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

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1answer
275 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
3
votes
1answer
235 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. ...
1
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0answers
48 views

Comparing cost of two alternative given their distribution

I have distribution for cost of two alternative through Monte Carlo simulation. The distributions are not normal. Given the benefit of the two alternatives is the same but ungiven, I want to choose ...
1
vote
1answer
266 views

Which sports are generally the best for trading on betting exchanges for a profit?

I am looking at trading bets on tennis, football and horse racing in particular as these appear to have the most liquidity. How much background research and how much trial and error is generally ...
0
votes
3answers
351 views

Parametric/Analytical VaR

Suppose I want to calculate VaR for a known distribution with mean $\mu$, variance $\sigma^2$ and $\alpha$-quantile as, $VaR_{\alpha}$ = $\mu + \sigma q_{\alpha}$. For a Gaussian distribution it is ...
2
votes
1answer
70 views

Variability in the Expected Shortfall estimator

Are there any results for calculating the variability in the Expected Shortfall measure. I am looking for Large sample confidence intervals under Normality for Expected Shortfall or calculation of ...
1
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0answers
146 views

Risk measures, Risk Management and Financial Risk Area

I'm currently searching material about market risk and I learned about coherent risk measures, VaR, CVaR (or expected shortfall), volatility. All that because I have to make a Financial Risk Area for ...
3
votes
2answers
962 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:
2
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1answer
56 views

What are the properties of the Expected Shortall measure when split in multiple time periods?

Suppose I have a single time series of losses $L$ that consists of two sub-parts $L_1$ and $L_2$. Is there a relationship that relates the expected shortfall of $L$ to the expected shortfall of $L_1, ...
6
votes
4answers
809 views

Is there anyone still using Markowitz modern portfolio theory?

I was reading about the MPT (Use standard deviation as risk measure) on "Mathematics for Finance by Marek Capinski". I was just wondering is there anyone actually applying this theory to their ...
0
votes
1answer
299 views

CAPM (SML) Problem

I got 1.3636 for beta for the problem below(165/121). But I became so unsure about the answer when I solved (c) because then the market risk becomes larger than the variance of Stock A. ...
3
votes
9answers
643 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 ...
1
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1answer
52 views

Hedging using relative values

Consider I have two stocks $A$ and $B$, $A$ is trading at $\$40$ and $B$ at $\$30$. The standard deviation of its returns are $\sigma_A=25\%$ and $\sigma_B = 30\%$. Correlation between the returns is ...
2
votes
0answers
106 views

Beta distribution - Holding period

Let's say I have a risk factor that is defined between [0,1], such as recovery rates. Assuming I have daily data, I can estimate the "daily VaR", i.e. the tails over 1 day period, since the data is ...
1
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0answers
58 views

how to find CVaR/AVaR for triangular fuzzy no

While going through different methods of risk measure i came across AVaR/CVaR, while i was calculating AVaR/CVaR in credibilistic environment using VaR, i got stuck in the calculations eg. For ...
8
votes
3answers
2k views

Gamma vs. Volatility Risk

Original Question: What is the link between Gamma and the Volatility Risk? It leads me to ask: - What is the Volatility Risk definition and what are the good practices to measure it? Thinking about ...
2
votes
4answers
430 views

Implementing A 50/50 Prediction Model Strategy

Reworded the question for clarity (see edits for original post): How can one knowingly foresee where a 50/50 prediction model will be profitable? For previous posts: I understand that if I have a ...
1
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0answers
38 views

Doubt on risk cost criterion

I want to minimize some kind of risk sensitive cost. But, I am confused what cost criterion should I use. I am aware of only expected exponential utility. I want to know what are the other such ...
2
votes
0answers
41 views

Formal Proof of Immunization Techniqu

Please correct me if I am wrong in understanding the Immunisation Technique behind bond interest rate risk management. It says that any change in interest rate can be neutralised by reinvesting the ...
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0answers
53 views

proper choice of risk aversion parameter in the risk-sensitive cost-criterion

Suppose I want to minimize certain risk sensitive cost. Is it a valid question to ask what is the proper (also in which sense) choice of risk aversion parameter in the risk-sensitive cost-criterion ? ...
0
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0answers
595 views

Difference between “basic risk” and “basis risk”

Returning to Futures contracts, basic risk refers to the risk remaining after the hedge has been put in place and essentially represents the difference between the Futures price – should the ...
4
votes
1answer
174 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 ...
-1
votes
1answer
92 views

Math basics of Equally-weighted Risk contributions

i'm writing my BA Thesis about "Equally-weighted Risk contributions". Can anyone recommend math books for further understanding of Risk contributions?
16
votes
2answers
753 views

Concentration risk in credit portfolio

How do you model concentration risk of credit portfolio in IRB/Basel II framework?
7
votes
3answers
979 views

cointegration applied to Portfolio Construction & Risk management

There are all sorts of applications of cointegration to generating alpha on mean-reverting timeseries: comparing spot vs. futures, bond spreads, identifying mean-reverting residuals, etc. But there ...
1
vote
2answers
142 views

Basis Risk for Futures/Options

I am just reading about basis risk. It is being described as risk of the price of the hedging instrument not fluctuating the same as the instrument itself. I was just wondering, if we bought a ...
0
votes
1answer
827 views

Directional/Non-Directional Risk

Can someone explain to me what is direction/non-directional risk? Went through few sites but couldn't understand much.
1
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1answer
151 views

regarding Basel II III model

I may have to get involved in some projects using Basel II, III model for risk modeling, to which I have no background. Are there any good book/tutorials to recommend? What are the underlying ...
7
votes
4answers
2k views

What does it mean to modify the factor loadings of a credit risk model?

