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Sep
12
comment Testing the validity of a factor model for stock returns
You might make it a little more clear using $i$s for the cross-sectional index and $t$s for the time index.
Sep
3
comment Why non-stationary data cannot be analyzed?
I think the (almost) always difference advice can be misleading. It's important to know why and when they should difference or not. For instance, if they were to difference interest rates, then you would be ignoring the longer-run mean-reversion. Estimating an AR model in differences wouldn't help matters. From the perspective of an AR model, it is only the dependent variables that would need to be differenced for the t statistics to make sense. Lags could still be in levels, allowing for mean-reversion effects.
Aug
29
comment ETF Negative Roll Yield
For your first question, I'm simply relying on the arbitrage arguments that lead to futures pricing. You seem to be very interested in the empirical dynamics, which I am silent on. For your second, imagine you had a CLU3 contract (WTI on CME) on 8/20 (priced at close at 104.96). It stopped trading that day, so you would need to switch to a CLV3 contract (priced at 105.11). You would have to put up more money to continue to have a 1 contract position. That's how I think about roll yield.
Aug
27
comment Portfolio optimization with absolute position constraints
Your response does not clarify anything. The first thing I mentioned is completely basic (and equivalent to the absolute value of individual positions being less than 10%). It is the same as just putting lower and upper bounds on the variables and every QP optimizer I've seen allows it. The second is called a booksize constraint and requires more work to set up. You basically have to create auxiliary variables (with appropriate constraints) that represent the positive values and the negative values of the securities separately. Then just add together.
Aug
23
comment Portfolio optimization with absolute position constraints
When you say absolute constraints, what exactly do you mean? For instance, you could mean the positions are between -10% and +10% or you could mean that you take the absolute value of all the positions, sum them up and see it is equal to or less than some number.
Aug
16
comment Covariance of a GMV portfolio with any asset
Am I correct in my reading of this proof that $w_{p}$ can be an arbitrary portfolio, rather than just a specific asset?
Aug
14
comment How popular is the IRR as a tool for capital budgeting, nowadays?
I liked Matt Wolf's answer's completeness, but yours really gets to the heart of the matter.
Aug
12
comment Is HMM of Volatility any different from a simple filter?
You do not mention how you construct your volatility variable (perhaps a rolling window). The regime-switching model can provide a conditional volatilities, which happens to be better than a rolling window volatility. You can also use the model for prediction, e.g., what will the volatility be over the next 3 months given what regime I'm in today.
Aug
9
comment what is a reasonable beta in CAPM?
I can't tell you precisely what to do. Play around with some until you find something you're comfortable with.
Aug
9
comment Average correlation of index/portfolio
If I use the method c in that first link, then I get a correlation below 1. I don't know if that method has other issues, though.
Aug
9
comment Average correlation of index/portfolio
When I find the eigenvalues for your proposed correlation matrix, I get a negative value for the smallest. This suggests your choice is not positive definite and thus not a valid correlation matrix. Setting $\rho_{2,3}=0.89$ would result in all positive eigenvalues, but I can confirm that the average correlation by this formula would be greater than 1. So your problem remains.
Aug
8
comment Average correlation of index/portfolio
For the first question, I tried some extreme weights (adding up to 500% or 0%) and did not see any incorrect average correlations (I may have used a modification of that formula because that didn't seem correct). The main reason is that so long as $\sigma^{2}$ is the correct portfolio variance, then the average correlation should be within normal bounds. For the second point, I'm not familiar with anyone writing about it, but you could presumably take a similar approach using the above formula as they do for contribution to variance (I would not take the absolute value).
Aug
7
comment what is a reasonable beta in CAPM?
The point I was trying to make is that I might set it up as the 95th (& 5th) or 99th (& 1st) percentile, or something like that, rather than selecting fixed values. Where to cut it off might be different for different periods of time or different markets or different groups of securities. I'd rather look to the data than make any arbitrary assumptions.
Aug
6
comment what is a reasonable beta in CAPM?
One option would be to winsorize all the betas above or below some quantiles. Alternately, you could model the beta itself as mean-reverting so that the extreme betas gradually go back to 1.
Aug
5
comment Why are indifference equations in mean-variance portfolio theory convex shaped
Do you mean utility function?
Aug
2
comment Trend in Cointegration relationship
@MattWolf That is useful, but I think his problem is more basic, related to the choices he is making in variables. For instance, if you are using the relative inflation rates versus the price levels, then you may or may not have needed to use include the trend term.
Jul
31
comment Real value of small numbers of shares of company stock
What I meant by there not being an objective value is that prices are not determined with reference to some objective value. Saying life has value is a different sort of value than what economists mean usually. If you wanted to sell me water, then the subjective value is very important. If I am in the city, I may not pay more than 1 dollar for a bottle. If I am in the desert and low on supplies but have lots of money, I might pay 500 dollars. What matters is the expected amount of subjective value an additional unit will give me (aka marginal utility).
Jul
31
comment A question on Monte Carlo method
It might be simpler if you thought about it in terms of sample mean of z. The standard error of the sample mean is given by $2^{-0.5 \times 16}$ and $2^{-0.5 \times 17}$, respectively. So the ratio between is thus the square root of 2.
Jul
31
comment Real value of small numbers of shares of company stock
According to economics, there is no such thing as "real inherent value", aka objective value. There is, however, subjective value, which is why we care about the value of a company being what someone else will pay for it. In your example, people will want to buy XCo because they think its stock price will go up.
Jul
25
comment Shrinkage Estimator for Newey-West Covariance Matrix
You may want to add the link to the preprint in the question. I still am curious as to what is the issue with simply replacing the sample estimate with the Newey West estimate. Anyway, the original paper implies that it is estimated through GMM rather than Maximum Likelihood. I would have suggested finding the Bayesian prior that would be equivalent to whatever shrinkage you want to make and then adopting the approach for the Newey-West estimator, but since it is not based on ML I'm not sure if that would work.