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comment Ornstein versus AR(1) for modeling stationary data
You're not really addressing the @user7889's point with respect to OU versus AR(1).
Apr
21
comment Estimating Beta from unevenly spaced price history
There's really no proper convention here. There are a lot of different options that might be better in some cases than others. Also, how much effort you put in might depend on what you're trying to do and what your boss wants.
Apr
18
comment Portfolio optimization with Portfolio CVaR Constraint
I would follow the progression of first getting the minimize CVaR to work, then max return given CVaR, then min variance given CVaR. The problem here is that you're not using Rockafellar & Urysev's approach at all. The weighted average CVaR of individual assets is not the CVaR of the portfolio. This doesn't work for variance, so it wouldn't work for CVaR. Read Rockafellar and Urysev's Optimization of Conditional Value at Risk. Both of the authors have presentations on their websites that explain it better. Check those out.
Apr
17
comment Portfolio optimization with Portfolio CVaR Constraint
That paper comes very close to solving your issue. They show how to constrain the CVaR of a portfolio to an amount while maximizing return. All you have to do is replace the objective with minimizing variance. Alternately, after setting it up that way, you could replace the linearization with Alexander et al's approach in "Minimizing CVaR and VaR for a portfolio of derivatives", though you couldn't use an LP anymore.
Apr
17
comment Portfolio optimization with Portfolio CVaR Constraint
Check out "Portfolio Optimization with Conditional Value-at-Risk Objective and Constraints" by Krokhmal, Palmquist, and Uryasev
Apr
14
comment Black Scholes well coded Python
I just meant that if someone on this site tried to run the code themselves to figure out what's wrong with it, they would have problems because they couldn't get self.sig. So perhaps re-write it as a function and provide sufficient code to re-produce the chart (and make it clear what the problem is). Also, people who write python typically don't use int and float the way you're using them. Python's dynamically typed for a reason.
Apr
14
comment Harnessing small correlations for reliable profit
What I meant is that someone could have misinterpreted something. For instance, they could say he uses small correlations for financial gain, but they also could say he diversifies. Who knows what they really mean. I wouldn't worry about it too much.
Apr
14
comment Black Scholes well coded Python
At a minimum, self is used for class methods in python.
Apr
14
comment Harnessing small correlations for reliable profit
Sounds like something that a marketing person wrote.
Apr
14
comment Sampling problem in portfolio optimization
@Schnabeltier Thanks, I think it makes it more clear as an answer.
Apr
14
comment Sampling problem in portfolio optimization
You might also check out regularization techniques. whitepapers.ipe.com/resources/…
Apr
14
comment Sampling problem in portfolio optimization
@Schnabeltier could you explain more what you mean?
Apr
11
comment quantiative risk measure how they are implemented in R and their use
More or less, yes. If you use the mean and covariance of returns to calculate Gaussian VaR/CVaR, you are implicitly making assumptions about the distribution of the securities in the future. For the second point, all measures of portfolio risk I'm aware of depend on correlations to some extent. Finally, the documentation for PerformanceAnalytics makes it clear that the sigma argument is variance if univariate and a covariance matrix if multivariate.
Apr
11
comment Beta and Frequency of Data
There could be many different betas (e.g., Fama-French, APT), but I'm referring more to how to calculate beta. See papers.ssrn.com/sol3/papers.cfm?abstract_id=1619923 In reality, returns are not normally distributed, why should I assume they are?
Apr
11
comment quantiative risk measure how they are implemented in R and their use
You are implicitly using time series analysis when you go from raw security prices to (log) returns, fitting a mean and covariance to those returns, and then assuming that distribution is what you will expect in the future when using those parameters to get portfolio means, variances, VaRs, or CVaRs. Further, like going from univariate variance to portfolio variance, univariate VaR or CVaR will not aggregate to the portfolio level by themselves since you assume away the correlation between the securities.
Apr
11
comment Beta and Frequency of Data
It is only true that the beta would be unchanged under particular assumptions about the underlying process and what beta you're using.
Apr
11
comment quantiative risk measure how they are implemented in R and their use
What is time series is really too basic for this site. Start with en.wikipedia.org/wiki/Time_series, then get a book on the subject if you want to learn more.
Apr
11
comment Delta of a standardized at-the-money 30-day put option
At a mathematical level, stock prices in the Black-Scholes model are assumed to be log normally distributed. The distribution of a log normal variable is not symmetric. The mean of the log normal distribution increases as the volatility increases. This means there's a greater chance a call option will be in the money at expiration and less of a chance the put will be in the money.
Apr
11
comment Delta of a standardized at-the-money 30-day put option
Okay, I undeleted my answer. I had to do an example to convince myself I was right again. However, there could be changes in the dividend yield that I effectively assumed away (higher dividend yields in the financial crisis should make the put delta increase away from -0.5).
Apr
11
comment Delta of a standardized at-the-money 30-day put option
I deleted my answer as I'm really not sure how that plot is created and if my answer correctly answers the question. I had assumed the strike equals the share price, but that likely isn't true for this chart and might be leading to the results you are seeing.