I came across an example where a well-known weakness of a credit risk model was dealt with by augmenting some of the existing risk factors via increased factor loadings. This made the the model more ...
21
votes
7answers
12k views

How does the “risk-neutral pricing framework” work?

I've struggled for a long time to understand this - What is this? And how does it affect you? Yes I mean risk neutral pricing - Wilmott Forums was not clear about that.
1
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1answer
634 views

Ex-Ante tracking error how to determine the look back period

I am looking to compare the ex-ante predictions against the post values. I am using a look back period of ranges from 1 year to 5 years to construct my covariance matrix that I am using for my ex-ante ...
11
votes
5answers
3k views

Why is the Drawdown measure not used for portfolio optimization?

I was asked yesterday by a colleague why we are doing asset allocation using optimizers which target, for a minimum expected return: the portfolio with the minimum variance or the portfolio with ...
2
votes
0answers
74 views

volume augmented garch(1,1) model in matlab

Actually I want to add volume traded of a stock in my Garch(1,1) model to forecast the volatility.In Matlab I can specify the model as garch(1,1) and then use estimate and forecast commands.But I am ...
4
votes
3answers
416 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 ...
2
votes
1answer
711 views

Divergent or Convergent Strategies? Which is the way to go?

Consider first the simple convergent strategy to invest some amount $X$ in a game, if you win you simply take the winnings and keep playing a subsequent game. In the case of a loss, you believe in ...
23
votes
4answers
9k views

What is the best way to “fix” a covariance matrix that is not positive semi-definite?

I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix). I am ...
2
votes
1answer
121 views

Is the volatility of a trader's wealth equal to the volatility of the underlying assets traded?

Assume that a trader trades in several stocks with different volatilities. The return of the trader's portfolio would be the weighted average of returns and the risk would be a function of the the ...
0
votes
0answers
77 views

Minimum PD under Basel II retail asset?

I have been told that under Basel II the minimum PD that one can assign to any portfolio/segment classified under the retail asset class is 0.33%. But Google searches return nothing and I can't seem ...
0
votes
2answers
164 views

Sharpe Ratio and time spent in loss

Is it possible to express, given an annualized Sharpe Ratio value, what is an expected maximum/average time spent in a draw-down or something in this manner? E.g. with SR of 10, you'd expect to spend ...
2
votes
0answers
210 views

regarding Basel III IRB method for credit risk

Would the exposures between standard method and internal rating based method for credit risk under Basel III remain same?I could not find any documents for IRB approach under Basel III. Is it still ...
1
vote
1answer
486 views

Pre-trade evaluation and risk assessment of option trading strategies (in market practice)

When a trader gets conclusion of the volatility is being underestimated (via volatility cone or some other technology), actually there are multiple ways for his trading. (Let's assume the underlying ...
1
vote
2answers
288 views

Risk management of options

Your client would like to buy a digital call option. the digital call option pays the buyer in one years time (i.e at maturity ) N=1m SGD, if the SGD USD spot rate at maturity is above a prescribed ...
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votes
2answers
99 views

What is the most amount of money the consumer would be willing to pay to play take this gamble?

Suppose a consumer has log-utility over wealth, defined by $u(W) = \ln(W)$. Suppose this consumer has $100$, and is considering taking a gamble in which the consumer flips a coin, and gets $20$ she ...
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votes
1answer
542 views

Interest Rate Swaps on Mortgages [closed]

Is it possible to get interest rate swaps on mortgages? If not, why not? Are there models that describe this? Any direction would be great.
1
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1answer
207 views

Downside deviation

have any practitioners here worked with the downside deviation metric? I've looked a little into its concepts but wish to know its utility in practice (if any). Does it bring any value to risk ...
2
votes
1answer
175 views

How did we get $W_g=W_b$ from $\dfrac{U'(W_g)}{U'(W_b)}=1$?

My question is from Nicholson-Snyder's text , E-book here. My question is here, from page 217 of the book. (I can't post image as my reputation is not enough.) How did we get $W_g=W_b$ from ...
0
votes
1answer
138 views

What is the realized volatility's estimation error?

Given an estimation procedure and real data, how would one compute the mean squared error? What value represents the "true" realized volatility in the case of calculating the Mean Squared Error in ...
1
vote
1answer
442 views

Unsystematic/Idiosyncratic/Firm-specific volatility/variance in the market model?

I was asked to use idiosyncratic volatility as a regressor in a cross-sectional regression upon cross-sectional returns as the dependent variable. Returns can be thought of as the raw log stock return ...
3
votes
1answer
303 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 ...
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 ...