see it discussed much because we tend to talk about the risk-neutral world alone, whereas the MPR defines the difference between the real and risk-neutral worlds. (You’ll find the MPR in the drift of the stochastic variables.) And once you calibrate to the market prices of derivatives you won’t see it anymore. (That’s why it’s hard to spot in the HJM and BGM models which calibrate right from the start.)

Nevertheless this quantity is very important since it levels the playing field for all investments, no matter how complex. You see it in Markowitz’s Modern Portfolio Theory, and the MPR for each source of randomness and the correlations between them can be used to choose optimal portfolios.

But what does the MPR look like? Is it a time-stable constant, representing the compensation for taking risk of rational investors. Is it slowly varying representing the changing attitude towards risk of different generations? No, neither of these. The figure above shows what the MPR looks like for US interest rates. (Technically, this is the Market Price of Spot Interest Rate Risk.) It appears random. The spikes can be interpreted as over or undercompensation for taking risk, fear versus greed.

Details of how to find this MPR and how to use it for modelling as a second stochastic factor (incidentally, introducing the Market Price of Market Price of Risk Risk!) and also for trading, as in stat arb, can be found in Ahmad, R & Wilmott, P 2007 The Market Price of Interest-rate Risk: Measuring and Modelling Fear and Greed in the Fixed-income Markets. Wilmott magazine, January 64-70.

Total Views: 631 ,

Related Posts

At Last: Education, Education, Education Theresa May wants to bring back grammar schools. According to one poll 60% of the British public agree with this idea. If I'd been asked I would have ...
“Algo My Way, You Go Your Way” My upcoming talk at the Quant Insights conference, 14th October, London, will be "Algo My Way, You Go Your Way - Four Decades in Business." More detai...
All Mod Cons For the UK and wilmott.com it's that once-in-a-generation moment. A new bathroom? No! While Mark Carney performs his fine balancing act of talki...
Sir Bob Geldof, We Who Are About To Thrive Salute ... A big, big thank you from those of us who wanted out of the EU to: Lord Stuart Rose, leader of the Remain camp, for his timely confession Da...
How I Successfully Forecast The Result Of The EU R... Gosh, this is embarrassing. I seem to have done the double. This is a sequel to my blog from last year How I Successfully Forecast The Results Of T...
A Proper Analysis Of The EU Referendum Polls I've been following the polling with obsessive interest. And finding the analysis somewhat feeble. I'm going to very quickly address the topic of poll...
Things That Haven’t Been Said About The EU R... Debate? Debate?? They don’t know the meaning of debate! The two sides have both in their own ways been like broken records. The same old arguments ...
Why I And All My Rich Pals Are Voting To Stay In T... I’m relatively rich. I can afford private healthcare. I don’t have to worry about long waiting lists for operations or the impossibility of getting...