# Questions tagged [distribution]

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### Do portfolio mean and portfolio variance have probability distributions?

If $X$ is a $T\times N$ matrix of multivariate asset returns, and $w$ is some optimal portfolio weight vector, then the portfolio return series is $r_p = X w \in\mathbb{R}^{T}$. This return series ...
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### Is asset return skewness hard to estimate?

The asset mean is known to be difficult to estimate, incurring more estimation error than estimates of asset return variance. How about asset return skewness, is it hard to estimate and how can that ...
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### Which financial time series have a PDF and/or CDF?

Consider the following types of financial time series for a single publicly-listed stock: Price data Log returns Cumulative returns Each is computed from the item listed before it: log returns are ...
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### Density of a portfolio's returns is the weighted average of asset distributions?

The expected return of a portfolio can be formulated as a weighted average of the constituent assets' returns: $$r_p = w_1 r_1 + w_2 r_2 + \dots + w_N r_N + \epsilon$$ Does it also follow that the ...
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### Why do cumulative returns have a bimodal distribution?

Regular returns (log-differenced prices) have statistical distributions that are bell-shaped and unimodal (one mode/peak) despite being non-normal and fat-tailed. Cumulative returns, on the other hand,...
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### Option implied distributions

I am having a bit of trouble understanding how to obtain the option implied distributions. I have strike levels, deltas and implied vols for a call option that expires in 6 months. Roughly 40 data ...
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### How to annualize skewness and kurtosis of a forecasted distribution

I have a (non-normal) distribution of expected cumulative returns 10 quarters in the future, from which I have calculated mean, standard deviation, skewness and kurtosis. I would like to annualize ...
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I want to determine the kurtosis of a straddle. My question is closely related with the following topic here. According to the following paper of Ben-Meir and Schiff (2012) the expected value of a ...
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### A quick and dirty loss distribution and Credit VaR

I need to create a loss distribution for a credit portfolio as the first steps to estimate the portfolio Credit VaR. I have historical monthly account snapshots (payment history) of all accounts ...
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### Calculate the implied loss rate on a loan, given the interest charged

My bank has a retail credit portfolio of 100 million in loans. I know the payment history,balance history of all these loans since inception. Are there any tools to calculate an expected loss, a loss ...
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### Why Jarque - Bera values are so high? Is this normal? [closed]

Please advise whether the following is a normal occurrence: In the above table I have Autocorrelation at lag1, LB, Skew, Kurt and JB test. I have noticed that whenever the value of Kurt increases, ...
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### Distribution of simple returns vs logreturns

I understand that stock prices are conditionally modeled using a log normal distribution by the relationship $y_t/y_{t−1}∼logN(μ_{daily},σ^2_{daily})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{daily}))$ ...
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### Compare two distributions for forecasting returns

Let's imagine that we have two separate models, both used to forecast the return for the next period. Both models are estimated everyday, and both models outputs a probability distribution. How can we ...
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### Convolution of generalized hyperbolic distribution

I have a question concerning the convolution of generalized hyperbolic distributions. Proposition 6.13 of McNeil, Embrechts, Frey states the following: If $X$ has a $d$-dimensional generalized ...
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### Alternative Method for Determining Option-Implied pdf

As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...
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### Sample distribution of cross-sectional statistics of returns

Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
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### How to price a barrier using monte carlo when return distribution is not iid?

this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 ...