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1

Volatility = Variance^1/2 = Standard Deviation


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You can use the known result, that when $X\sim N(0,1)$, then $aX\sim N(0,a^2)$ where $a=\sigma_t$ is conditionally constant.


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The concrete (general) answer to part (ii) of my question seems to be contained in Equation 8 of the following link: http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-portfolio-I.pdf In particular, interpreting $\sigma$ as volatility, take for example $E_A=0.10,\sigma_A=0.15,E_B=0.25,\sigma_B=0.40$ and $\rho =−0.2$. I get that about 83 percent of the ...


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Firstly, to answer your question for part (i), this part of the question makes no sense - your expected return is unbounded and is asymptotically linear with respect to risk. Let ${\bf w}\in\mathbb{R}^{2}$ denote your vector of weights, $\Omega$ denote the covariance matrix and $\iota$ denote a unit exposure vector (defined by $\iota_{j}:=1\ \forall j, j ...


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One could use a GARCH of his choice to estimate the volatility. A mean over your period would be a good indicator, otherwise the instant conditional sd is as good as it gets. Another way could be via an exponential smoothing of the risk-metrics type. Your question is not so clear is to be honest.


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$$ E\left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = E\left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = {\sigma _t}E\left[ {{z_t}} \right] = 0 $$ $$ {\mathop{\rm var}} \left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = {\mathop{\rm var}} \left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = \sigma _t^2{\mathop{\rm var}} \left[ {{z_t}} \right] = \sigma _t^2 $$ $$ ...


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std(PPS) PPS = Packets Per Second (wiki article: network packets) The standard deviation of packets per second received from a liquidity source are directly related to the number of quotes per second, or the number of trades per second occurring on that liquidity source. Thus, the higher the number of network / data packets per second, the more volatility ...


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One common point is that both implied volatility and interest rates come with term structures. This is exploited by H Buehler in this paper (and a few of his others). In particular, in Equation 2.10 he defines a variance curve model $v$ as a martingale represented as $$ dv_t(T) = \sum_{j=1}^d \beta^j_t(T) \, dW^j_t $$ which is more or less the same as ...


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Inhomogeneous time/sampling. Autocorrelation. Stochastic volatility. Jumps. Leverage.


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It appears to be related to behavioral psychology. In "space," there will be a statistical chance to two asteroids colliding, and a much larger number of near misses. But no asteroid will observe the "near miss" of two other asteroids and adjust its behavior or trajectory accordingly. In human affairs, a "near miss" could produce just the result that was ...


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A naive reason has been explained by Nassim Nicholas Taleb in his book titled Black Swan. In a deeper look, one should be aware that no historical data analysis can truly estimate the real tail risk of financial markets. By the same token, standard deviation, max drawdown, expected shortfall, VaR, Conditional Var... No single or combination of such ...


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Volatility changes over time. Even if daily returns are normal, assuming the conditional volatility each day is known, the unconditional distribution of daily returns will have excess kurtosis. For example, if daily returns have a standard deviation of 1%, 90% of the time, and a standard deviation of 3%, 10% of the time, the presence of the high-volatility ...


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Windham Capital Management is using hidden markov models for their Risk Regime Strategies. Mark Kritzman, who is also CEO, has published an article about the general outline of the strategy (with source code so you can replicate the results!): Regime Shifts: Implications for Dynamic Strategies (corrected August 2012) by M. Kritzman, S. Page, D. ...


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Extreme events in financial markets, like the crash of 1987, occur more frequently in the real world than a normal distribution would predict. The economic facts that drive those extreme events are varying. Such extreme declines have been observed over many different time periods (Tulip-mania for instance), which suggests that it is more likely inherent to ...


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The computation of Beta is rather simple. Please try using my following procedures: $$ ret_i = ret_{i} - ret_{rf} $$ $$ ret_b = ret_{benchmark} - ret_{rf} $$ then $$ \beta_{i} = \frac{cov(ret_p, ret_b)}{var(ret_b)} $$ where $ ret_b $ is the benchmark return net of risk-free rate, $ret_i$ is the stock return net of risk-free rate, $ cov $ is the ...



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