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

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5
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4answers
372 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 ...
5
votes
1answer
893 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
4k 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 ...
5
votes
1answer
145 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
5answers
900 views

Do binary options make any sense?

Reading from "www.nadex.com" - the copy reads "Binaries are similar to traditional options but with one key difference: their final settlement value will be 0 or 100. This means your maximum risk and ...
4
votes
7answers
30k views

How to calculate unsystematic risk?

We know that there are 2 types of risk which are systematic and unsystematic risk. Systematic risk can be estimate through the calculation of β in CAPM formula. But how can we estimate the ...
4
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 ...
4
votes
3answers
269 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
421 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 ...
4
votes
1answer
121 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
213 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 ...
4
votes
1answer
226 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 ...
4
votes
1answer
1k 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
145 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
412 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
352 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
3answers
424 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 ...
3
votes
2answers
779 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
212 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
2answers
1k 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 ...
3
votes
1answer
151 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
98 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
1answer
86 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
127 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 ...
3
votes
1answer
213 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 ...
3
votes
3answers
283 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
557 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
433 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
289 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 ...
2
votes
1answer
214 views

Picking from two correlated distributions

Can anyone provide a simple example of picking from two distributions, such that the two generated time series give a specified value of Pearson's correlation coefficient? I would like to do this in ...
2
votes
1answer
577 views

Is it possible to derive the “risk tolerance” from the portfolio efficient frontier?

I am trying to solve the Portfolio Optimization Problem using a "Multi-objective Evolutionary Algorithm". After obtaining the efficient frontier, I would like to know if we can infer for each point of ...
2
votes
1answer
2k views

Drawdown calculation for strategies

I am developing a trading strategy for currencies. I am trying to find an indication for risk, something like Sharpe ratio or Sterling ration; for that, I thought of using the (maximum) drawdown ...
2
votes
1answer
232 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 ...
2
votes
1answer
126 views

Hedging differences between equity and index options?

Suppose we hedge an index option using futures on that index. How would the hedging strategy be different if the underlying could be traded directly (from a risk point of view)?
2
votes
1answer
52 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 ...
2
votes
1answer
48 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, ...
2
votes
1answer
113 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 ...
2
votes
1answer
61 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?
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 ...
2
votes
1answer
239 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 ...
2
votes
2answers
196 views

Portfolio risk-return when assets have limited and inconsistent historical data / time series?

Lets say we have "today's" snapshot of asset allocation and need to determine the 6mo, 1 yr and 5 yr risk and returns of this portfolio. If the time series for every asset is very long, longer than ...
2
votes
0answers
65 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 ...
2
votes
0answers
35 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 ...
2
votes
4answers
319 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 ...
2
votes
0answers
241 views

Market risk stress testing?

I am doing a research for a paper for market risk stress testing. In fact I found some information on the web about this important topic such as: Stress Testing from Art to Science Stress Testing ...
2
votes
0answers
93 views

Benchmarking risk

Given the portfolio return $R$ and the benchmark return $B$, I want to define a risk indicator, measuring the ability to beat the benchmark ($R>B$), given the downside risk taken; the latter not ...
2
votes
0answers
526 views

How to Calculate Risk of Ruin [closed]

I'm reading a book titled "A Trader's Money Management System" and it discusses risk of ruin(ROR) tables. It says that you can have a zero probability of ROR with a payoff ratio of 2 to 1 and a win ...
1
vote
1answer
343 views

Why does $\hat{\epsilon}'\hat{\epsilon}$ of a factor model measure risk?

$\hat{\epsilon}'\hat{\epsilon}$ from the market model: $R_{it} - \hat{\alpha} - \hat{\beta}R_{mt} = \hat{\epsilon}$, or from a factor model such as the Fama-French 3 factor model, is often used in the ...
1
vote
2answers
217 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 ...
1
vote
1answer
199 views

Portfolio risk decreased by increasing share of riskiest asset?

In Parker's The Economics of Entrepreneurship he explains how certain theoretical models predict seemingly bizzare things (e.g. people becoming more risk-averse resulting in them taking riskier jobs) ...