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1

It depends on your (assumed) underlying data generation process. In general, Weighted Least Squares (WLS) can be used when your data is heteroscedastic but still uncorrelated. Assume a linear model $$Y_i = \beta_0 + \beta_1 X_i + \epsilon_i \tag{1}$$ If you assume $var(\epsilon_i) = \sigma^2$, i.e. the error terms are homoscedastic, OLS is the best ...


5

I have also been looking into this stuff for a while. Apparently there are not that many tail risk funds, the prominent ones being Taleb and Spitznagel's Universa and Bhansali's LongTail Alpha. Obviously, all these guys have tons of papers and books on this topic. Spitznagel provides some nice case study on prototypical tail hedging in his book called The ...


2

One of the most straighforward way to hedge tail risk and buy insurance is just buying the Vix. A few hedge funds made a lot of money on the VIX lately. What's the downside? Well in normal times (which are most of them) you actually need to pay for that insurance. That's called the variance risk premium. So imagine, that you think this are normal times. ...


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There's no easy answer to your question, as noob2 pointed out. You can look online for info from Universa. That fund does exactly what you are asking: https://www.universa.net/riskmitigation.html Of course, post a crash, such as the one we just experienced, the cost of hedges is larger than it is prior to such events. Understand that you aren't going ...


3

OK, I'll share a lot of the scepticism voiced in the comments to the OP above. There is an important marekting>reality dimension here. The problem is that if an investor wants a core traditional risk premium like Treasuries or the S&P, there's an ETF costing single-digit basis points. Institutions can do liquid futures (or swaps on interest rates) at the ...


0

It's worth reiterating the assumptions underlying CAPM. The first set assumes individuals are rational, mean-variance optimizers, etc. The second set is a bit more interesting. The model assumes no taxes, no transaction costs, and that investors can borrow or lend at the risk-free rate and take short positions. You can't build an efficient frontier without ...


0

Suppose you are given the historical data of 20 days. You calculate the asset returns and covariance matrix. Then you minimise the variance $$ Min \ \sigma^2 = w\Sigma w^T \\ s.t. wI^T = 1 \\ and \ w\mu^T = r_p \\ $$ Where $\mu$ is the asset returns and $r_p$ is the target return, to find the optimal weight allocation. This is a prediction of what your ...


0

The Frontier is a hyperbola (it’s underlying problem is a quadratic one). To fully define it, we need at least two of its points.


2

There can be zero weights, and for that matter there can be (and often will be) negative weights as well unless you specifically have a constraint saying there can't be. Consider the case where you have 2 risky assets with different variance that are perfectly positively correlated with each other. The minimum variance portfolio will then consist only of the ...


1

Try showing the full scale of the x axis. You’re starting at a vol of ~12% and going up to 30%. If the x axis starts at 0% vol and goes up from there, your CML may come closer to intersecting your red star.


0

That looks correct to me apart from the calculations at the end which aren't in line with the formula you posted above. You could however immediately use the fact that the beta of the portfolio is just the weighted average of the beta of the stocks and save yourself some notation. Just insert $\beta_i * \sigma_w^2$ instead of the covariance terms in your ...


0

"Could we just run the OLS regression and get the alpha as part of the coefficients that way?" NO! For more, see CAPM is neither a cross sectional model, nor a time series model


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