The possibility that a negative event (such as a loss) will happen.

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6
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1answer
2k views

How can I use Entropy-pooling of Atillio Meucci to constuct a portfolio?

I am trying to get my hands on Entropy Pooling which was introduced by Meucci in this paper. As an example, assume I want to construct a portfolio with five stocks and I have my view on CVaR. How ...
6
votes
1answer
5k views

Annualzing the log of daily returns riddle

Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
6
votes
2answers
216 views

Is it better to grade hedging strategies based on the sum of absolute or squared hedging errors?

Let's say I have one strategy that has a hedging error of: 2, 2, -2, -2 Let's say I have another strategy that has a hedging error of .5, .5, 3, 3 Would it be a better idea to grade the hedging ...
6
votes
1answer
527 views

Calculating VaR/CVaR on high frequency data and returns

As we converge on the minute time scale and below for our unit time interval, the return distributions tend to be leptokurtotic and more discretized (due to fixed values such as minimum price ...
5
votes
7answers
2k views

Recommendation for a book on CVA/Credit Risk and PD/LGD/EAD modeling?

I need suggestions for some good books on the following topics: Credit Value Adjustment (CVA) / Credit Risk Probability of Default / Loss-Given-Default / Exposure-At-Default modeling Any pointers ...
5
votes
4answers
841 views

Do low volatility stocks outperform high volatility stocks over the long run?

A recent article from Forbes seems to indicate that low volatility stocks outperform high volatility stocks over the long run. Does anyone have any supporting or contradicting evidence to this claim? ...
5
votes
3answers
125 views

Which lags or percentiles should be run in a batch when calculating Value-at-Risk?

Are there any "standard" VaR calculations run in a batch? For example, testing a VaR calculation with a lag of 1,2, 5 or 10 days over 2 years? Same question for the percentile, 1%, 2.5%, 5% etc.
5
votes
2answers
460 views

Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction. The sell point of these priors ...
5
votes
2answers
490 views

What is the significance of Relative Risk Aversion

I know that the relative risk aversion is defined as $$R(c) = cA(c)=\frac{-cu''(c)}{u'(c)}$$ where $u(c)$ denotes the utility curve as a function of wealth $c$. But I do not understand the intuition ...
5
votes
1answer
1k views

Value at Risk backtesting (kupiec)

I m doing my research on estimating Value at risk using different assumptions on volatility and then compare my results based on backtesting. I obtained results and just on question based on my ...
5
votes
1answer
290 views

Are there any well known methods of testing through-the-cycle rating systems?

Rating systems, as defined by the Basel II Accord, can be classified into two broad types - through-the-cycle (TTC) or point-in-time (PIT) - and the probability of default predicted by such a system ...
5
votes
2answers
246 views

Impact on bid/offer due to volume/size of trades placed

When observing bid/offer in the market I came across a question. How much trading a bond would impact its spread for subsequent trades ie. what is the impact on bid/offer due to volume/size of ...
5
votes
2answers
307 views

quantiative risk measure how they are implemented in R and their use

So far I have just theoretical knowledge of risk measure and never used them in application. Therefore I have some basic question how risk measures are used in reality and how they are implemented in ...
5
votes
1answer
416 views

Definition of risk factors for market risk scenario testing

I am doing a research for stress testing in market risk. The usual process I found out for scenario testing is: Define risk factors upon the portfolio Define the desired scenarios Vary the risk ...
5
votes
1answer
150 views

Are there quantitative models which can guide one's choice of target risk?

Note: This question was written for the weekly topic challenge. Many asset allocation funds presume the investor knows his target risk level, typically on some spectrum from conservative (mostly G7 ...
4
votes
3answers
499 views

Why should there be an equity risk premium?

After years of mathematical finance I am still not satisfied with the idea of a risk premium in the case of stocks. I agree that (often) there is a premium for long dated bonds, illiquid bonds or ...
4
votes
1answer
510 views

Why using the swap curve as riskfree rate and no longer gov bonds?

