# Tagged Questions

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

741 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 ...
142 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)?
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### 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 ...
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 ...
219 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 ...
269 views

### Optimization procedure for entropy pooling

I was wondering if those who used the entropy pooling code provided by Attilio Meucci had issues with the optimization procedure (especially regarding the fminunc function in Matlab). When I stress ...
236 views

### Regression giving the return on a stock

I have this regression equation: $$R_{stock} = 3,28\% + 1,65*R_{market}$$ Where $R_{stock}$ is the expected return on a stock and $R_{market}$ being the market risk premium. I have a one-year ...
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 ...
497 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 ...
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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 ...
232 views

### Does entropy pooling apply to distributions with time-varying drift?

I have a returns process that is drawn from a normal distribution with a nonlinear time-varying drift, so I was wondering if the entropy pooling method still applies or if I need an invariant ?
666 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 ...
397 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 ...
901 views

### Show that convexity of call price as a function of the strike is violated [closed]

European call options with strikes 90, 100 and 110 on the same underlying asset and with the same maturity are trading for 22.50, 18.84 and 13.97 respectively. show that the convexity of the call ...
2k views

### Conditional or unconditional volatility?

I am reading a paper (reference below) that states "The conditional volatility for each underlying security (or for a market index) can be estimated using the standard deviation of the stock’s ...
165 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 ...
391 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 ...
209 views

### Modeling asset performance to Bitcoin revenue

I'm attempting to model asset performance to Bitcoin revenue, which is a driving force in the Bitcoin community. Question Is there any model, or research being done that tracks "hashes per second" ...
528 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 ...
3k 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 ...
40 views

### Inferring Returns From Minimal Data Points [duplicate]

Possible Duplicate: How much data is needed to validate a short-horizon trading strategy? Suppose I have daily returns for a trading strategy against one month of data. Before starting ...
383 views

### What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
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 ...
465 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 ...
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 ...
901 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 ...
269 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 ...
761 views

### How are Expected Shortfall and Variance related?

I would like to know how Expected Shortfall $SF_\alpha$ and variance $\sigma^2$ are related. If I follow what Aaron Brown answered in this post, when the underlying distribution is Normal with ...
721 views

### How to manage equity portfolio risk intraday?

Lets assume that I have an equity strategy that generates signals intraday to buy and sell. I run this strategy across the SP500 names. Now within my strategy I want to incorporate a method to help me ...
149 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 ...
1k views

### How to apply risk-parity portfolio construction to a dollar-neutral portfolio?

Long-only risk-parity portfolios have proliferated in recent years. An optimized long-only risk-parity portfolio requires that the asset weight * marginal contribution to risk of the asset is ...
791 views

### Models for measuring insurance risk exposure

I've recently begun working as a quant for a large bank, and one of my first tasks will be to improve the model determining the risk exposure of their insurance portfolio. The portfolio is fairly ...
420 views

### performance of historical VaR parameters

An historical VaR measure is parameterized in terms of the confidence level and also number of periods. Specifically, the $\alpha$% T-period VaR is defined as the portfolio loss x in market value over ...
258 views

### How would I calculate a stop on a pair trade? [closed]

I have a trading strategy that I use on single tickers. I'd like to start using it with pairs as well. However, I'm somewhat math challenged and not sure how to best calculate the stops of the ...
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 ...
41k 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 ...
41 views

### What are useful indexes for rapid evaluation of country economic risk?

The World Economic Forum Global Competitiveness Report offers a comprehensive view of individual country risk/reward. There has been an explosion of these types of indexes over the past few years. ...
580 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 ...
444 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 ...
8k 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 ...
1k views

### When should you build your own equity risk model?

Commercial risk models (e.g., Barra, Axioma, Barclays, Northfield) have evolved to a very high level of sophistication. However, all of these models attempt to solve a very broad set of problems. ...
830 views

### How to compute modified-CVaR in the PerformanceAnalytics package?

My objective is to measure the modified-CVAR for a portfolio given its weights and matrix of security returns. Luckily the wonderful package PerformanceAnalytics has an ES() function that does just ...
212 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 ...
118 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.
341 views

### Do you know a good article on ETF's counterparty risk analysis?

I am at the moment considering investing into ETFs, but I am looking first to understand how these products really work. Indeed, it is my understanding that ETF can vary in terms of structure, thus ...
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 ...
2k views

### Is the risk-free rate really limited by inflation?

In all the classic texts on equities derivatives, there is an assumption of the risk-free rate r. We can immediately dismiss the concept of a fixed rate; all interest rates are variable (and ...
1k views

### What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?

Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...