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Anthis
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Joined: October 22nd, 2001, 10:06 am

How is risk defined in mathematical terms?

January 13th, 2003, 1:46 pm

Kr you are rightThe following text is taken from Truman F. Bewley (2002) : “Knightian decision theory. Part I” Decision in Economics and Finance pp79-110“A random variable is risky if its probability distribution is known, uncertain if its distribution is unknown. Knight argued that uncertainty in this sense is very common in economic life and he based a theory of profit and entrepreneurship on the idea that the function of the entrepreneur is to undertake investments with uncertain outcome.”RegardsAnthis
 
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Johnny
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Joined: October 18th, 2001, 3:26 pm

How is risk defined in mathematical terms?

January 13th, 2003, 2:03 pm

"A random variable is risky if its probability distribution is known, uncertain if its distribution is unknown"I believe that Keynes argued that it wasn't even possible to know what states of the world could exist, let alone ascribe probability distributions to them.
 
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WaaghBakri
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Joined: March 21st, 2002, 4:07 am

How is risk defined in mathematical terms?

January 14th, 2003, 5:58 am

An old but neat quote posted by rgowka1 on the Profound Quotes thread: "Nothing in nature is random..... A thing appears random only through the incompleteness of our knowledge."- Spionza Ethics 1 and I wonder if we can paraphrase it ...."Nothing in nature is risky..... A thing appears risky only through the incompleteness of our knowledge." Okay, okay, I know I've murdered an elegant quote ......
 
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verhoeven
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Joined: January 20th, 2003, 8:04 am

How is risk defined in mathematical terms?

January 29th, 2003, 12:46 am

This is valid in terms of beta risk, not standard deviation!
 
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slowlearner
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Joined: September 27th, 2002, 12:15 pm

How is risk defined in mathematical terms?

February 7th, 2003, 4:41 pm

Can you cite examples of assymetrical distributions?
 
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baekhoefe
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Joined: November 1st, 2002, 12:01 pm

How is risk defined in mathematical terms?

February 17th, 2003, 5:43 pm

Examples of asymetric distributions are provided by:1) Hedge Funds returns2) Credit Losses expressed as a % of a loan portfolio exposureFP
 
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Buscador
Posts: 48
Joined: July 14th, 2002, 3:00 am

How is risk defined in mathematical terms?

February 24th, 2003, 4:58 pm

Some asymetric distributions are Gumbel pdf (Extreme Values)Fisk pdf (also known as the log logistic)Weibul pdf (By the way Walodi Weibul and Gumbel were friends)Lognormal pdf (of course)There are several more and I suggest that you get hold of the late Sir Maurice Kendall's tome!
 
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nikol
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How is risk defined in mathematical terms?

February 25th, 2003, 2:23 pm

generaly speaking, VAR is determined as quantile:knowing parent distribution of portfolio PnL and threshold probability, the VAR is known as well.another story is how to get idea what parent distribution is and how to estimate its parameters. This is usualy described in chapters "Parameter estimation" and "Hypothesis testing"
 
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verhoeven
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Joined: January 20th, 2003, 8:04 am

How is risk defined in mathematical terms?

June 12th, 2003, 12:17 am

You may need to be aware of the distinction between uncertainty and risk.The Oxford Reference Dictionary defines risk as ‘The possibility of meeting danger or suffering from harm or loss.’The Merriam Webster Dictionary defines uncertainty as "indefinite, indeterminate” and "not known beyond a doubt."In his PhD thesis ’About Risk and Profits’, Knight (1921) tries to make a distinction between risk and uncertainty. “It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We shall accordingly restrict the term "uncertainty" to cases of the non-quantitive type.” (Knight, 1921, paragraph I.I.26)Thefore, it is evident that attributing the term risk to the uncertainty of future economic outcomes is potentially inaccurate and often misleading. Knight sets out to study (amongst other things) this distinction as follows: 1. With the case of risk, the probabilities that certain events will occur in the future are measurable and therefore precisely known, i.e., there is randomness but with measurable probabilities. This can be further distinquished into: • a priori risk, for example, the outcomes of the toss of a fair coin; and• estimable risk, where the probabilities can be estimated through statistical analysis of past experience, for example, the probability of a fire in a particular factory in the next year. 2. In the case of uncertainty, the probabilities of future events are indefinite or incalculable. This is because the situation dealt with is too irregular or to a high degree unique, for example, the likelihood of success of a brand new product. The realm of risk is therefore one of measurable uncertainty (randomness with measurable probabilities), which is the focus of QF, whereas uncertainty is the unexpected and unquantifiable risk. which can be dealt with stress testing. Hence, risk entails not only an estimated possibility of loss, it also entails the uncertainty of loss. Practically, this means that you may need to think not only about the probable but also about the improbable.
 
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verhoeven
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How is risk defined in mathematical terms?

June 12th, 2003, 12:27 am

In reply to: newton: "Risk, it appears, has an interesting math property: Risk (A+B) = Risk(A) + Risk (B) ; yes, it's linear." This is complete nonsense! Ever heard of the concept of asset diversification? You seem to have forgotten about the "time" aspect, i.e., the covariance between asset returns.
 
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oneinfinitezero
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Joined: June 28th, 2003, 3:18 am

How is risk defined in mathematical terms?

July 2nd, 2003, 8:10 pm

QuoteOriginally posted by: verhoevenIn reply to: newton: "Risk, it appears, has an interesting math property: Risk (A+B) = Risk(A) + Risk (B) ; yes, it's linear." This is complete nonsense! Ever heard of the concept of asset diversification? You seem to have forgotten about the "time" aspect, i.e., the covariance between asset returns.How does the covariance between asset returns increase or decrease the overall risk? The assets covary whether or not you put them into a single portfolio... the covariance is not a function of the model; however, the model may be a function of the covariance...someone who knows more please explain this to me a bit further if you would... thanks.
 
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oneinfinitezero
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How is risk defined in mathematical terms?

July 2nd, 2003, 8:15 pm

ignore that last post; i'm confusing myself. (where's the delete button?)
 
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Netwalker
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Joined: July 14th, 2002, 3:00 am

How is risk defined in mathematical terms?

August 10th, 2003, 8:18 am

How is risk defined in mathematical terms? Interpreting the market risk as variance of returns, shouldn’t we define the variance in mathematical terms? I suggest the theory of quadratic variation:V(t) = r^2(t,1) + … + r^2(t,k)where V(t) is the variance of returns within the period t, r^2(t,i) are squared returns sampled k times over the period t.If [k -> infinity] then [V(t) -> V_true(t)], where V_true(t) is the true variance within the period t.Is that mathematical enough?
 
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captainharlock
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Joined: May 28th, 2003, 12:39 pm

How is risk defined in mathematical terms?

August 11th, 2003, 2:50 pm

a question (curiosity) to everyone.Practitioners and academics assume returns are, generally, normally distributed or however, simmetrically and use standard deviation (or variance) as a measure of stock return variability.But if returns are not well described by a symmetric distribution, how can I have an idea of the error I do if I keep on calculating risk as standard dev. or variance?