I recently had an interview where I was asked what to use as risk-free rate. In all my textbooks it was always the US treasury yield curve. But they said no its now the "swap curve". Why is the swap ...
4
votes
3answers
397 views

Why are factor models so popular for risk analysis of portfolios?

As titled, my question consists on asking for why in the most of academic papers one almost always finds that when you try to model asset returns, one needs to adjust for risk factors before analyzing ...
4
votes
2answers
2k views

Computing the Sharpe Ratio

The building blocks of the Sharpe ratio—expected returns and volatilities—are unknown quantities that must be estimated statistically and are subject to estimation error. The main problem I have is ...
4
votes
1answer
165 views

questions on VAR manipulation

The book of Financial Risk forecasting by Danielsson gives the following example about VAR manipulation. I have two questions: 1) If $0> VAR_1 > VAR_0$ , why the following figure plots it as ...
4
votes
2answers
123 views

Estimating an appropriate haircut for illiquid stocks

I am trying to determine an appropriate haircut for a basket of illiquid stocks that barely traded during the year. Can someone suggest me an approach to estimate the risk? My dataset has a lot of ...
4
votes
1answer
2k views

Performance Attribution : Annualizing alpha & factor return contributions

Let's say I have a factor model which I am using for Performance Attribution. I'd like to separate returns from alpha vs. returns from exposure to various risk factors. For each date, the factor ...
4
votes
1answer
130 views

Optimal Choice of exceeding time

Suppose you hold a share from company $Z$ whose vaue at time $t$ is $S_0+\sigma B_t$ where $B_t$ is Brownian Motion and $\sigma$ denotes some volatility. Now lets assume that company $Z$ may go ...
4
votes
1answer
151 views

Estimating investor's utility from the trades data

Is it possible to infer investor's utility function from the set of decisions she is making? Let's assume for simplicity that the market consists of a single traded asset whose return distribution is ...
4
votes
1answer
447 views

How to model the risk of a CFD

I'm struggling to understand why the risk on an equity CFD is not the same as for the corresponding equity. The RiskMetrics FAQ mentions two ways to model a CFD, but it does not explain why this is ...
3
votes
9answers
600 views

Why would there be a positive risk-free rate?

Most financial models include a risk-free rate or risk-free asset. Why should there be such thing as a positive risk-free rate? I dont see why an asset would provide a positive (real) return if it ...
3
votes
2answers
939 views

Covariance for arbitrarily large portfolios

I am implementing a method in Java to calculate the variance, covariance, and value at risk for a portfolio, which should be flexible for use with any number of assets in a portfolio. I am struggling ...
3
votes
1answer
230 views

Risk and Reward in practice

My question is a bit philosophical. As a risk manager I often have to tell portfolio managers to reduce risk (e.g. due to VaR limits or exposure limits). Then usually the discussion arises that if ...
3
votes
1answer
167 views

How do I model risks for specific short-term short calls in a portfolio with limited data?

I'm trying to do some risk analysis on a portfolio of bonds, currency, stocks and short calls. The short calls expire in approximately 15-30 days and I've only got around 20 days of pricing data on ...
3
votes
2answers
750 views

Where can I find a list of VaR and CVaR formulas for continuous distributions?

Where can I find more VaR and CVaR formulas for continuous distributions? I collected a list here:
3
votes
2answers
77 views

Dollar-Neutral Strategy

Here is an excerpt from E. Chan's book Quantitative Trading, However, if the strategy is a long-short dollar-neutral strategy (i.e., the portfolio holds long and short positions with equal ...
3
votes
2answers
54 views

Can Economic Capital cover Regulatory Capital?

If economic capital is set by the institution to cover unexpected loss (given a confidence level) and regulatory capital is set by the regulator, can one "absorb" the other? For example, if I ...
3
votes
2answers
372 views

Why is that a risk averse consumer buys the optimum insurance when there is actuarially fair insurance?

I think I understand the fact that when marginal utilities of the same function are equal (a consequence of the actuarially fair insurance), the independent variables in it must be equal -- right? But ...
3
votes
1answer
93 views

Is this comment right about subadditivity?

I found this comment in a book I bought about risk management: Risk Management in Banking by Joel Bessis. This is the well-known rule that states that the sum of individual risks is less than ...
3
votes
1answer
101 views

Spectral and distortion risk measures

Is there any difference between the spectral and distortion risk measure? Or is it just a different name for the same kind of risk measure?
3
votes
2answers
89 views

Futures Parameters for Value at Risk

I am new to risk management. I am calculating the VaR for a portfolio of futures contracts, long and shorts. I calculated it using the historical, parametric, and ...
3
votes
1answer
231 views

Constant Relative Risk Aversion

The question: Consider a person with constant relative risk aversion p. (a) Suppose the person has wealth of 100,000 and faces a gamble in which he wins or loses x with equal probabilities. ...
3
votes
2answers
76 views

Mathematical definitioln of Potential Future Exposure

I have come across a risk measure called "Potential Future Exposure" and I have not really understood the meaning of it. Knowing that this has to do with counterparty credit risk, I read different ...
3
votes
1answer
129 views

What are recent important papers on credit portfolio risk modeling?

I'm interested in papers which consider mathematical models of risks of different portfolios of retail credit. This is not my area of research, so I may be misusing some terms. The idea is simple: I ...
3
votes
1answer
240 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
3
votes
1answer
72 views

Longevity risk modelling

What is Longevity risk, and how to model it under DC and DB pension plans? characters|characters|characters|characters|characters|
3
votes
1answer
277 views

Which is the better risk sensitive measure?

Consider the two following optimization problem 1) $$ \min_{\theta} \ln E_{\theta}[ e^{X}]$$ 2) $$ \min_{\theta} E_{\theta}[ X]$$ with the constraint $$ Var_{\theta}[X] <c$$ Is it true that ...
3
votes
2answers
77 views

Finding Credit Risk Population Data

Are there any free or relatively cheap sources of aggregate data on credit risk for specific geographic regions, ages, and so on?
3
votes
1answer
288 views

Which measure to determine Risk?

Say I hold an equity and I want to calculate the Value-at-Risk over some period. Would one calculate the Value-at-Risk of the equity under a risk-neutral (as in martingale) measure or under the ...
3
votes
3answers
318 views

Risk prediction based on financial statements

I have a profit loss statement and balance sheet with the following fields: Example P&L Turnover420,363 - Cost of sales £118,730 £140,169 - Gross Profit ...
3
votes
1answer
821 views

Risk-free rate for ex-post evaluation of investment strategy

When evaluating the strategy ex-post using e.g. Sharpe ratio, what should one use as the risk-free rate? Let's suppose I am using a 1Y sample of weekly returns, sampled between 2012-01-01 and ...
3
votes
1answer
566 views

Long-term vs short-term strategies \ investing

Suppose most investors have very short investing horizons and use appropriate (for them) strategies, but investor X has a very long horizon. He would like to trade some advantages (early withdrawal ...
3
votes
0answers
50 views

Non-parametric estimator - CVAR / Expected shortfall

Is the estimation of the CVAR using known non-parametric methods (histogram , kernels) is different than the estimation of any other R.V.? If the answer is yes, then I am interested to know whether ...
3
votes
0answers
56 views

What is the difference between gross and net enterprise wide risk?

Reading a Basel paper on recommendations on internal economic capital models. One of the recommendations says members of the bank's board should be able to demonstrate understanding of the difference ...
3
votes
1answer
36 views

What is the date of reserve (operational risk)

One of the BCBS papers on operational risk says the following: Consistent with other operational risk losses, a bank should use a date no later than the date of reserve for including legal ...